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Towards improvements in radiographic growth measurement of long leg bones in children Hassanein, Ossama Rashad 1974

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TOWARDS IMPROVEMENTS IN RADIOGRAPHIC GROWTH MEASUREMENT OF LONG LEG BONES IN CHILDREN  by  Ossama Rashad Hassanein B . A . S c , The U n i v e r s i t y o f A l e x a n d r i a , Egypt, 1970 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  i n the Department of Electrical  Engineering  We accept t h i s t h e s i s as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA September 1974  In p r e s e n t i n g an the  this  thesis  in partial  advanced degree a t t h e U n i v e r s i t y Library  shall  make i t f r e e l y  I f u r t h e r agree t h a t p e r m i s s i o n for  scholarly  of B r i t i s h  available  h i s representatives.  of  this  gain  I agree  copying o f t h i s  thesis  shall  that  copying o r p u b l i c a t i o n  n o t be a l l o w e d w i t h o u t my  permission.  Department  of £ L£  £ T  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  l\ I CflL Columbia  that  by t h e Head o f my D e p a r t m e n t o r  I t i s understood  thesis for financial  Columbia,  f o r r e f e r e n c e and s t u d y .  for extensive  p u r p o s e s may be g r a n t e d  by  written  f u l f i l m e n t o f the requirements f o r  izLN G\ < NizlEfW N C,  ii  ABSTRACT The problem o f determining i n r a d i o l o g i c a l estimates  o f the bone lengths and d i f f e r e n t i a l growth o f  children's legs i s discussed. first  classified  and c o r r e c t i n g measurement e r r o r s  Sources o f p o s s i b l e measurement e r r o r are  as b e i n g p h y s i o l o g i c a l , p s y c h o p h y s i c a l , or p s y c h o l o g i c a l .  The extent o f the c o n t r i b u t i o n o f each o f the i d e n t i f i e d sources  of e r -  r o r t o the o v e r a l l measurement e r r o r i s then e s t i m a t e d by experiments u s i n g a bone phantom and s p e c i a l l y c o n s t r u c t e d t e s t  fixtures.  Procedures a r e s p e c i f i e d f o r r e d u c i n g s i g n i f i c a n t c o n t r i b u t o r s to the o v e r a l l e r r o r .  I n p a r t i c u l a r , the problem o f r a d i o l u c e n c y o f  bone c a r t i l a g e i s t r e a t e d by combining a mammographic x-ray w i t h computer p r o c e s s i n g o f the radiogram.  A l s o , suggestions  technique a r e made  as to how to reduce the human e r r o r . A d e s c r i p t i o n of the s p e c i a l purpose scanning use i n the computer p r o c e s s i n g s t u d i e s i s included.. offers  system b u i l t f o r  The scanning  system  the unique advantage of d i g i t i z i n g an 11 by 11 i n c h radiogram, o r  s m a l l e r s u b s e c t i o n s , w i t h v i r t u a l l y any p r e s p e c i f i e d r e s o l u t i o n .  iii  TABLE OF CONTENTS PAGE ABSTRACT  i i  TABLE OF CONTENTS  i i i  LIST OF ILLUSTRATIONS  .  v  LIST OF TABLES  i  l  x  ACKNOWLEDGEMENT  x  I.  INTRODUCTION  1  1.1  Problem F o r m u l a t i o n  1  1.2  Research O r g a n i z a t i o n  6  II.  THE PHYSIOLOGICAL, PSYCHOPHYSICAL AND PSYCHOLOGICAL ASPECTS OF THE PROBLEM OF MEASUREMENT ERRORS OF LONG LEG BONES IN CHILDREN 2.1  Introduction  8  2.2  Physiological Errors  9  2.2.1  Geometric and r a d i o g r a p h i c  d e s c r i p t i o n of l o n g  l e g bones i n c h i l d r e n  2.3  2.2.2  Trabecular  2.2.3  Anatomical s t r u c t u r e e r r o r s  Psychophysical 2.3.1  2.3.2 2.4 III.  8  patterns  Errors  15 16 18  Image c l a r i t y  18  2.3.1.a  Contrast  21  2.3.1.b  Image Q u a l i t y  25  Properties  o f t h e HVS  Psychological Errors  AN ANALYSIS OF ERRORS IN THE RADIOGRAPHIC MEASUREMENT OF LONG LEG BONES 3.1  9  The Apparatus  35 37  38 38  iv  3.2  E f f e c t o f Bone R o t a t i o n  42  3.3  E f f e c t o f Beam Center L o c a t i o n  44  3.4  E f f e c t o f Beam Height  47  3.5  E f f e c t of Knee I n c l i n a t i o n on the Femur Radiogram ....  48  3.6  E f f e c t o f L u f k i n R u l e r O r i e n t a t i o n and Human V a r i a b i l ity  48  Conclusion  52  3.7 IV.  ON .THE PROBLEM OF RADIOLUSCENCY OF UNOSSIFIED CARTILAGE IN CHILDREN 4.1  The R a d i o g r a p h i c  4.2  Image P r o c e s s i n g  4.3 V.  VI.  53  Imaging Technique  53 •••  54  4.2.1  P r e f i l t e r i n g c o n t r a s t enhancement  54  4.2.2  R e s u l t s and e v a l u a t i o n  59  4.2.3  Filtering  63  Conclusion  ,  79  EDGE DETECTION AND CONTOUR TRACING  82  5.1  Introduction  82  5.2  Edge p o i n t :  5.3  The edge d e t e c t i o n a l g o r i t h m  85  5.4  Experimental  92  Definition  and L o c a t i o n ,  r e s u l t s and d i s c u s s i o n  THE DATA ACQUISITION SYSTEM  84  96  6.1  Introduction  96  6.2  The image d i s s e c t o r camera  96  6.3  Noise removal system  99  6.4  L i g h t source  6.5  The computer i n t e r f a c e  102  6.6  The software  102  and movable stage  implementation  101  V  VII.  6.6.1  Axes alignment  102  6.6.2  Stage p o s i t i o n i n g  6.6.3  Focusing  105  6.6.4  Data a c q u i s i t i o n  107  6.6.5  Data t r a n s f e r  107  control  105  CONCLUSION AND SUMMARY  APPENDIX (A)  APPENDIX (B)  114  THE TRANSFORMATION OF A GREY LEVEL HISTOGRAM AN APPROXIMATELY RECTANGULAR DISTRIBUTION UNDETERMINATE  TO 117  POINTS OF THE SIX LINEAR FILTERS OF  CHAPTER 4  118  APPENDIX (C)  THE IOT INSTRUCTIONS  119  APPENDIX (D)  LISTING OF PIPLN9  120  APPENDIX (E)  LISTING OF EDGE DETECTION ALGORITHM  125  REFERENCES  .  128  vi  LIST OF  ILLUSTRATIONS  FIGURE 1.1  PAGE T e l e o r o e n t g e n o g r a p h i c and O r t h o r o e n t g e n o g r a p h i c posure t e c h n i q u e s  ex4  2.1  Axial relationships  o f the s h a f t of the femur  10  2.2  Axial relationships  of the h i p j o i n t  10  2.3  Cartilage  2.4  Osseous changes i n the knee w i t h age i n the male and female  14  Normal v a r i a t i o n s i n the s i z e and c o n f i g u r a t i o n a n t e r i o r t i b i a l process  15  2.5  space at knee j o i n t o f new  born i n f a n t  12  of the  2.6  T r a b e c u l a r p a t t e r n s o f the neck o f the femur  16  2.7  M o d e l l i n g the p s y c h o p h y s i c a l e r r o r  19  2.8  Parameters  2.9  Characteristic  2.10  F i l m t r a n s m i s s i o n x r e l a t i v e exposure  23  2.11  Diagrams f o r geometric a n a l y s i s o f unsharpness  27  2.12  Diagram of r a d i a t i o n d i s t r i b u t i o n on a r o t a t i n g anode..  29  2.13  F i e l d c h a r a c t e r i s t i c s o f the MTF  33  2.14  Mach phenomenon  36  3.1-J  Photograph o f the apparatus used tioning errors  3.2  components  a f f e c t i n g image c l a r i t y  Top view o f one markers  (H & D) curve  20 23  to s i m u l a t e d l e g p o s i 39  end of p l e x i g l a s s b a r showing the w i r e 40  3.3  Top view o f x-ray tube cap frame  41  3.4  Measurements on the r o e n t g e n o g r a p h i c exposures  43  3.5  L a b e l l i n g the markers on the p l e x i g l a s s p l a t e  44  3.6  Axial relationships  50  at the bone e x t r e m i t i e s  vii  4.1  H i s t o g r a m o f o r i g i n a l d i g i t i z e d radiogram  56  4.2  Histogram a f t e r l o g a r i t h m i c c o n v e r s i o n  56  4.3  Ideal  56  4.4  Histogram a f t e r histogram e q u a l i z a t i o n  56  4.5  Histogram a f t e r gamma c o r r e c t i o n  58  4.6  H i s t o g r a m a f t e r smoothing  4.7  Picture  4.8  Radiogram a f t e r l o g a r i t h m i c c o n v e r s i o n  62  4.9  Radiogram a f t e r h i s t o g r a m e q u a l i z a t i o n  62  4.10  Radiogram a f t e r gamma c o r r e c t i o n  62  4.11  Radiogram a f t e r smoothing  4.12  Magnitude  t r a n s f o r m space i n u - d i r e c t i o n  65  4.13  Magnitude  t r a n s f o r m space i n v - d i r e c t i o n  65  4.14  R o l l - o f f f u n c t i o n s o f low-pass  4.15  The two f u n c t i o n s G ( f ) & K ( f ) used t o generate the p r o posed f i l t e r response Hg(f)....•  66  4.16  E f f e c t of high-emphasis  69  4.17  Comparison H 6  and a c t u a l  commulative  d i s t r i b u t i o n functions....  & pixels  redistribution  of o r i g i n a l d i g i t i z e d femur's  of the weight  & pixels  58  radiogram  58  redistribution  62  prototypes  filtration  67  on i d e a l edge  f u n c t i o n s o f f i l t e r s H ,H lZ  and 69  £  4.18  Radiogram a f t e r Gaussian f i l t e r i n g  (a = 2.24, a = 1.0).  72  4.19  Radiogram a f t e r G a u s s i a n f i l t e r i n g  (a = 2.24, a = 2.0).  72  4.20  Radiogram a f t e r H a = 1.0)  4.21  s  filtering  Radiogram a f t e r H, f i l t e r i n g  ( f = 0.1071, f c  = 0.357, 72  ( f = 0.1071, f  = 0.357,  a = 4.0)  72  4.22  H i s t o g r a m o f radiogram a f t e r Gaussian f i l t e r i n g  73  4.23  Histogram o f radiogram a f t e r H  73  4.24  Histogram o f radiogram a f t e r n o n - l i n e a r f i l t e r i n g  5  filtering  73  viii  CDF  4.26  Contrast  enhanced v e r s i o n of F i g . (4.18)  75  4.27  Contrast  enhanced v e r s i o n of F i g . (4.19)  75  4.28  Contrast  enhanced v e r s i o n of F i g . (4.20)  75  4.29  Contrast  enhanced v e r s i o n of F i g . (4.21)  75  4.30  Radiograms a f t e r Gaussian f i l t e r i n g  ( a = 5.602, a = 2.5).  76  4.31  Radiograms a f t e r Gaussian f i l t e r i n g  ( a = 6.162, a = 2.0).  76  4.32  Radiograms a f t e r H a = 2.0)  filtering  Radiograms a f t e r H a = 4.0)  filtering  4.33  o f Gaussian, n o n - l i n e a r  and H 5 f i l t e r e d images  4.25  (f  c  = 0.3213, f  73  = 0.0714, 77  ( f = 0.2856, f .  = 0.0357,  c  filtering  process  77  4.34  Block diagram o f n o n - l i n e a r  5.1  Block diagram of p i c t o r i a l p a t t e r n  5.2  Edge d e t e c t o r  83  5.3  T y p i c a l edge c o n f i g u r a t i o n s  85  5.4  I n t e n s i t y p r o f i l e s o f the radiogram i n F i g . (4.7)  87  5.5  Smoothed i n t e n s i t y p r o f i l e s  90  5.6.a  Contour t r a c i n g w i t h o u t Gaussian w e i g h i n g f u n c t i o n  94  5.6.b  Contour t r a c i n g u s i n g Gaussian weight w i t h cr = 2.0  94  5.6.c  F a l s e contour due  94  5.6.d  Complete t r a c e of c h i l d ' s femur  6.1  Photograph o f the d a t a a c q u i s i t i o n system  97  6.2  Data a q u i s i t i o n system o r g a n i z a t i o n  100  6.3  Photograph of an o u t - o f - f o c u s  106  6.4  Photograph of an i n - f o c u s  6.5  Flow c h a r t o f the r o u t i n e PIPLN9  recognition  t o l a c k of edge p o i n t s a t c o n d y l e s  edge t r a n s i t i o n  edge t r a n s i t i o n  78 82  94  106 112  ix  LIST OF TABLES TABLE  PAGE  2.1  Normal degrees o f a n t e v e r s i o n of the f e m o r a l neck  11  3.1  E f f e c t of r o t a t i o n  45  3.2  E f f e c t of beam c e n t e r l o c a t i o n  3.3  E f f e c t o f beam h e i g h t on the femur radiogram  47  3.4  E f f e c t of Lufkin  51  4.1  Redundancy i n radiograms a f t e r p r e f i l t e r i n g c o n t r a s t enhancement  61  4.2  Gaussian High-Emphasis  78  4.3  H,. High-Emphasis  on the femur radiogram on the femur radiogram ...  ruler orientation  and human v a r i a b i l i t y .  f i l t e r i n g parameters  f i l t e r i n g parameters  46  78  ACKNOWLEDGEMENT The i n t e r e s t , a d v i c e and encouragement that I have r e c e i v e d from my s u p e r v i s o r , Dr. G.B. Anderson, of this  thesis i s greatly I would l i k e  throughout the r e s e a r c h and w r i t i n g  appreciated.  t o express my s i n c e r e g r a t i t u d e t o Dr. A.E. Burgess  of the Department o f D i a g n o s t i c R a d i o l o g y , F a c u l t y o f M e d i c i n e , U n i v e r s i t y of B r i t i s h  Columbia  f o r the time and e f f o r t he devoted t o the p r e p a r a t i o n  of the radiograms used i n t h i s r e s e a r c h , and f o r h i s h e l p f u l s u g g e s t i o n s and comments.  I would  a l s o l i k e t o thank my f r i e n d Mr. M.E. Koombes f o r  p r o v i d i n g the software f o r d i s p l a y i n g p i c t u r e s ,  f o r d e s i g n i n g and w i r i n g  p a r t o f the hardware and f o r h i s e x p e r t guidance and a d v i c e . I am i n d e b t e d t o Drs. G.E. Trueman and J.P. Gofton of the F a c u l t y of M e d i c i n e , U n i v e r s i t y o f B r i t i s h Columbia  f o r t h e i r h e l p and encourage-  ment, and to Dr. D. Ozonoff o f the Department o f R a d i o l o g y , Harvard Medic a l S c h o o l , Boston and Dr. E.L. H a l l o f the Department o f E l e c t r i c a l E n g i n e e r i n g , U n i v e r s i t y o f Southern C a l i f o r n i a f o r t h e i r generous and s t i m u l a t i n g correspondence. I would butions :  also l i k e  to thank the f o l l o w i n g people f o r t h e i r  contri-  Mr. G.E. A u s t i n f o r many h e l p f u l d i s c u s s i o n s , Mr. H.H. B l a c k f o r  p r e p a r i n g many photographs  and s l i d e s , Mr. G.F. B r o c k l e s b y f o r b u i l d i n g  the mechanical s t a g e i n the data a c q u i s i t i o n system and the apparatus f o r the phantom bone and Miss Shelagh Lund  f o r h e r p a t i e n t and e f f i c i e n t  t y p i n g o f the t h e s i s . Many thanks to a l l my c o l l e a g u e s a t the E.E. Department, t i c u l a r l y my f r i e n d s Mr. J.A. McEwen and Mr. W.P. A l s i p encouragement and a s s i s t a n c e .  par-  f o r invaluable  xi  TO MY PARENTS  1  CHAPTER 1  INTRODUCTION  1. 1 - Problem  Formulation.:  The measurement of c h i l d r e n ' s bone l e n g t h s  from roentgeno-  grams o f the e x t r e m i t i e s has been r o u t i n e l y used s i n c e 1935 to answer many q u e s t i o n s growth d i f f e r s  about the p a t t e r n of long-bone growth; how  i n boys and g i r l s , what v a r i a t i o n s e x i s t i n b o d i l y  p r o p o r t i o n s , and how b o d i l y p r o p o r t i o n s change w i t h growth and age. Also, i n planning  the c o r r e c t i o n o f i n e q u a l i t y o f growth i n the lower  e x t r e m i t i e s , i t has proved h e l p f u l to observe s e r i a l  changes i n the  l e n g t h s o f the p a t i e n t ' s l o n g bones r e l a t i v e to the t y p i c a l n o r m a l v a l u e s f o r c h i l d r e n o f the same age and sex {1}. past  growth a b n o r m a l i t y  Moreover, the assessment o f  and o f f u t u r e growth p o t e n t i a l i n i n d i v i d u a l  p a t i e n t s i s c o n s i d e r a b l y enhanced by c h a r t i n g t h e c h i l d ' s against a reference Maresh  progress  standard.  [2] determined the l e n g t h o f t h e t u b u l a r bones i n  h e a l t h y s u b j e c t s from age 2 months t o 18 y e a r s .  One s h o u l d  consult  h i s t a b l e s p u b l i s h e d i n 1955 f o r comprehensive and d e t a i l e d s t a t i s tical  treatment o f normal growth i n l e n g t h o f the t u b u l a r bones.  roentgenographic  technique  i s as f o l l o w s ([3^:  The  I n i n f a n c y and e a r l y  c h i l d h o o d years measurements c o u l d n o t i n c l u d e u n o s s i f i e d and t h e r e fore i n v i s i b l e epiphyses.  Length measurements were made between the  e p i p h y s e a l p l a t e s i n the l o n g a x i s o f the bone.  I n the p r e a d o l e s c e n t  and l a t e r y e a r s , i t seemed a d v i s a b l e to i n c l u d e the o s s i f i e d and  epiphyses,  a g a i n measurements were made i n the s i m p l e s t p o s s i b l e manner -  2  along  the l o n g a x i s of the bone from the p r o x i m a l  epiphysis  to the most d i s t a l edge o f the lower e p i p h y s i s o f t h a t bone,  to the n e a r e s t two  edge o f t h e upper  0.5 mm w i t h  sets of data:  a Lufkin steel  ruler.  There a r e , t h e r e f o r e ,  (1) measurements from the 1 s t x-ray  examination a t  2 months o f age and ending a t an a r b i t r a r y age o f 12 y e a r s i n f a n c y and c h i l d h o o d y e a r s , the epiphyses  and (2) those measurements which i n c l u d e  and were measured from an a r b i t r a r y age o f 10 y e a r s to  f u l l bone growth i n l e n g t h , u s u a l l y to 16 o r 17 y e a r s 17 o r 18 y e a r s  f o r the  i n boys.  in girls  and to  No c o r r e c t i o n o f t h e measurements has been  made f o r image d i s t o r t i o n .  Maresh c a l c u l a t e d the m a g n i f i c a t i o n from roentgeno-  grams o f d r i e d bone specimens o f i n f a n t s , c h i l d r e n and a d u l t s as between 1.0 and with  1.5% o f the t o t a l bone l e n g t h a t a f o c a l f i l m d i s t a n c e o f 7 1/2 f t . (2.3 m) the bone i n d i r e c t  contact with  the c a s s e t t e s u r f a c e .  However, the d i s -  t o r t i o n , because of the o b j e c t - f i l m d i s t a n c e i n the l i v i n g s t a t e , v a r i e s cons i d e r a b l y from areas escents little  such as the femoral neck and head, where i n chubby a d o l -  the d i s t a n c e my be. from as much as 10 cm to the c a s s e t t e s u r f a c e to as as 1 cm f o r the d i s t a n c e from the lower end o f the r a d i u s t o t h e c a s s e t t e . '  These measurements a r e , tomical lengths.  t h e r e f o r e , e q u i v a l e n t o f s i z e , r a t h e r than t r u e  On the o t h e r hand, the use o f h i g h  speed s c r e e n s  would  s a c r i f i c e some o f the f i n e r d e t a i l s o f bone s t r u c t u r e i n the i n t e r e s t o f speed. Green and Anderson i [ l ] , {4 ] p u b l i s h e d  t a b l e s f o r t h e average  l e n g t h s o f the femur and t i b i a f o r boys and g i r l s  together with  t a i n f i g u r e s which d e s c r i b e t h e d i s t r i b u t i o n o f the observed around the mean a t each age.  cer-  values  These t a b l e s are v a l u a b l e i n d e t e r m i n -  i n g the r e l a t i v e l e n g t h o f t h e bones o f a p a r t i c u l a r c h i l d i n r e -  ana-  3  l a t i o n t o the expected d i s t r i b u t i o n f o r h i s c h r o n o l o g i c a l age and s k e l e t e c a l age, and they a r e o f a s s i s t a n c e  i n estimating  the f u t u r e  growth o f the i n d i v i d u a l bone a f t e r a g i v e n age and as an a i d i n p r e d i c t i n g the e f f e c t from e p i p h y s e a l  arrest.  I f t h e p a t i e n t ' s bones a r e  long f o r h i s age and a l l the o t h e r  f a c t o r s are e q u a l , he may be expected  to r e q u i r e more c o r r e c t i o n than an i n d i v i d u a l - w i t h - s h o r t e r bones. As i n Maresh's t a b l e s , the roentgenograms o f the younger c h i l d r e n i n t h i s s e r i e s were teleoroentgenograms, made w i t h one exposure of an e n t i r e bone on a s i n g l e f i l m at a 6 - f t . tube - to film distance.  On the other hand, orthoroentgenograms were made of  the lower e x t r e m i t i e s  o f the o l d e r c h i l d r e n employing a three  exposure  t e c h n i q u e , f o c u s i n g s u c c e s s i v e l y o v e r h i p , knee & a n k l e : Femur l e n g t h was recorded a r t i c u l a t i n g surface on  the l a t e r a l  o f the c a p i t a l e p i p h y s i s  l i n e drawn across  The  from the p r o x i m a l  to the most d i s t a l  point  condyle.  T i b i a l e n g t h was recorded  articulating  as the d i s t a n c e  as the most d i s t a l mid-point o f a  the p r o x i m a l condyles to the mid-point o f the d i s t a l  surface. accuracy o f these measurements i s d i s c u s s e d  following section.  i n the  4  Teleoroeritgeriograpliy arid Orthoroentgenography  ( F i g . (1.1)):  \ Length of X-ray shadow ' (a)  Teleroentgenography  Fig.  (b) Orthoroentgenography  (1.1) T e l e o r o e n t g e n o g r a p h i c and O r t h o r o e n t g e n o g r a p h i c Exposure Techniques  Both t e l e o - and orthoroentgenography produce measurement i n a c c u r a c i e s . However, i n orthoroentgenography, because  o n l y p e r p e n d i c u l a r rays a r e  d i r e c t e d at the ends o f the l o n g bones, m a g n i f i c a t i o n o f l e n g t h i s m i n i m i z e d , and v i s u a l i z a t i o n o f each u n d i s t o r t e d e p i p h y s e a l l i n e i s possible. two (a)  The two methods w i l l be compared s t r i c t l y  to demonstrate  f a c t s concerning magnification ( a l l other sources o f e r r o r  ignored):  orthoroentgenography i s somewhat i n a c c u r a t e ,  (b) t e l e o r o e n t g e n o g r a p h y as compared t o t h e former method fairly  (considered  a c c u r a t e by r a d i o l o g i s t s ) proves to g i v e v e r y erroneous  measurements.  5  (a) Some d i s t o r t i o n i n l e n g t h can occur the tube i s not centered,  i f the bone were not  to the o b l i q u e p o s i t i o n of the bone.  femur.  Even i f p e r f e c t l y parallel  In the femur a minimal amount of s h o r t e n i n g must  e l e v a t i n g the knee and  ankle  T h i s c o u l d be  occur  c o r r e c t e d by  to the same l e v e l as the head o f  Such a p r o c e d u r e , however, i s u n d e s i r a b l e  l o s s of bone d e t a i l due the  over the end o f the bone.  s l i g h t s h o r t e n i n g would o c c u r  to the f i l m . due  centered  i n the orthoroentgenogram i f  the  as i t would l e a d to  to the i n c r e a s e d d i s t a n c e of the t a r g e t from  film.  (b) In teleoroentgenography  the d i v e r g e n c e  produces c o n s i d e r a b l e m a g n i f i c a t i o n .  The  o f the rays from the  tube  amount of m a g n i f i c a t i o n i s  v a r i a b l e , depending upon the l e n g t h of the bone, the d i s t a n c e o f bone from the f i l m , and  the c e n t e r i n g of the tube.  the  If teleroent-  genograms are used f o r s e r i a l measurements o f growth, then a v a r i a b l e d i s t o r t i o n a r i s e s which makes them u n s a t i s f a c t o r y , s i n c e the c a t i o n becomes g r e a t e r w i t h creased  the growth o f the i n d i v i d u a l .  d i s t o r t i o n i s produced b o t h by  magnifi-  This i n -  the i n c r e a s e i n the bone - to -  f i l m d i s t a n c e , r e s u l t i n g from the t h i c k e n i n g of the p o s t e r i o r s t r u c t u r e s , and by  the i n c r e a s e d l e n g t h o f the bones themselves, which  p l a c e s the bone ends n e a r e r  the p e r i p h e r y of the d i v e r g i n g roentgen-  o g r a p h s beam. As  r e p o r t e d by  Green & Anderson  orthoroentgenograms show l i t t l e bones.  [4] the measurements from  d e v i a t i o n from the r e a l l e n g t h o f  O r t h o r o e n t g e n o g r a p h i c measurement of a d i s s e c t e d a d u l t femur,  45.7  cms  l o n g , gave a l e n g t h o f 45.5  37.0  cms  l o n g was  37.0  cms;  t h a t of an a d u l t  by orthoroentgenogram.  The  tibia,  lengths of  these  6  bones, as recorded 49.2  on a teleoroentgenogram centered  at the knee were  cms f o r the femur and 38.5 cms f o r the t i b i a !  1. 2 - Research The sion.  organization: present  study has been m o t i v a t e d by the above d i s c u s -  The l e n g t h measurement o f bones by radiography i s . c o m p l i c a t e d ,  the outcome b e i n g  i n f l u e n c e d by many f a c t o r s i n c l u d i n g the  p o s i t i o n i n g o f a p a t i e n t at t h e time the x - r a y i n g ability  o f the t e c h n i c i a n  parameters, the c l a r i t y  t o choose  i s performed, the  the c o r r e c t x-ray exposure  o f the radiogram used f o r l e n g t h  evaluation,  the p s y c h o p h y s i c s o f v i s i o n and i t s i n f l u e n c e on p e r c e i v i n g  relevant  details, etc.. . Our  approach to the problem was to f i r s t  f a c t o r s that would seemingly c o n t r i b u t e  i s o l a t e a l l the  to an e r r o r i n measurement,  to assess the magnitudes o f t h e i r r e s p e c t i v e c o n t r i b u t i o n s and,  to e r r o r ,  f i n a l l y , i f pronounced enough, t o suggest methods f o r c o r r e c t i n g  or e l i m i n a t i n g these sources o f e r r o r . In chapter I I , a thorough d i s c u s s i o n o f t h e geometric s t r u c t u r e and r a d i o g r a p h i c ducted. gated.  c h a r a c t e r i s t i c s o f l o n g l e g bones i s con-  A x i a l r e l a t i o n s h i p s & patterns Part  psychophysical  o f growth are a l s o  investi-  I I o f the same c h a p t e r i s an o v e r a l l review o f the f a c t o r s i n f l u e n c i n g t h e outcome of t h e x-ray imaging  system, w h i l e p a r t I I I i s concerned w i t h the e f f e c t of t h e s e a r c h b e h a v i o u r on a c c u r a t e  and c o n s i s t a n t  'reading'  of a radiogram.  In chapter I I I , we i n v e s t i g a t e the e f f e c t o f the p a t i e n t ' s p o s i t i o n i n g with respect measurement.  to the x-ray tube on the o v e r a l l l e n g t h  A phantom bone i s used t o o b t a i n a s e r i e s o f exposures,  7  through which the bone i s r o t a t e d and i n c l i n e d , and the beam c e n t e r and h e i g h t a r e v a r i e d ; the bone p r o j e c t i o n on the radiogram i n each case i s measured and compared to a standard how the p l a c i n g o f the leg  measuring  length.  A l s o , i t i s shown  r u l e r underneath t h e c h i l d ' s  t o measure h i s bone l e n g t h a f f e c t s  the r a d i o l o g i s t ' s judgement on  where the bone end i s l o c a t e d . In chapter  IV we attempt to s o l v e the problem o f the  r a d i o l u s c e n c y o f the bony c a r t i l a g e great e f f e c t  a  on l e n g t h measurement.  t  t  n  e  j o i n t s i n i n f a n t s and i t s  T h i s i s done by u s i n g a non-  r o u t i n e r a d i o g r a p h i c technique where very low energy x-rays to  accentuate  fat.  a r e used  the c o n t r a s t between the c a r t i l a g e - , and the muscle and  The r e s u l t i n g image i s then p r o c e s s e d  r a t i o s and the v i s i b i l i t y o f contours After processing  f o r x-ray  to enhance x-ray  o f the e p i p h y s e s . image enhancement, an edge  d e t e c t i o n - c o n t o u r " t r a c i n g a l g o r i t h m i s proposed i n chapter f o l l o w the borders  contrast  o f the bone, thereby  accentuating  V to  t h e edges and  s i n g l i n g o u t the bone from i t s n o i s y background. Chapter VI c o n t a i n s a g e n e r a l d e s c r i p t i o n o f the data a c q u i s i t i o n system.  This i n c l u d e s a b l o c k diagram o f the system  o r g a n i z a t i o n , a review o f i t s r e s o l v i n g c a p a b i l i t i e s and n o i s e t a t i o n s , and f i n a l l y  the software  e s t a b l i s h e d to o p e r a t e  limi-  the system  and  to t r a n s f e r data between the PDP-9 and the IBM system 370/67,  and  the PDP-9 and the DATA GEN 840A f o r p i c t u r e d i s p l a y .  8  CHAPTER 2 The  P h y s i o l o g i c a l , Psychophysical  and P s y c h o l o g i c a l  Aspects o f the Problem o f Measurement E r r o r s o f Long Leg Bones i n C h i l d r e n 2.1 - I n t r o d u c t i o n Many f a c t o r s can a f f e c t the f i n a l e s t i m a t e of a bone l e n g t h , yet  the i n d i v i d u a l c o n t r i b u t i o n s o f each o f these has been l a r g e l y  unknown.  There are many reasons f o r t h i s .  The g e o m e t r i c a l  i s t i c s o f the bone are f a r from b e i n g e a s i l y and  formulated  misalignments i n making a radiogram l e a d to v a r y i n g  patterns sities  character-  mathematically radiographic  s i n c e we only see the p r o j e c t i o n s o f t i s s u e s o f d i f f e r e n t den-  on a two-dimensional s e n s o r .  b o r d e r s and o t h e r  features  Also  the v i s i b i l i t y o f d e t a i l s ,  i n the image i t s e l f i s a f u n c t i o n o f parameters  o f the x-ray imaging system, of the t r a n s i l l u m i n a t i o n and o f p r o c e s s i n g by  the p e r i p h e r a l human nervous system, each o f which have a r a t h e r  w e l l - d e f i n e d p h y s i c a l c h a r a c t e r i z a t i o n that corresponds c l o s e l y t o the e x p e r i m e n t a l s i t u a t i o n [18]. and  F i n a l l y , the unconscious c o g n i t i v e p r o c e s s  the c o n s c i o u s d e c i s i o n - m a k i n g , a f f e c t e d by t r a i n i n g and o t h e r  i n t e r a c t i o n between v i s u a l and n o n - v i s u a l  factors, w i l l  u l t i m a t e l y have  a f i n a l e f f e c t on the magnitude o f the e r r o r i n the l e n g t h Our the  approach to i s o l a t i n g  following general  complex  estimation.  the e r r o r c o n t r i b u t o r s w i l l i n v o l v e  aspects o f the problem:  a - P h y s i o l o g i c a l - the geometric m o d e l l i n g  o f the bone, i t s a n g u l a r  r e l a t i o n s h i p s and i t s changing, r a d i o g r a p h i c terns i n c h i l d r e n due t o growth.  pat-  9  b - P s y c h o p h y s i c a l - the f a c t o r s a f f e c t i n g t h e image c l a r i t y and the system's r e s o l u t i o n , and the l i m i t a t i o n s they impose on the p e r i p h e r a l nervous system's  cognitive  capability. c - Psychological  - t h i s r e l a t e s to the f a c t t h a t  there  t i c a l l y no 'unbiased' e s t i m a t i o n length  from a radiogram.  i s prac-  o f t h e bone  T h i s i s b a s i c a l l y be-  cause many p e r c e p t f o r m a t i o n r u l e s a r e n o n - v i s u a l and i n c l u d e  t h e o r e t i c a l d e d u c t i o n from c l i n i c a l  h i s t o r y o r p r e v i o u s e x p e r i e n c e w i t h the same o r similar  patients.  The r e s t o f t h i s c h a p t e r i s d e d i c a t e d  t o the d i s c u s s i o n o f the  sources o f the above-mentioned types o f e r r o r s .  2.2 - P h y s i o l o g i c a l E r r o r s  2.2.1  - Geometric and R a d i o g r a p h i c D e s c r i p t i o n o f Long Leg Bones i n C h i l d r e n  i ) The Femur:  The femur i s t h e l a r g e s t and l o n g e s t bone i n the s k e l e t o n .  The head o f the femur i s a smooth, h e m i s p h e r i c a l i s rather i n Figs. (a)  cylindrical.  s t r u c t u r e , and i t s s h a f t  The a x i a l r e l a t i o n s h i p s o f the femur a r e d e p i c t e d  (2.1) and (2.2) and are d e s c r i b a b l e The m e d i o - l a t e r a l  as f o l l o w s :  angle which the neck forms w i t h the s h a f t o f  the femur measures about 160° a t b i r t h ; i n the a d u l t , i t v a r i e s  between  110° and 140° (approximately- 125° on the a v e r a g e ) . r  (b)  The neck i s a n t e v e r t e d  with respect  t o the s h a f t , which  wise v a r i e s w i t h the age o f the i n d i v i d u a l as i n d i c a t e d i n Table  like(2.1).  Axis  of  Femur  Shaft  Axis  of  •Neck  of  V-i/5"- 20'  Femur  I  *i\approx.  Axis  of the -  Femora!  Condyles  u^'100 I  0  i Axis  170'  of  Lower  the Shaft  Fig.  (2.1) A x i a l R e l a t i o n s h i p s o f the Shaft o f the Femur  Fig.  (2.2) A x i a l R e l a t i o n s h i p s o f the Hip J o i n t  11  T h i s angle may about  8 degrees  Table (2.1)  measure as much as 50 degrees i n the  adult.  Normal Degrees o f A n t e v e r s i o n o f the Femoral  Neck  (Average's''adapted  [5])  from s e v e r a l i n v e s t i g a t o r s  AGE  ANTEVERSION (DEGREES)  B i r t h t o 1 Year  30 - 50  2 years  30  3-5  25  6-12  20  12 - 15  17  16 - 20  11  G r e a t e r than  (c)  at b i r t h and d i m i n i s h e s to  20  A l i n e drawn through  8  the lowermost margins o f the femoral  condyles forms an angle of 10° w i t h the p e r p e n d i c u l a r ( o r 100° w i t h a x i s o f the (d)  the  shaft).  There i s a s l i g h t a n t e r i o r bowing o f the s h a f t o f the femur,  so t h a t the a x i s o f the upper two  t h i r d s o f the s h a f t of the femur forms  an angle o f 170° w i t h the a x i s of the lower one  t h i r d o f the s h a f t o f the  femur, and t h i s l a t t e r a x i s i s continuous w i t h t h a t o f t h e l e g i n the extended (e)  position. A h o r i z o n t a l l i n e drawn p e r p e n d i c u l a r to the a x i s of the s h a f t  o f the femur through s h o u l d pass through  the uppermost margin o f the g r e a t e r t r o c h a n t e r through o r below the f o v e a c e n t r a l i s o f the head o f  the femur ( S k i n n e r ' s l i n e ) . F i n a l l y , an important  remark c o n c e r n i n g the femur i s t h a t  the  12  d i s t a l e p i p h y s i s of the femur d u r i n g i t s development may  take on a v e r y  markedly i r r e g u l a r appearance.  appear r a d i o -  lucent i n part.  T h i s i s a normal v a r i a n t .  As p o i n t e d hood years ible  A l s o , t h i s e p i p h y s i s may  out  i n references  measurements c o u l d not  epiphyses.  As  [7] and  [ 2 ] , i n i n f a n c y and  i n c l u d e u n o s s i f i e d and  therefore  shown i n the s c h e m a t i c diagram o f F i g . ( 2 . 3 ) ,  childinvisthe  c a r t i l a g e space between the ends of the opposing bones a t the knee j o i n t of a new  born i n f a n t i s r a d i o l u c e n t .  of water d e n s i t y i n the roentgenogram. shown to be  filled  completely  by  T h i s space i s o c c u p i e d In the  the e p i p h y s e a l  by  a shadow  drawing, t h i s space i s c a r t i l a g e s and  their  overlying articular cartilages.  Tibial  Epiphyseal  Cartilage  F i g . 2.3  C a r t i l a g e Space at knee j o i n t o f new  born i n f a n t  13  The  osseous changes i n the knee w i t h age i n the male and female are shown  in Fig. ii)  (2.4).  The T i b i a :  The upper end o f the t i b i a  contains  the m e d i a l and l a t -  e r a l condyles which a r t i c u l a t e w i t h the c o r r e s p o n d i n g condyles o f the femur.  A n t e r i o r l y , the condyles meet t o form the t u b e r o s i t y o f the t i b i a .  This s n o u t - l i k e t i b i a l  t u b e r o s i t y which p r o j e c t s  face of the proximal epiphysis  from the a n t e r i o r  sur-  and hangs down i n f r o n t o f the s h a f t i s  an extremely v a r i a b l e s t r u c t u r e which o s s i f i e s i r r e g u l a r l y , see F i g . (2.5) and  i s subject  t o d e g e n e r a t i v e changes d u r i n g  the- growth p e r i o d  [5].' Not  i n f r e q u e n t l y , the t u b e r o s i t y w i l l appear d i f f e r e n t on the two s i d e s . The  s h a f t o f the t i b i a has a prominent c r e s t (the a n t e r i o r  c r e s t ) a n t e r i o r l y i n i t s upper two t h i r d s , which g r a d u a l l y extends medially  towards the m e d i a l m a l l e o l u s .  forms the i n t e r o s s e o u s  crest.  The l a t e r a l b o r d e r o f t h e t i b i a  In a f u l l  f r o n t p r o j e c t i o n , the l a t e r a l  and  medial c o r t i c a l w a l l s  10°  and 15° r o t a t i o n r e s p e c t i v e l y , t h e l a t e r a l c o r t i c a l w a l l becomes  progressively thicker. rior tibial  are a p p r o x i m a t e l y e q u a l i n t h i c k n e s s .  In a  The t h i c k e n i n g i s due t o the f a c t t h a t the ante-  c r e s t comes p r o g r e s s i v e l y more i n t o p r o f i l e on the l a t e r a l  edge o f t h e s h a f t as the t i b i a i s r o t a t e d e x t e r n a l l y . cannot be demonstrated r o e n t g e n o g r a p h i c a l l y l i f e , however. The  during  T h i s phenomenon  the f i r s t y e a r s o f  [Roentgenograms a r e shown i n F i g . 8-186, Ref. 6, p. 934]. upper margin o f the i n t e r o s s e a l c r e s t i s f r e q u e n t l y o f a  l e s s e r d e n s i t y than the remainder o f t h i s r i d g e and s i m u l a t e s elevation or thickening. normal c u r v a t u r e  T h i s appearance i s normal.  a periostal  There i s a s l i g h t  of the t i b i a , both l a t e r a l l y and a n t e r i o r l y .  9,38 WKS.  9, 5  YKo.  C f , ci Y K S .  9,1.8 YRS.  i l l '  '  d\9YRS. 9,7 YRS.  Fig.  O, 7.5 MOS.  9, I  r\7 [if  y <J,Z  MOS.  9,  ' l l  2.3 YRS.  I  O " , 3.5  9,  Y'HS.  2.7 YRS.  11)'' ! C>\ 13 YRS. 9 , 10 YRS.  9,15  YR.  0\4.5  YRS.  9, 3.5 Y R S .  !_!_!  !  O " , 5.b  i U  MOS.  YKii.  9, 4.6  YRS.  !_J  1  d\ 18 YRS. 9, 15.5 YRS.  (2.4) Osseous changes i n the knee w i t h age i n the male and female (Ref. [5]) .  15  Fig.  (2.5)  2.2.2  Normal V a r i a t i o n s i n the S i z e and C o n f i g u r a t i o n of the A n t e r i o r T i b i a l P r o c e s s amongst I n d i v i d u a l s  - Trabecular  Patterns  In any bone t h e r e are two  major groups o f  trabeculae:  the  r e l a t i v e l y broad t r a j e c t o r y t r a b e c u l a e  or p r i m a r y t r a b e c u l a e which  concerned w i t h  and  support, weight bearing  along major l i n e s or t o r c e and  s t r e s s ; and  resisting static  distortion  tne i n t e r v e n i n g f i n e mesh  trabeculae  (secondary  t r a b e c u l a e ) which add  trabeculae  and permit  a b s o r p t i o n of complex s t r e s s e s i n terms o f  dynamic p r e s s u r e s  further strength  a p p l i e d through m o b i l e j o i n t s u r f a c e s .  weight b e a r i n g  observed.  coarse  are concerned w i t h  and bone ends, f i n e t r a b e c u l a e  t r a j e c t o r y and  to changing f o r c e s , predominate. trabeculae  f u n c t i o n , dynamic  ations i n both represent  responses to m e c h a n i c a l demands and  v a r i a t i o n s i n h e a l t h and  disease  The  metabolic  antero-posterior 6  roentgenogram o f the neck o f the  alter-  [8].  appearance of the t r a b e c u l a e i n an  where  c a l c a r fem-  the f i n e c r o s s b r a c i n g  the same b a s i c s u p p o r t i n g  changing  Where s t r e s s e s o f  and muscle p u l l are c o n s t a n t l y s u b j e c t e d  such as at j o i n t s u r f a c e s S i n c e both the  can be  to the main  In areas  major d i r e c t i o n a l s t r e s s e s can be w e l l d e f i n e d , such as the o r a l , major t r a j e c t o r y t r a b e c u l a e  are  femur i s shown i n F i g . (2.6) :  16  Area  1  i s the primary v e r t i c a l group of the t r a b e c u l a e ,  Area  2  i s the secondary t r a n s v e r s e  Area  W  i s the Ward's t r i a n g l e .  Fig.  (2.6)  Trabecular  group, and  Patterns  2.2.3 - A n a t o m i c a l S t r u c t u r e  o f the Neck o f the Femur  Errors  From the above b r i e f d i s c u s s i o n , we can conclude t h a t are m a i n l y two a n a t o m i c a l f a c t o r s t h a t a f f e c t a c c u r a t e  there  bone measurement;  these a r e : 1 - The r a d i o l u s c e n c y  of u n o s s i f i e d c a r t i l a g e i n i n f a n t s .  2 - The i r r e g u l a r a n a t o m i c a l s t r u c t u r e o f the l e g bones. The f i r s t  f a c t o r i s a c c e n t u a t e d by the f a c t t h a t as the c h i l d  grows, more o s t e o b l a s t s shaft.  In a s s e s s i n g  inescapable  are formed adding l e n g t h  the c h i l d ' s bone e l o n g a t i o n  to the opaque  calcified  a f t e r s e v e r a l months, an  e r r o r w i l l o c c u r due t o the f a c t t h a t the d i f f e r e n c e i n  17  l e n g t h between the two measured bones w i l l be the sum o f two e n t i t i e s : the n a t u r a l bone growth, and the e x t r a l e n g t h  that i s no l o n g e r  radio-  l u s c e n t i n the radiogram due t o c a r t i l a g e c a l c i f i c a t i o n . The second f a c t o r , the i r r e g u l a r a n a t o m i c a l bone s t r u c t u r e , c o u l d a f f e c t the measurement  i n many ways.  The neck a n t e v e r s i o n , f o r  example, would n e c e s s a r i l y a l t e r the measurement  because i t s magnitude  changes over the y e a r s , hence d i s t u r b i n g the p e r s p e c t i v e i n the bone and consequently changing the m a g n i f i c a t i o n  relationships r a t i o s that  u l t i m a t e l y c o n t r o l the measured l e n g t h .  The same e f f e c t w i l l  the  to a p r e v i o u s  l e g i s s l i g h t l y rotated with respect  t a k i n g the radiogram.  p o s i t i o n i n g when  On the other hand, the measurement  f e c t e d at the femoral d i s t a l e p i p h y s i s  occur i f  c o u l d be a f -  and the t i b i a l p r o x i m a l  f o r example, due to t h e i r h i g h l y i r r e g u l a r development p a t t e r n  epiphysis, i n early  childhood. From the above d i s cuss i o n , we _are le.dw^to. i n v e s t i g a t e the f o l l o w ing : 1 - The p o s s i b i l i t y o f r e g i s t e r i n g and a c c e n t u a t i n g  the c o n t r a s t  between the u n o s s i f i e d epiphyses and the s u r r o u n d i n g medium (muscle and fat).  T h i s i s done i n Chapter IV w i t h c o n s i d e r a b l e  success.  2 - The magnitude o f the e r r o r caused by v a r y i n g t i o n s o f the x-ray tube and the bone. t i o n are d i s c u s s e d  the r e l a t i v e p o s i -  The r e s u l t s o f such an i n v e s t i g a -  i n Chapter I I I .  3 - The i m p l i c a t i o n s o f s u b j e c t i v e e s t i m a t i o n  o f the bone a x i s l o c a -  t i o n when p r o d u c i n g a radiogram on the angular r e l a t i o n s h i p s above and on the o v e r a l l bone l e n g t h . III.  described  T h i s i s a l s o t r e a t e d i n Chapter  18  2.3-  Psychophysical  In o r d e r  Errors  to be u s e f u l to the r a d i o l o g i s t , c l i n i c a l l y  significant  f e a t u r e s i n the p a t i e n t must be transformed i n t o c o r r e s p o n d i n g two dimens i o n a l p r o j e c t i o n s i n the x-ray image.  The "x-ray imaging system", com-  p r i s e d o f the x-ray s o u r c e , r e l e v a n t p h y s i c a l p r o p e r t i e s o f t h e p a t i e n t , r e c o r d i n g medium, and v i e w i n g mode, a f f e c t s t h i s t r a n s f o r m a t i o n . any  Clearly,  t e c h n i c a l inadequacy i n the system which r e s u l t s i n the n o n r e g i s t r a -  t i o n of u s e f u l information  w i l l adversely  a f f e c t the performance o f t h e  radiologist. The  imaging system cannot be c o n s i d e r e d  i n t e r f a c e w i t h the human o b s e r v e r .  O p t i c a l p r o p e r t i e s o f the eye, char-  a c t e r i s t i c s of the r e t i n a l receptors, and  the i n f o r m a t i o n radiologist.  recorded  image.  i s transilluminated with u l t r a - v i o l e t  on the f i l m w i l l  What i s a t s t a k e ,  desired information  light,  remain i n a c c e s s i b l e t o the  then, i s n o t o n l y  the p a s s i n g  o f the  over a l l the l i n k s i n the x-ray imaging system  itself,  a l s o t o and through the human v i s u a l r e c e i v e r (see F i g . (2.7)) The  its  and parameters o f t h e p e r i p h e r a l  l o w - l e v e l c e n t r a l nervous system a f f e c t p e r c e p t i o n . o f . t h e  Thus, i f a good r a d i o g r a p h  but  i n i s o l a t i o n from i t s  psychophysical  f o l l o w i n g two g e n e r a l  human v i s u a l system 2.3.1 The  e r r o r w i l l be s t u d i e d  sources:  then i n the context o f  image c l a r i t y , and p r o p e r t i e s o f t h e  (HVS).  - Image C l a r i t y term 'image c l a r i t y ' i s used t o d e s c r i b e  the d i a g n o s t i c a l l y important d e t a i l i n the r a d i o g r a p h . determine the c l a r i t y o f the r a d i o g r a p h i c quality.  Figure  image:  the v i s i b i l i t y o f Two b a s i c  factors  c o n t r a s t and image  (2.8) i s a d e t a i l e d t r e e s t r u c t u r e of the parameters  X-RAY  FILM PERIPHERAL  TRANSILLUMINATION  ~1  1  1 adaptive  1  characteristics  \  !  of  !  brightness  NERVOUS  retinal  receptors, optical properties  \  of the  r~ poor  contrast  eye  - i  unsharpness limited  resolution  I  X-RAY  _ ]  IMAGING  SYSTEM  F i g . (2.7) Modelling the psychophysical error components  SYSTEM  Brightness Levels , TO Contours  CNS  IMAGE CLARITY  I  1 IMAGE QUALITY  CONTRAST  r  T  SUBJECT CONTRAST  FILM  r  CONTRAST  FOG AND SCATTER  RADIOGRAPHIC MOTTLE  SHARPNESS  RESOLUTION  1- Thickness D i f f e r e n c e s Screen  2- D e n s i t y D i f f e r e n c e  I  MTF  Mottle  PTF Structure Mottle  3- Atomic Number D i f f e r e n c e  Quantum Mottle  4- R a d i a t i o n Q u a l i t y 1- C h a r a c t e r i s t i c  Curve  2- D e n s i t y 3- Screen  Film Graininess 1- Geometric Unsharpness 2-Motion Unsharpness  o r D i r e c t Exposure  4- F i l m P r o c e s s i n g  3- A b s o r p t i o n Unsharpness 4- Screen  Unsharpness  5- P a r a l l a x Unsharpness  Fig.  (2.8) Parameters A f f e c t i n g Image C l a r i t y  21  a f f e c t i n g image c l a r i t y .  The  f o l l o w i n g i s a b r i e f d i s c u s s i o n of  the  most important of these parameters.  2.3.1.a The  Contrast  term r a d i o g r a p h i c  contrast  r e f e r s to the d i f f e r e n c e i n  d e n s i t y between areas i n the r a d i o g r a p h and film  contrast  and  fog and  through another p a r t .  Subject contrast  through one  three  w i l l be  I t depends upon t h i c k n e s s  of these f a c t o r s are  further elaborated  Chapter IV.  i s the d i f f e r e n c e i n x-ray  p a r t of the s u b j e c t  d i f f e r e n c e , r a d i a t i o n q u a l i t y (KVp) first  contrast,  scatter.  1 - Subject Contrast: i n t e n s i t y transmitted  depends on s u b j e c t  and  compared to  difference,  that  density  atomic number d i f f e r e n c e .  classical.  The  fourth  The  f a c t o r , however,  because of i t s importance to our work i n  In d i a g n o s t i c  radiology,  attenuation  of the x-ray beam by  the p h o t o e l e c t r i c e f f e c t makes the most important c o n t r i b u t i o n to subject contrast. high  P h o t o e l e c t r i c absorption  i s increased  i n substances w i t h  atomic•.numbers, e s p e c i a l l y when low-KVp x-rays are used.  proximate atomic numbers of bone, muscle and  Muscle and show l i t t l e  Bone  13.8  Muscle  7.4  Fat  5.9  f a t , with l i t t l e  fat  d i f f e r e n c e i n t h e i r atomic number,  process.  produces the g r e a t e s t  p o s s i b l e d i f f e r e n c e i n p h o t o e l e c t r i c x-ray fat.  of v e r y low  KVp  (below 30)  the  t o e l e c t r i c absorption  s o r p t i o n between muscle and  ap-  are:  d i f f e r e n c e i n t h e i r a b i l i t y to a t t e n u a t e x - r a y s by Use  The  pho-  x-rays ab-  S o f t - t i s s u e r a d i o g r a p h y , such as  mam-  22  mography, r e q u i r e s the use ferences  of v e r y low KVp  i n atomic number between b r e a s t  x-rays because the s m a l l d i f -  t i s s u e s produce no  subject  con-  t r a s t u n l e s s maximum p h o t o e l e c t r i c e f f e c t i s used. 2 - F i l m Contrast: x-ray  The  i n f o r m a t i o n content  of the i n v i s i b l e , l a t e n t  image ( the p a t t e r n of v a r y i n g i n t e n s i t y of the x-ray  by d i f f e r e n t i a l a t t e n u a t i o n of x-rays the x-ray  by the s u b j e c t ) i s "decoded" by  f i l m i n t o a p a t t e r n o f v a r i a t i o n s i n o p t i c a l d e n s i t y which  determine f i l m c o n t r a s t .  T h i s p a t t e r n depends on f o u r f a c t o r s ; s e n s i t -  o m e t r i c p r o p e r t i e s of the f i l m , exposure (MAS) screens,  and  film  The were not  beam caused  intensifying  processing.  l a s t t h r e e f a c t o r s w i l l not be e l a b o r a t e d h e r e because  taken i n t o account i n our work.  the f i l m , on the o t h e r hand need be The  , the use of  The  they  s e n s i t o m e t r i c p r o p e r t i e s of  considered.  r e l a t i o n s h i p between the d e n s i t y produced on a f i l m and  exposure i t r e c e i v e s i s p l o t t e d as a curve known as the c u r v e , F i g . (2-9).  Observe t h a t x-ray  films w i l l  the  characteristic  characteristically  generate harmonic d i s t o r t i o n s i n c e the t r a n s m i t t e d l i g h t of an exposed and processed  f i l m i s q u i t e non-linear with  the f i l m ' s e x p o s i n g  r a d i a t i o n [21].  r e s p e c t to the i n t e n s i t y  Some i n v e s t i g a t o r s ( f o r example  have taken t h i s i n t o account and produced r a d i o g r a p h s between 0.5  s i t o m e t r i c readings response.  In our  o b s e r v e d , they would c o r r e c t den-?  t h i s was  not  necessary  a linear  done, mainly because of a l a c k  of a v a i l a b l e p r e c i s i o n i n c a l c u l a t i n g the H and However, i t was  I f any n o n - l i n -  to those which would have been o b t a i n e d w i t h  research  [12])  w i t h peak d e n s i t i e s  and 1 d e n s i t y u n i t s f o r r e s e a r c h purposes.  e a r i t y i n the c h a r a c t e r i s t i c curve was  of  D curve  experimentally.  to l i m i t our work on radiograms to those where  23  d e n s i t y v a r i a t i o n s were w i t h i n 0.5 able  to a d e q u a t e l y q u a n t i z e  Relative  Fig.  3 - Fog  and  and  2.0  d e n s i t y u n i t s , so as  the radiograms u s i n g  to  a 64 l e v e l grey s c a l e .  Exposure  Relative  (2.9)  be  Exposure  Fig.(2.10)  scatter:  Fog  is strictly  defined  as those s i l v e r  halide  g r a i n s i n the f i l m emulsion which are developed even though they were not exposed by  radiation.  radiographic its  contrast.  T h i s produces unwanted f i l m d e n s i t y , which lowers The  fog e f f e c t  c o u l d be  e l i m i n a t e d by  d e n s i t y l e v e l from the d e n s i t y o f e v e r y p o i n t on  simpler  approach was  image q u a n t i z a t i o n sired  .  adopted and  subtracting  the radiogram.  c o n s i s t s o f a d j u s t i n g an o f f s e t  to a s s i g n to zero  intensity  any  ,A  during  intensity level  de-  24  The e f f e c t o f s c a t t e r e d r a d i a t i o n  (Compton S c a t t e r ) on c o n t r a s t  r a t i o s i n radiograms can be e s t i m a t e d by a simple Let of  procedure:  1^ be the average r a d i a t i o n i n t e n s i t y o f a very narrow beam  r a d i a t i o n emerging from a s m a l l segment o f a body p a r t and A I ^ be the  r e d u c t i o n i n t h i s primary  i n t e n s i t y as t h i s beam passes  cent s t r u c t u r e of g r e a t e r d e n s i t y .  through  an a d j a -  The r a d i a t i o n c o n t r a s t CL^ (N s i g n i -  f y i n g narrow beam) between the two a d j a c e n t areas i s then g i v e n by the equation: A I. [ P Let  us now r e p l a c e the narrow beam by a broad beam, l a r g e  enough to cover the e n t i r e a r e a o f i n t e r e s t ; L e t I the s c a t t e r e d r a d i a t i o n r e a c h i n g the f i l m . CL  a  (B s i g n i f y i n g broad beam) w i l l  be the i n t e n s i t y o f  The new r a d i a t i o n c o n t r a s t  then be g i v e n by the e q u a t i o n : AI  C  and hence  B  I + I P s  (2.2)  CL = B 1 + I /I s p  (2.3)  The r a t i o I / I depends on the body t h i c k n e s s , tube p o t e n t i a l s p J  and f i e l d  s i z e , b u t to a l e s s e r e x t e n t i s a l s o i n f l u e n c e d by such  as the body anatomy, beam f i l t r a t i o n  and the r e l a t i v e d i s t a n c e s between  the f o c a l s p o t , the body p a r t and the f i l m . in  factors  Seeman [19] has shown that  the case o f chest e x a m i n a t i o n ,  I / I i s o f the o r d e r o f 2. Morgan s p [20] has shown t h i s r a t i o to range from 4 t o 9 f o r s k u l l and abdominal  examinations.  I t f o l l o w s t h a t the c o n t r a s t CL o b t a i n e d w i t h B  the f i e l d  25  s i z e s n o r m a l l y encountered  i n r o u t i n e chest radiography w i l l be  35% o f the narrow beam c o n t r a s t C„ and o n l y about N  about  10 - 20% of C, i n the N  case of s k u l l and abdominal p r o c e d u r e s . To our knowledge I / I has not been c a l c u l a t e d f o r l e g r a d i o ° s p grams.  However, the s i z e of the beam needed i n  suggests  teleoroentgenography  a poor c o n t r a s t r a t i o and hence poor f e a t u r e p e r c e p t i o n . 2.3.1.b - Image Q u a l i t y The second b a s i c f a c t o r d e t e r m i n i n g image c l a r i t y i s image  quality. ability  The q u a l i t y o f the r a d i o g r a p h i c image may  be d e f i n e d as  the  of the f i l m to r e c o r d each p o i n t i n the o b j e c t as a p o i n t i n  the f i l m .  Image q u a l i t y i s a f f e c t e d by r a d i o g r a p h i c m o t t l e ,  and l i m i t e d  unsharpness  resolution.  1 - Radiographic Mottle Detail v i s i b i l i t y  i n a radiograph, e s p e c i a l l y  high-frequency  components a s s o c i a t e d w i t h bone edges, i s reduced by r a d i o g r a p h i c m o t t l e . R a d i o g r a p h i c m o t t l e i s mainly due  to quantum m o t t l e , which i s m a n i f e s t e d  by coarse d e n s i t y f l u c t u a t i o n s i n s t e a d o f the i d e a l u n i f o r m background on a radiogram,  and f i l m g r a i n i n e s s , which i s due  d i s t r i b u t i o n o f exposed g r a i n s i n the  to the b u i l t - i n  random  emulsion.  Quantum m o t t l e i s a s t a t i s t i c a l , e s t h e t i c a l l y d i s t u r b i n g due  to s p a t i a l f l u c t u a t i o n s o f x-ray. quanta  screens.  absorbed  effect  i n intensifying,  Film graininess i s usually n e g l i g i b l e r e l a t i v e  to quantum mot-  tle. Rossman [22] p r e s e n t e d an a n a l y t i c e x p r e s s i o n f o r the s t a n d a r d d e v i a t i o n from average  density C D )  the e f f e c t o f the o v e r a l l MTF  o f a radiogram,  taking into  (Modulation T r a n s f e r F u n c t i o n ) on  account limiting  26  t r a n s m i s s i o n of h i g h - f r e q u e n c y components. of x-ray quanta h i t t i n g a u n i t a r e a i s IT  Assuming the average number (hence the number absorbed i n  some area element  'a' i s n a) and f o l l o w s a P o i s s o n ' s d i s t r i b u t i o n , x the m o t t l e s t a n d a r d d e v i a t i o n w i l l be g i v e n by:  a(D) =  [a (D) 2  . + (.43G) =^F ] gram n a 2  then  2  J  x  > 0  .  (2.4)  0  system  unsharp  1  system sharp  !  and G i s the f i l m g r a d i e n t . We the  exposure  can e a s i l y conclude then t h a t , s i n c e time, any attempt  i s p r o p o r t i o n a l to  to decrease the exposure  time t o l e s s e n the  e f f e c t o f the p a t i e n t ' s l e g motion w i l l o n l y i n c r e a s e the r a d i o g r a p h i c mottle.  The n o i s e r e s u l t i n g  from t h i s m o t t l e i n the radiogram i s n o t  c o n c e n t r a t e d at the h i g h - f r e q u e n c y end of the spectrum as might be assumed from the s a l t - a n d - p e p p e r e f f e c t . evenly d i s t r i b u t e d  over a l l f r e q u e n c i e s passed by the system.  s e q u e n t l y , a simple LPF cases and may  Con-  (Low pass F i l t e r ) cannot remove n o i s e i n many  even r e s u l t i n a p o o r e r image than the o r i g i n a l by p r o -  d u c i n g a clumping o r m o t t l e d e f f e c t 2 -  Rather, the n o i s e i s somewhat  [23].  Sharpness Sharpness  Edge unsharpness  i s the a b i l i t y o f the x-ray f i l m t o d e f i n e an edge.  may  a - Absorption b - Screen  be caused by any or a l l of the f o l l o w i n g Unsharpness  Unsharpness  c - Parallax  Unsharpness  factors:  27  d - Geometric  Unsharpness  e - Motion Unsharpness • The  first  three f a c t o r s  described here/  are commonly understood  Geometric  and motion  [49]  unsharpness  and w i l l not be •  however are  interesting  to c o n s i d e r . •  0  h e  Fig.  (2.11)  Diagrams f o r geometric  In the diagrams target,  at l o c a t i o n  analysis  o f F i g . ( 2 . 1 1 ) , the s o u r c e of r a d i a t i o n  T, w i t h e f f e c t i v e f o c a l spot s i z e  a b s o r b i n g o b j e c t i s at l o c a t i o n 0 and has diameter d i s t a n c e from T to 0 i s TO. F has o v e r a l l s i z e  ation  a t T, and  'a'.  'd'.  The  i s the  x-ray  The p e r p e n d i c u l a r  The shadow image c a s t on the f i l m at  's' and may  be d i v i d e d  up i n t o  the w i d t h o f the m a g n i f i e d image o f the o b j e c t due radiation  4H  two  segments:  to a p o i n t  'e' the s i z e o f the geometric e r r o r  of the f o c a l spot from a p o i n t  source.  due  T h i s geometric  location 'i'.is  source of  t o the  devi-  division  28  can be g e n e r a l i z e d to h i g h m a g n i f i c a t i o n more m e a n i n g f u l l y v i s u a l s e p a r a t i o n i n t o umbra and penumbra.  than the  The m a g n i f i c a t i o n f a c t o r ,  m, i s d e f i n e d as the r a t i o o f t h e s i z e o f the m a g n i f i e d  image, i , t o the  o b j e c t s i z e , d, or m = i/d  i = md  I f we take s i m i l a r t r i a n g l e s i n Fig.(2.11) i t i s e v i d e n t i / d = TF/TO  that:  m = TF/TO  e/a = OF/TO S u b s t i t u t i n g OF = TF - TO and s o l v i n g f o r 'e' g i v e s e = a(m - 1)  (2.5)  S i n c e s== i + e, t h e r e f o r e s = md + a(m - 1) One, of course, by  (2.6)  can w r i t e down these  two e q u a t i o n s  automatically  c o n s i d e r i n g a p i n h o l e at 0 and w r i t i n g e/a = m - 1, which i s obvious. These r e l a t i o n s determine the amount o f c o r r e c t i o n needed i n  conjunction with  teleoroentgenography  due to penumbral shadows  alone.  A l s o , we observe t h a t i f 'd' i s much s m a l l e r than 'a', the image comes to r e f l e c t p r i n c i p a l l y the f o c a l spot s i z e might show a t the knee j o i n t l a r shape at the p r o x i m a l eminence t o g e t h e r w i t h  ( F i g . (2.11.c)).  This  radiogram, because of the markedly  end o f the t i b i a .  effect  irregu-  Here, the i n t e r c o n d y l o i d  the l a t e r a l and medial c o n d y l a r s u r f a c e s w i l l be  projected into a rather blurred region.  The f o c a l spot may even appear  on a double penumbra and hence propose f a l s e c o n t o u r s .  These  contours  are enhanced, o r r a t h e r c o n t r a s t i s enhanced a t these penumbral  regions  of t h e f o c a l spot because o f the non-uniform i n t e n s i t y d i s t r i b u t i o n of r a d i a t i o n from the t a r g e t .  We w i l l  reconsider this l a t e r i n conjunction  29  with  the l i n e spread  function.  The n a t u r e and c o n f i g u r a t i o n of t h i s  non-uniform i n t e n s i t y d i s t r i b u t i o n can be e x p l a i n e d  Effective Focal Spot  emission that there  as f o l l o w s :  J^_J *- sail  Fig.  (2.12)  Diagram of r a d i a t i o n d i s t r i b u t i o n on a r o t a t i n g anode and x - r a y beam  Fig.  (2.12) shows the r e c t a n g u l a r  d i s t r i b u t i o n of r a d i a t i o n  from e l e c t r o n bombardment o f a t y p i c a l r o t a t i n g anode.  the cup s u r r o u n d i n g  the f i l a m e n t  focuses  i s a zone o f decreased e l e c t r o n d e n s i t y  Note  the e l e c t r o n s so t h a t i n the m i d d l e .  T h i s has  been done to f a c i l i t a t e heat d i s s i p a t i o n i n the anode, p r e v e n t i n g development o f a c e n t r a l hot s p o t .  the  The o v e r a l l w i d t h o f t h e r a d i a t i o n  zone i s a l s o due to the f o c u s i n g c h a r a c t e r i s t i c s o f the cup and i s the e f f e c t i v e w i d t h o f the f o c a l spot angle i s c o n s i d e r a b l y foreshortened; as p o s s i b l e .  itself.  Since  the anode  l e s s than 4 5 ° , the r e c t a n g u l a r  surface  r a d i a t i o n zone i s  the e f f e c t i v e shape i s d e s i g n e d to be as n e a r l y The dimension o f the e f f e c t i v e  f o c a l spot  square  i n the cathode-  anode a x i s i s t h e r e f o r e a f u n c t i o n of the l e n g t h o f the f i l a m e n t and the a n g u l a t i o n  of the anode s u r f a c e .  How  uniformly  radiation i s dis-  t r i b u t e d i n t h i s d i r e c t i o n depends on the steepness o f anode  angulation  30  ( h e e l e f f e c t ) and whether there i s any ends of the cup,  the  j u s t as the sharpness o f the two bands of h i g h r a d i a t i o n  i n t e n s i t y depends on  the f o c u s i n g by  image of the f o c a l s p o t , i f not source  f o c u s i n g o f the e l e c t r o n s by  the s i d e s of the cup.  overexposed, w i l l  A pinhole  c l e a r l y show the double  of r a d i a t i o n [26].  Motion Unsharpness: S u b j e c t motion a f f e c t s both the sharpness of image edges the o v e r a l l system r e s o l u t i o n . next s e c t i o n ) due  Morgan  [13] has  to o b j e c t motion i s given by T f  sin  MTF  =  0  and  shown t h a t the MTF the  (see  equation:  v t  T TTf Vt D  where f  (cycles/mm) i s the s p a t i a l frequency  of a t e s t o b j e c t of s i n u -  s o i d a l t r a n s m i s s i o n , v (mm/second) i s the v e l o c i t y of motion and onds) i s the time of exposure. we  I f the product  t (sec-  v t i s l e s s than 0.1  mm,  can s a f e l y n e g l e c t motion unsharpness. 3 -  Resolution The  r e s o l v i n g power of a system can be  to r e c o r d separate i e n t l y expressed  images o f c l o s e o b j e c t s .  d e f i n e d as i t s a b i l i t y  R e s o l u t i o n i s most conven-  i n terms of the system modulation t r a n s f e r f u n c t i o n (MTF).  In the f o l l o w i n g we b r i e f l y e x p l a i n t h i s  entity.  A s i n u s o i d a l t e s t o b j e c t i s d e f i n e d as one whose x-ray mission v a r i e s s i n u s o i d a l l y with i n a direction perpendicular i n g from a p o i n t source,  d i s t a n c e along one  to t h i s a x i s .  i s transmitted  is  constant  I f a beam of r a d i a t i o n , a r i s -  through the t e s t o b j e c t , the  i a t i o n of i n t e n s i t y I ( x ) on an "image p l a n e " may equation:  a x i s and  trans-  be d e s c r i b e d by  the  var-  31  I(x) = I Where I  0  + l£ cos(2Trf x)  Q  (2.7)  ±  i s the mean i n t e n s i t y o f t h e r a d i a t i o n , I * i s the m o d u l a t i o n  a m p l i t u d e , x i s the d i s t a n c e  from some r e f e r e n c e p o i n t on the image  p l a n e i n the d i r e c t i o n o f the a x i s o f the t e s t o b j e c t , and f ^ i s the s p a t i a l frequency o f t h e t e s t o b j e c t when p r o j e c t e d onto the image plane. The x-ray beam d i v e r g e s the image p l a n e , by  uniformly;  t h e r e f o r e , the frequency on  f ^ , i s r e l a t e d t o the frequency o f the t e s t o b j e c t , f  Q  ,  the expression f. = f d / ( d Q  where d image  1  1  1  + d )  (2.8)  2  i s the f o c u s - t o - t e s t r - o b j e c t d i s t a n c e  and d  2  i s the o b j e c t - t o -  distance. In p r a c t i c e , x-rays do n o t a r i s e from a p o i n t source but from  an extended source w i t h h i g h l y i r r e g u l a r e m i s s i o n .  Therefore,  the:; r a -  d i a t i o n t r a n s m i t t e d by the t e s t o b j e c t w i l l be s u b s t a n t i a l l y d i f f e r e n t from t h a t g i v e n by e q u a t i o n I(x) = I  0  (2.7) and may be d e s c r i b e d by the e q u a t i o n  + I * M(f) cosUTrf-iX - <f>(f)]  where M ( f ) i s the m o d u l a t i o n t r a n s f e r f u n c t i o n .  ( 2  The term (f>(f) i n d i c a t e s  that the maximum and minimum i n t e n s i t i e s may occur those c o r r e s p o n d i n g of the t e s t o b j e c t .  at points other  to the p o i n t s o f maximum and minimum  than  transmission  <f>(f) i s c a l l e d the phase t r a n s f e r f u n c t i o n  The MTF has become a w i d e l y  .9)  (PTF)[12].  accepted concept f o r the s p e c i f i -  c a t i o n of the r e s o l u t i o n c a p a b i l i t i e s o f e n t i r e r a d i o l o g i c systems, groups o f components o f a system, and i n d i v i d u a l components i n a system.  32  Morgan square  [13] d e r i v e d a t h e o r e t i c a l e x p r e s s i o n f o r the MTF  f o c a l spot w i t h u n i f o r m e m i s s i o n .  of a  However, x-ray f o c a l s p o t s are  not p e r f e c t squares o r p e r f e c t r e c t a n g l e s , nor do they have u n i f o r m emission. Takenaka e t a l [14] expanded the i n t e n s i t y d i s t r i b u t i o n o f the roentgen  f o c a l s p o t i n t o symmetric and antisymmetric  b a s i s of r e c t a n g u l a r f u n c t i o n s . d i s t r i b u t i o n by i t s MTF  components u s i n g a  They s t a n d a r d i z e d the parameters o f i t s  and c u t - o f f frequency.  However, s i n c e x-ray  f o c a l spots are g e n e r a l l y designed on the l i n e - f o c u s p r i n c i p l e , the  size  and shape of the p r o j e c t e d f o c a l spot vary w i t h the angles o f p r o j e c t i o n . Hence the MTF  o r r a d i o g r a p h i c r e s o l u t i o n a l s o depend on the p o s i t i o n  and  d i r e c t i o n of i n t e r e s t i n a p l a n e normal to the d i r e c t i o n of the beam. T h i s e f f e c t i s f u r t h e r accentuated by the f a c t that the shape of the f o c a l spot i s q u i t e i r r e g u l a r . Doi  [15] i n d i c a t e d t h a t , because the p o i n t spread f u n c t i o n i s  not i s o t r o p i c , one-dimensional MTF's s h o u l d be determined rection.  He  f o r every d i -  a l s o d i s c u s s e d the f a c t t h a t s i n c e the t a r g e t p l a n e of the  x-ray tube i s p o s i t i o n e d at an angle a w i t h both  the o b j e c t p l a n e  and  image p l a n e because of the geometry of the x-ray tube (see F i g . ( 2 . 1 3 ) ) , the p o i n t s p r e a d f u n c t i o n of the f o c a l spot on the image p l a n e depends on the f i e l d p o s i t i o n of the image p l a n e . r e f e r r e d to as the  'field  characteristics'  f o c a l spot which depends on the f i e l d at  This property i s  as i n o p t i c s .  a considerable extent.  The MTF  c h a r a c t e r i s t i c s can be  some s p e c i f i e d p o s i t i o n s by a geometric method.  v a l u e s o f a and 3, the f i e l d  characteristics  can  strongly  o f the  determined  Depending on  the  m a n i f e s t themselves to  A c t u a l l y , the change i n MTF w i t h a and  B i s so  33  pronounced t h a t the q u e s t i o n a u t o m a t i c a l l y a r i s e s whether t h e r e i s an o p t i m a l 'target angle better resolution  t h a t i s x^orth b e i n g  determined f o r f l a t t e r MTF and  [25].  y X <"? . 1  The  F T P I H  experimental  fJiflrflrt-p.ristip.fi  o f thp  WVV  c a l c u l a t i o n o f the MTF u s i n g o p t i c a l F o u r i e r  t r a n s f o r m a t i o n by D o i [15], and the MTF and PTF u s i n g P e r r i n ' s [16]  *  (Equations  (2.10) and ( 2 . 1 1 ) ) * by  Rao  and Bates  equations  [12] l e a d s us t o  I f the l i n e spread f u n c t i o n l ( x ) o f an image-forming system i s known, the MTF, M(f) , and the PTF, <j>(f) can be e v a l u a t e d u s i n g the e q u a t i o n s :  -°°  J  M(f)  cos<f>(f)  l ( x ) cos(2-rrfx) dx -«> °°l(x) dx ;  M(f)  sin<J>(f)  (2.10)  -<*•' l ( x ) sin(2Tffx) dx -°°  J  l ( x ) dx  (2.11)  34  the f o l l o w i n g important  conclusions:  1 - The net b l u r r i n g i n a radiogram  depends on  causing parameters ^ i n .the "image-forming-chain. due  to the l i m i t e d r e s o l u t i o n of the f i l m  f i l m - s c r e e n combination. shape of the f o c a l  o r the  to the f i n i t e s i z e  and  spot.  anode-cathode a x i s ) , where the MTF f u n c t i o n r a t h e r than a sampling  but  P a r t of t h e . b l u r r i n g i s  (40 1/mm)  Another p a r t i s due  2 - The PTF i s zero o n l y i n the  ([0.1] and  several blur-  [ 1 . 0 ] ) , the MTF  [1.1] d i r e c t i o n  i s approximately  function.  (with r e s p e c t to g i v e n by a  Gaussian  In the o t h e r 2 d i r e c t i o n s  c o u l d be n e g l e c t e d below f - 0.4  lines/mm,  the PTF would l e a d to s p u r i o u s r e s o l u t i o n and i n t e r f e r e n c e p a t t e r n s  at h i g h e r f r e q u e n c i e s . 3 - R e l a t i v e f o c a l - o b j e c t and  o b j e c t - f i l m d i s t a n c e s (or i n o t h e r  words, m a g n i f i c a t i o n ) d r a m a t i c a l l y change the c u t - o f f frequency. best r e s o l u t i o n i s obtained with non-magnification The  reader may  imaging  The  [16].  r e a l i z e a t t h i s stage t h a t i t i s i m p o s s i b l e f o r  us to compensate f o r the net image b l u r r i n g caused by unsharpness l i m i t e d r e s o l v i n g power. t o l e r a n c e s and  manufacturing  the other c o n t r i b u t o r s of t e c h n i c a l o r i g i n  hence not measurable. can be  Much o f the b l u r i s caused by  and  and  T h i s means t h a t no a c c u r a t e mathematical model  c o n s t r u c t e d t h a t encompasses a l l the image degrading  factors.  T h e r e f o r e no mathematical scheme can be used to r e s t o r e the degraded r a d i o g r a p h i c image, and any details  attempt to enhance the v i s i b i l i t y  t h e r e i n w i l l be p u r e l y e x p e r i m e n t a l  and h e u r i s t i c .  On  of  the  the  other  hand, t h r e e p o s i t i v e c o n c l u s i o n s can be drawn from the above i n v e s t i g a tion.  The v i s u a l c u t - o f f frequency  (0.4 1/mm)  s h o u l d be  taken  into  35  account when s e l e c t i n g the d i g i t i z a t i o n frequency to prevent aliasing.  The  field  frequency  c h a r a c t e r i s t i c s o f the f o c a l spot imply m i n i m i z i n g  the d e v i a t i o n - f r o m - n o r m a l angle 3 as a measure to a t t a i n f l a t t e r F i n a l l y , as mentioned remains  to be  e a r l i e r , the problem o f optimum t a r g e t  MTF.  angle  investigated.  2.3.2  - P r o p e r t i e s of the Human V i s u a l System  As mentioned  (HVS)  b e f o r e , the x-ray imaging system cannot be  dered i n i s o l a t i o n from i t s i n t e r f a c e w i t h the human o b s e r v e r .  consi-  The  i n t e r f a c e i s b a s i c a l l y through a t r a n s i l l u m i n a t i n g source t h a t forms a p a t t e r n of b r i g h t n e s s v a r i a t i o n s and contours t h a t i s r e c o g n i z a b l e by the p e r i p h e r a l nervous f i l m when viewed  system.  The degree  of i l l u m i n a t i o n of the x - r a y  f o r l e n g t h measurement s h o u l d be based on a comprehen-  s i v e knowledge of the c o n t r a s t s e n s i t i v i t y of the eye.  Much psycho-  p h y s i c a l r e s e a r c h has been d i r e c t e d to measurement o f the c o n t r a s t tivity  of the eye.  about 2.2  I t has been shown t h a t the eye's  l o g u n i t s , c e n t e r e d about  sensi-  dynamic range i s  the a d a p t i n g b r i g h t n e s s [31].  means t h a t v a r y i n g the a d a p t i n g b r i g h t n e s s over a wide range  This  can make a  c e n t r a l t a r g e t appear to change from completely white to c o m p l e t e l y black. Other p r o p e r t i e s o f the HVS of  t h e i r importance  w i l l be b r i e f l y  to our work i n Chapter  reviewed,  because  IV.  The s u b j e c t i v e e f f e c t known as "sharpness" i s more c l o s e l y r e l a t e d to the r e n d i t i o n of edges and o b j e c t s much l a r g e r than barely v i s i b l e ,  those  than i t i s to o b j e c t o r i e n t a t i o n , l o c a t i o n and t e x t u r e .  The s e n s i t i v i t y of the o b s e r v e r to d i f f e r e n t s p a t i a l f r e q u e n c i e s i s a l s o important.  Measurements by Lowry and de Palma  [32] have shown t h i s  36  sensitivity  to peak at middle f r e q u e n c i e s (around 10 1/mm).  A related  e f f e c t i s the s u b j e c t i v e enhancement of edge t r a n s i t i o n s due t o the s o c a l l e d Mach Phenomenon ( F i g . (2.14) curve a ) , which i s the r e s u l t of l a t e r a l i n h i b i t i o n i n the r e t i n a l r e c e p t o r s .  Fig.  (2.14) Mach Phenomenon  Along w i t h s u b j e c t i v e a c c e n t u a t i o n o f edges goes a remarkable acceptance of a wide range of edge r e n d i t i o n . is  Edge (c) i n F i g . (2.14)  a l s o a c c e p t a b l e , but seems l e s s sharp and o f lower c o n t r a s t than edge  (a).  The b e s t s u b j e c t i v e - response i s a t t a i n e d by h i g h - f r e q u e n c y  t u a t i o n , w i t h a r o l l - o f f slow enough to p r e v e n t underdamped i n the t r a n s i e n t response.  overshoot  T h i s p r o p e r t y i s used as an i m p o r t a n t  t e r i o n i n the d e s i g n o f a d i g i t a l f i l t e r  accen-  cri-  f o r edge enhancement i n Chapter  IV. A f i n a l a s p e c t of human v i s u a l response the v i s i b i l i t y  of  radiographic noise.  f o r us to c o n s i d e r i s  R a d i o g r a p h i c images are c h a r a c t e r -  i z e d by t h e i r low S i g n a l to N o i s e R a t i o (S/N) .  Takenaka [28] s t u d i e d  S/N r a t i o s and v i s u a l c u t - o f f f r e q u e n c i e s i n bones by o p t i c a l and d i g i t a l simulations. details.  S/N was 7.4 db on the average  f o r acceptable v i s i b i l i t y of  S e l e c t e d f e a t u r e s were c o m p l e t e l y obscured at 4.4 db and t o t a l l y  37  d i s c e r n a b l e at 16.7  db.  He  v i s u a l c u t - o f f frequency T r a b e c u l a t i o n s had  of c o m p l i c a t e d  radiograms to be 0.53  the h i g h e s t c u t - o f f frequency  ence of n o i s e reduces cantly.  e s t i m a t e d by o p t i c a l s i m u l a t i o n the average  c o n t r a s t and  sharpness  1/mm.  (3.8 1/mm).  The  i n p i c t u r e s very  pres-  signifi-  A l s o n o i s e i s g e n e r a l l y more v i s i b l e i f i t i s c o r r e l a t e d w i t h  the p i c t u r e than i f i t i s random. 2.4-  Psychological Errors  As mentioned b e f o r e , " s e e i n g " a r a d i o g r a p h i c image i s a complex i n t e r a c t i o n between v i s u a l and n o n v i s u a l f a c t o r s . v i s u a l d a t a has  One's a b i l i t y  be a p p l i e d and  the accuracy o f the  to d e r i v e meaning, from raw  e s t i m a t i n g a bone contour  data  e x p e c t a t i o n of the o b s e r v e r determines, t h i n k s , the p o s s i b l e p e r c e p t s  resulting  (like)  and i n d i c a t e s t h a t  the  to a much g r e a t e r e x t e n t  t h a t may  result  from a g i v e n  mechanism by which the s t i m u l u s i s reduced  than  stimulus  [18], and hence u l t i m a t e l y i n f l u e n c e s h i s f i n a l bone measurement The  per-  l o c a t i o n ) can be s t u d i e d i n the c o n t e x t of the  c l a s s i c a l phenomenon of " s e t " i n psychology  he  the  a v e r y s t r o n g i n f l u e n c e on the ease w i t h which the  cept f o r m a t i o n r u l e s may percept.  The n a t u r e of  accuracy.  to the- r e s u l t i n g  p e r c e p t i s n o t . w e l l understood,and hence i t i s - d i f f i c u l t -to c o n s t r u c t s u f f i c i e n t models f o r a n a l y z i n g the p s y c h o l o g i c a l e f f e c t s on measurement. F o r a comprehensive study on the n a t u r e r e f e r r e d to  [18], [29], [30], [43] and  of these e f f e c t s , the reader i s [44].  38  Chapter 3 An  Analysis  of E r r o r s  i n the  o f Long Leg  R a d i o g r a p h i c Measurement Bones  .....As..mentioned i n Chapter I , the  a c c u r a t e measurement o f  long  l e g bones i n c h i l d r e n i s o f paramount importance when a s s e s s i n g  the  amount of bone growth over a s p e c i f i e d p e r i o d .  The  seriousness of  any  e r r o r i n d i f f e r e n t i a l l e n g t h measurement can be  put  i n perspective  by  recognizing s h o u l d be  that  i t may  to whether a bone  allowed to grow n o r m a l l y w i t h o u t i n t e r v e n t i o n  growth s h o u l d be relative  l e a d to a wrong d e c i s i o n as  stopped or a c c e l e r a t e d .  I f the  o r i e n t a t i o n of the bone  to the x-ray tube i s d i f f e r e n t when t a k i n g  the  to be used i n making a d i f f e r e n t i a l measurement, then we that  two  radiograms  would expect  a c e r t a i n amount of measurement e r r o r would consequently  In a d d i t i o n , s i n c e  the bone l e n g t h  matching the bone e x t r e m i t i e s that  or whether i t s  the  o r i e n t a t i o n of the  a f f e c t the To  i s measured from the radiogram  p o s i t i o n s on a L u f k i n  r u l e r , we  r u l e r and human v a r i a b i l i t y would  can  by expect  also  error. assess the magnitude of the measurement e r r o r due  mentioned f a c t o r s , a phantom bone was  in leg positioning.  done i s the  of the next  subject - The  Figure of a r e c t a n g u l a r  to the  above-  used i n a s e r i e s o f experiments  simulate v a r i a t i o n s  3.1  occur.  The  manner i n which t h i s  to  was  section.  Apparatus  (3.1)  i s a photograph o f the apparatus used.  wooden frame(a) whose l e g s are 0.9  It  consists  i n c h e s h i g h , or j u s t  h i g h enough to allow f o r i n s e r t i o n of an x-ray f i l m c a s s e t t e  underneath.  F i g . (3.1) The  A p p a r a t u s Used t o S i m u l a t e Bone P o s i t i o n  Variances  40  The  h o r i z o n t a l p l a t e (b) i s made of s t e e l to h o l d the magnetic s t a n d  in a fixed position. a l o n g i t s l e n g t h and wire  The  p l e x i g l a s s bar  (c) has  a t h i n wire  imbedded i n i t s lower s u r f a c e .  (d)  stretched  Near i t s ends,  the  i s c r o s s e d by o t h e r w i r e s which t o g e t h e r w i t h markers p l a y a p a r t  i n a l l o w i n g p r e c i s e r e g i s t r a t i o n of the x-ray beam c e n t e r d u r i n g  the  experiments; see F i g . ( 3 . 2 ) .  plexiglass  r  wire un  ( Figure  marker  1  U-7.  (3.2)  Top  View o f One End of P l e x i g l a s s Bar Wire Markers  Showing  the  When the c a s s e t t e i s i n s e r t e d underneath the frame, the w i r e i s very  c l o s e to the c a s s e t t e s u r f a c e .  The  markers can  then be used to  l o c a t e the beam c e n t e r of the x-ray beam r e l a t i v e to the phantom bone. T h i s i s done by u s i n g an aluminum and p l e x i g l a s s frame which p o s i t i o n s a plumb bob into  the cap  can s l i d e Fig.  over the p l e x i g l a s s p l a t e . of the x-ray  along one  (3.3).  The  I t c o n s i s t s of a p l e x i g l a s s b a r which  d i r e c t i o n i n a square aluminum frame as shown i n  p l e x i g l a s s b a r i s s l o t t e d and h o l d s  p i e c e which can s l i d e p i e c e i s attached  along  the b a r ' s  length.  a small p l e x i g l a s s  This small p l e x i g l a s s  to a t h i n s t r i n g which hangs down from the  i n turn i s attached  to a f u s e l a g e - s h a p e d  a l i g n i n g the plumb bob marker and w i r e  tube.  T h i s frame s l i d e s h o r i z o n t a l l y  plumb bob  t i p to c o i n c i d e w i t h one  c r o s s , the x-ray beam c e n t e r may  frame and :>  of p l e x i g l a s s .  By  of the p o i n t s where a be p r e c i s e l y r e g i s t e r e d .  41  longitudinal slot  Figure  (3.3)  Top  View o f X-ray Tube Cap  The magnet i n the magnetic s t a n d external switch.  F i x e d i n the s t a n d  can be  Frame  turned  on or o f f by  an  i s a v e r t i c a l r o d , along which a  p clamp(e) can s l i d e smoothly to an a d j u s t a b l e h e i g h t . a t r a n s v e r s e rod angular end  ( f ) that can be  position.  A hollow  and  c o a x i a l to*the  i n n e r c y l i n d e r equals  r o t a t e d about i t s a x i s to any  holds  desired .  c y l i n d e r (g) i s f i x e d p e r p e n d i c u l a r  of the t r a n s v e r s e rod and  also hollow  T h i s clamp  to  the  houses a second c y l i n d e r ( h ) , which i s first  cylinder.  The  the i n n e r r a d i u s o f the o u t e r  outer  r a d i u s of  cylinder.  The  the inner  c y l i n d e r c l a s p s the c e n t r a l p a r t of the s h a f t o f an a d u l t femur 43.0 long.  The  gap between the smooth c y l i n d r i c a l s u r f a c e and  bone s h a f t i s f i l l e d w i t h an adhesive  s t e e l springs. long wire  grooves  ( i ) , ( j ) by  The two  the  Lufkin powerful  l o n g i t u d i n a l a x i s o f the r u l e r i s p a r a l l e l to  the  embedded i n the p l e x i g l a s s p l a t e .  Any x-ray  The  irregular  cement, so t h a t the bone and  i n n e r c y l i n d e r r o t a t e as a u n i t about the c y l i n d e r a x i s . r u l e r i s h e l d i n f i x e d p o s i t i o n i n two  the  cms  taken,  l e g o r i e n t a t i o n can be and  simulated  u s i n g t h i s apparatus,  the femur l e n g t h as i t appears on  an  the radiogram measured.  42  The  r e s u l t s o f such measurements as a f u n c t i o n o f v a r i o u s parameters a r e  d i s c u s s e d i n the r e s t o f t h i s  chapter.  3.2 - E f f e c t of Bone R o t a t i o n I t i s i n t e n d e d here t o e s t i m a t e the v a r i a t i o n s i n r a d i o g r a p h i c a l l y - m e a s u r e d l e n g t h due t o r o t a t i o n o f the femur about  i t s axis.  We  assumed the z e r o - r o t a t i o n p o s i t i o n t o be where the lowermost p o i n t s i n the medial and l a t e r a l condyles a t t h e d i s t a l end of the femur are a t the same h e i g h t from the c a s s e t t e ( r a d i o l o g i s t s acknowledged t h i s as a reasonable assumption).  The d i s t a n c e from the c a s s e t t e t o e i t h e r o f  these p o i n t s was 4.60 cms. i n t h i s p o s i t i o n .  The d i s t a n c e from the  lowermost p a r t of the h e m i s p h e r i c a l femoral head to the c a s s e t t e was 10.90  cms.  At these h e i g h t s , the bone was i n a p o s i t i o n above the c a s -  s e t t e s i m u l a t i n g an i n v i v o s i t u a t i o n . exposures 5/6  were taken.  A s e r i e s of orthoroentgenographic  A l l exposures were made w i t h a s e t t i n g o f 70 KVp,  mAs and a nominal beam h e i g h t of 40 i n c h e s , f o r a l l experiments  cussed i n t h i s c h a p t e r i n c l u d i n g t h i s one.  dis-  From these exposures, the  f o l l o w i n g measurements were made (see F i g . ( 3 . 4 ) ) : 1 - The r u l e r r e a d i n g c o r r e s p o n d i n g to t h e tangent head (H).  to the femoral  T h i s tangent, as w e l l as o t h e r s a t the medial and l a t e r a l  condyles a r e normal t o the r u l e r , 2 - the r u l e r r e a d i n g s c o r r e s p o n d i n g to the medial and l a t e r a l dyles  con-  (MC, L C ) , 3 - the maximum width a t the p r o x i m a l end (PW), 4 - the maximum w i d t h at the d i s t a l end (DW). 5 - The angle between the tangent to the f e m o r a l head and the g r e a t e r  44  t r o c h a n t e r and  the r u l e r ,  Table (3.1) l i s t s r o t a t e d femur.  "0". the measurements taken from radiograms  A p o s i t i v e r o t a t i o n angle i s c o n s i d e r e d to cause  femur head to move f a r t h e r away from the c a s s e t t e s u r f a c e . ( 3 . 1 ) we  can conclude t h a t the r o t a t i o n of the bone has  on the o v e r a l l measured l e n g t h o f the femur. the measurements o f l e n g t h over the range i s 0.9 mm.  the  the  From t a b l e  a slight  ejffect  The maximum d i f f e r e n c e i n  of r o t a t i o n angle c o n s i d e r e d  Observe t h a t the angle 0 i n c r e a s e s a p p r o x i m a t e l y  w i t h the angle <of r o t a t i o n , and c o u l d be used, i f d e s i r e d , t o bone  of  linearly determine  rotation. 3.3 - E f f e c t o f Beam C e n t e r L o c a t i o n The marker system used on the p l e x i g l a s s p l a t e a l l o w s p r e c i s e r* rs •*-»+- r\ -v  of-  f T no  A -t F •£ o T* o r» t"  the femur f o r o r t h o r o e n t g e n o g r a p h i c exposure  r\ r\n  (see F i g u r e ( 3 . 5 ) ) .  The  markers were p l a c e d at the c o r n e r s of t h r e e i n c h s q u a r e s , s i n c e a v a r i a t i o n i n beam c e n t e r l o c a t i o n of t h r e e i n c h e s i s not uncommon i n s e t s of radiograms. different  Measurements were made from radiograms  produced  combinations o f beam c e n t e r l o c a t i o n s at the p r o x i m a l and  d i s t a l ends of the bone.  The r e s u l t s o f these measurements a r e p r e s e n t e d  i n table (3.2).  Proximal End Fig.  for  (3.5) L a b e l l i n g the Markers  Distal  End  on the P l e x i g l a s s  Plate  45  Table Rotation (degrees)  3.1  The E f f e c t o f R o t a t i o n on the Femur Radiogram  e  H (cms)  MC (cms)  LC (cms)  PW (cms)  DW (cms)  14  27.46  70.76  69.95  8.10  7.23  30.6  43.30  10  27.45  70.66  70.06  8.28  7.23  31.9  43.21  8  27.38  70.65  70.06  8.39  7.23  32.2  43.27  6  27.35  70.60  70.06  8.43  7.23  32.8  43.25  4  27.31  70.60  70.06  8.46  7.23  33.2  43.29  2  27.28  70.60  70.05  8.50  7.235  33.4  43.32  0  27.31  70.60  70.05  8.50  7.30  34.0  43.29 '  -2  27.35  70.575  70.045  8.65  7.30  35.0  43.225  -4  27.36  70.57  70.045  8.65  7.32  35.5  43.21  -6  27.31  70.54  70.04  8.675  7.335  36.0  43.23  -8  27.29  70.525  70.05  8.72  7.38  36.5  43.235  -10  27.30  70.52  70.05  8.72  7.38  36.8  43.22  (degrees)  Femur Length(cms)  46  T a b l e 3.2  The E f f e c t of Beam Center L o c a t i o n on the Femur Radiogram ( A l l e n t r i e s i n cm.)  DISTAL END  PROXIMAL END  *  B • C•L•  „** H  B. C. L. A B C D . O 1  1  A  27.60  1  1  B  27.315  A B C D O  1  1  1  1  1  C  D  0  27.04  27.3  27.31  A B C D O  1  1  1  1  1  A B C  1  b o  1  A B C D O  1  1  1  1  1  1  1  1  1  BONE  • ^ l\  LENGTH  MC  LC  70.60 70.68 70.58 70.465 70.60  70.025 70.19 70.01 69.89 70.05  43.00 43.08 42.98 42.865 43.00  70.60 70.68 70.58 70.465 70.60  70.025 70.19 70.01 69.89 70.05  43.185 43.265 43.165 43.05 43.185  70.60 70.68 70.58 70.465 70.60  70.025 70.19 70.01 69.89 70.05  43.56 43.64 43.54 43.425 43.56  70.60 70.68 70.58 70.465 70.60  70.025 70.19 70.01 69.89 70.05  43.30 43.38 43.28 43.165 43.30  70.60 70.68 70.58 70.465 70.60  70.025 70.19 70.01 69.89 70.05  43.29 43.37 43.27 43.155 43.29  * B.C.L. = BEAM CENTER LOCATION ** H, MC, LC = R u l e r Readings at Head o f Femur, M e d i a l Condyle and L a t e r a l Condyle r e s p e c t i v e l y  47  The  r e s u l t s i n the r i g h t m o s t column o f t a b l e  (3.2) i n d i c a t e a maximum  d i f f e r e n c e i n l e n g t h measurements o f 7.75 mm.  The s h o r t e s t l e n g t h  r e c o r d e d i s 42.865 cms and the l o n g e s t 43.64 cms.  Observe t h a t when  the beam c e n t e r has a f i x e d p o s i t i o n at the p r o x i m a l end and i s allowed to vary i n p o s i t i o n a t the d i s t a l end, d i f f e r e n c e s i n measured l e n g t h tend t o be s i g n i f i c a n t l y  l e s s than the d i f f e r e n c e s which r e s u l t i f the  beam c e n t e r i s v a r i e d a t the p r o x i m a l end. 3.4 - E f f e c t o f Beam Height A series of orthoroentgenography bone were taken  o f the phantom  to study the e f f e c t o f v a r i a t i o n s i n the beam h e i g h t on  measured l e n g t h .  The bone was p o s i t i o n e d as e x p l a i n e d i n s e c t i o n  w i t h zero degree r o t a t i o n .  Table 3.3  The r e s u l t s a r e summarized i n t a b l e  (3.2),  (3.3).  The E f f e c t o f Beam Height on the Femur Radiogram  BONE LENGTH(cms)  H (cms)  MC (cms)  .LC (cms)  42"  27.32  70.60  70.06  43.28  40"  2 7.31  70.60  70.06  43.29  38"  27.27  70.62  70.06  43.33  36"  27.17  70.62  70.06  43.43  34"  27.13  70.63  70.07  43.47  BEAM HEIGHT  The  exposures  r e s u l t s i n column H i n d i c a t e t h a t the g r e a t e s t v a r i a t i o n s i n the  measured l e n g t h occur due t o changes i n the measured p o s i t i o n o f t h e p r o x i m a l end o f the femur w i t h changes i n the beam h e i g h t .  As  expected,  the h i g h e r t h e x-ray tube the c l o s e r the measurement i s t o the a c t u a l  48  bone l e n g t h .  The measured l e n g t h  v a r i e d over a range o f 1.9 mm  beam h e i g h t was reduced from 42 t o 34  as the  inches.  3.5 - E f f e c t o f Knee I n c l i n a t i o n on the Femur Radiogram The l e n g t h measurement e r r o r due to i n c l i n a t i o n at the knee can be roughly e s t i m a t e d by c o n s i d e r i n g  the bone as a c y l i n d e r .  I f the  beam c e n t e r i s d i r e c t l y overhead the end o f the bone, then the e r r o r i s the  actual length  of the bone times the s i n e of the i n c l i n a t i o n a n g l e .  For  our phantom bone of l e n g t h  43 cm. and assuming an i n c l i n a t i o n of as  much as three degrees, the e r r o r i s l e s s than 0.6 mm, relative  to the e r r o r from o t h e r 3.6 - E f f e c t of L u f k i n  clearly negligible  contributors. Ruler O r i e n t a t i o n  and Human V a r i a b i l i t y  A t e l e o r o e n t g e n o g r a p h i c exposure of the phantom bone was made. The x-ray p r e p a r e d from the exposed f i l m was then used t o e s t i m a t e the magnitude o f l e n g t h measurement changes due t o v a r i a t i o n s i n o r i e n t a t i o n of the L u f k i n r u l e r and human v a r i a b i l i t y . Several  s t r a i g h t l i n e s with d i f f e r e n t angular  orientations  were drawn on the radiogram to s i m u l a t e p o s s i b l e placements o f the r u l e r by  a radiological technician.  Tangents to the e x t r e m i t i e s  were drawn as normals t o each o f these l i n e s and l e n g t h determined. of  o f the bone  measurements thus  Since r o t a t i o n of the r u l e r always r e s u l t s i n a  shortening  the bone at one end and a l e n g t h e n i n g a t the other end due to t r a n s -  l a t i o n s o f the i n t e r s e c t i o n s of the tangents w i t h the r u l e r , measurement e r r o r s at the ends of the bone due to improper a n g u l a r o r i e n t a t i o n o f the  r u l e r tend to c a n c e l  one another.  A more s i g n i f i c a n t f a c t o r i n  c a u s i n g e r r o r i s human v a r i a b i l i t y i n c o n s t r u c t i n g of the bone.  tangents at the ends  49  The  r u l e r placement which gave the maximum l e n g t h measurement  u s i n g tangents  at the e x t r e m i t i e s normal to the r u l e r was found  an angle o f 109° w i t h .the tangent  to both  of the bone as shown i n F i g . (3.6.a).  the condyles a t the d i s t a l end  T h i s o r i e n t a t i o n was t h e r e f o r e  c o n s i d e r e d to be p a r a l l e l w i t h the a x i s o f the bone. so t h a t i t a l s o b i s e c t s  the tangent  t o form  P l a c i n g the r u l e r  to the condyles a t the d i s t a l end  of the bone r e s u l t s i n a p o s i t i o n i n g of the r u l e r w i t h r e s p e c t to the femoral head as shown i n F i g . (3.6.b).  The l e n g t h measured a l o n g the  r u l e r i n t h i s p o s i t i o n w i t h p r o p e r l y c o n s t r u c t e d tangents In a r o u t i n e radiogram, low  i s 47.80 cms.  due to the x-ray image d e g r a d a t i o n ,  c o n t r a s t and poor edge d e f i n i t i o n , r a d i o l o g i s t s i n most cases  the r u l e r anywhere between p o i n t s a and b ( s e e F i g . ( 3 . 6 . a ) ) . tance a-b i s 0.685 cms. a l o n g the a x i s . from  'read'  The d i s -  A t the p r o x i m a l end, a d e v i a t i o n  the n o r m a l - t o - t h e - r u l e r by + 9 ° was c o n s i d e r e d an upper l i m i t to the e r r o r  i n e s t i m a t i n g the tangent  t o the femur head ( s e e F i g . ( 3 . 6 . b ) ) .  This,  e r r o r i s p a r t i c u l a r l y p r e s e n t w i t h c h i l d r e n , as the appearance o f the head o f the femur i n e a r l y c h i l d h o o d , f a r from b e i n g h e m i s p h e r i c a l , i s rather f l a t .  I n F i g . (3.6.b), p o i n t s c and d r e p r e s e n t the i n t e r s e c t i o n s  o f the i n c l i n e d  tangents w i t h the r u l e r .  and and ce = 0.46 cm.  The l e n g t h o f cd = 0.57 cm  The range of the p o t e n t i a l e r r o r a t the f e m o r a l  head i s t h e r e f o r e cd + ce = 1.03 cm.  (3.1)  The maximum r e a s o n a b l e e r r o r , t h e r e f o r e , t a k i n g d i s t a l and p r o x i m a l ends i n t o account  i s e q u a l to the maximum e r r o r at the knee  j o i n t p l u s the maximum e r r o r at the femur head; t h a t i s : e = 0.685 + 1.03 = 1.715 cms.  (3.2)  50  given  the r u l e r i s c o i n c i d e n t w i t h the bone a x i s .  l a t e d away from the femur head, the measurement increase.  T h i s was s i m u l a t e d  a x i s and l a t e r a l l y -9°  e r r o r i s e x p e c t e d to  by c o n s t r u c t i n g a l i n e p a r a l l e l to the  removed by 1 cm.  tangents i n c r e a s e d  I f the r u l e r i s t r a n s -  The p o t e n t i a l e r r o r between the  from 1.03 cm to 1.22 cm, hence i n c r e a s i n g t h e  maximum p o s s i b l e e r r o r t o 1.935 cm.  Moving the r u l e r l a t e r a l l y by 1 cm  c l o s e r t o the f e m o r a l head decreases the maximum p o s s i b l e e r r o r t o 1.46 cm.  Of course, the e r r o r at the d i s t a l end when moving the a x i s  to i t s e l f was c o n s i d e r e d  Fig.  parallel  constant.  (3.6) A x i a l R e l a t i o n s h i p s  a t the Bone  Extremities  The above measurements were r e p e a t e d on axes making a n g l e s o f 107°  and 111° w i t h the tangent t o the c o n d y l e s .  The r e s u l t s a r e summar-  ized i n table  T a b l e 3.4  (3.4).  E f f e c t of Lufkin Ruler Orientation  A x i s I n c l i n a t i o n to tangent t o Condyles  Length between m e d i a l condyle and femoral head Probable e r r o r  (a-b) a t knee  •107°  47.25  109°  47.8  111°  47.7  0.525  0.685  0.875  Probable e r r o r (c-d) a t femoral head  0.59  0.57  0.47  Probable e r r o r  (c-e) a t f e m o r a l head  0.59  0.46  0.71  T o t a l p r o b a b l e e r r o r a t femoral head  1.18  1.03  1.18  Maximum reasonable e r r o r i n l e n g t h measurement  1.705  1.715  2.055  Maximum r e a s o n a b l e e r r o r when a x i s i s d i s p l a c e d 1 cm l a t e r a l l y  1.995  1.935  2.375  Maximum r e a s o n a b l e e r r o r when a x i s i s d i s p l a c e d 1 cm m e d i a l l y  1.40  1.45  1.725  A l l e n t r i e s i n cms.  joint  and Human V a r i a b i l i t y *  52  3.7  -  The as r e p o r t e d  Conclusion r e s u l t s o f t h e o r t h o r o e n t g e n o g r a p h i c l e n g t h measurements  i n t h i s chapter  when r a d i o g r a p h i n g  i n d i c a t e that the p a t i e n t ' s p o s i t i o n i n g  h i s l e g s f o r the purpose o f measuring t h e i r  a f f e c t s by a v a r y i n g degree the accuracy  of these measurements.  length The  magnitude o f the e r r o r r e s u l t i n g from l e g r o t a t i o n , knee i n c l i n a t i o n and x-ray beam h e i g h t was found to be n e g l i g i b l y s m a l l .  A greater c o n t r i b -  u t o r to measurement e r r o r , though n o t a s e r i o u s one, i s the x-ray beam c e n t e r l o c a t i o n when exposing the femoral head. 1.8%  o f the anatomical  bone l e n g t h .  the r a d i o l o g i s t ' s s u b j e c t i v e estimate respect  T h i s e r r o r i s l e s s than  The most s e r i o u s e r r o r i s caused by o f t h e bone end l o c a t i o n w i t h  to the L u f k i n r u l e r grades. Because o f the f a c t t h a t these t e c h n i c a l e r r o r s a r e n e g l i g i b l e  as compared t o the e f f e c t o f the r a d i o l u s c e n c y on  of u n o s s i f i e d c a r t i l a g e  the> ^measured l e n g t h o f i n f a n t s ' l e g bones, we attempted t o s o l v e the  l a t t e r problem.  T h i s i s the s u b j e c t o f the next  chapter.  53  CHAPTER 4 On the Problem o f R a d i o l u s c e n c y of U n o s s i f i e d Cartilage i n Children  As mentioned  i n c h a p t e r I I , a key- problem i n the a c c u r a t e  measurement o f l o n g l e g bones i n c h i l d r e n i s the r a d i o l u s c e n e y o f the u n o s s i f i e d c a r t i l a g e at the bone e x t r e m i t i e s .  T h i s problem n o t  treated  p r e v i o u s l y , has been d e a l t w i t h by u s i n g a n o n - r o u t i n e r a d i o g r a p h i c imaging technique and by computer p r o c e s s i n g the r e s u l t i n g image f o r enhancement and contour e x t r a c t i o n .  4.1  - The R a d i o g r a p h i c Imaging  The bone,used new  born c h i l d .  Technique  i n t h i s i n v e s t i g a t i o n i s the femur of a deceased  T h i s femur was  removed and r a d i o g r a p h e d u s i n g v e r y  s o f t X-rays generated by a molybdenum anode a t 25KVp. c u r r e n t was  m a i n t a i n e d at 150 mA  The  filament  and the exposure time v a r i e d .  The  b e s t r e l a t i v e image q u a l i t y i n terms o f c o n t r a s t r a t i o s was o b t a i n e d u s i n g a 0.7  second exposure  time.  The low energy photons  i n the  r a d i a t i o n spectrum o f the molybdenum t a r g e t were f i l t e r e d out by a molybdenum f i l t e r .  Only those X-rays whose energy i s around the  c h a r a c t e r i s t i c r a d i a t i o n of molybdenum (18Kev) were r e t a i n e d .  This  monochromatic r a d i a t i o n , w i t h i t s low energy, i s mainly absorbed i n the body t i s s u e s by p h o t o e l e c t r i c a b s o r p t i o n (see c h a p t e r 2 ) . mentioned  As  b e f o r e , s u b j e c t c o n t r a s t i s maximized when the a t t e n u a t i o n  of the X-rays i s mainly due to the p h o t o e l e c t r i c e f f e c t and  this  p h o t o e l e c t r i c e f f e c t i s most pronounced when u s i n g low -KVp  X-rays.  54  4.2  - Image P r o c e s s i n g  X - rays are c h a r a c t e r i z e d by very l o w - c o n t r a s t superimposed on a changing, l o c a l l y uniform  background  a b l e to r e g i s t e r maximum i n f o r m a t i o n d u r i n g  the scanning  a m p l i f i e r g a i n , the a m p l i f i e r o f f s e t v o l t a g e  and  opening of the image d i s s e c t o r were so a d j u s t e d the photocathode i n the r e g i o n c o r r e s p o n d i n g of the bone.  S a t u r a t i o n , of course,  i s not  because of the r e s u l t i n g edge b l u r r i n g and d e t a i l s w i t h i n the s a t u r a t i o n r e g i o n .  features  [23].  To  be  process,  the  the l e n s a p e r t u r e as to t o t a l l y  saturate  to the o s s i f i e d p o r t i o n u s u a l l y desired mainly  a l s o the masking of  T h i s , however, was  no  fine  serious  handicap f o r our p a r t i c u l a r problem s i n c e the s a t u r a t i o n r e g i o n i s contoured  by a very d i s t i n c t edge t h a t c o u l d l a t e r , i f d e s i r e d , be  perfectly outlined. are of no  A l s o the f i n e r d e t a i l s w i t h i n the o s s i f i e d  shaft  importance as f a r as o v e r a l l l e n g t h e s t i m a t i o n i s concerned,  and hence can be d i s r e g a r d e d .  On  the o t h e r hand, because of the  s i g n a l - to - n o i s e r a t i o of the radiogram, p a r t i c u l a r l y  due  m o t t l e , s t r o n g i l l u m i n a t i o n and l a r g e a m p l i f i e r g a i n were the  low  to quantum only  answer t o the problem of r e c o r d i n g the d i f f u s e d , j u s t - n o t i c e a b l e t r a c e o f c a r t i l a g e at the femoral  4.2.1 The  head.  - P r e f i l t e r i n g Contrast  Enhancement  o r i g i n a l d i g i t i z e d X-ray i s shown i n F i g . (4.7)  g r e y - l e v e l histogram  i s shown i n F i g . ( 4 . 1 ) .  and i t s  I t i s apparent t h a t  the  g r e y - l e v e l d i s t r i b u t i o n i s b i a s e d toward h i g h d e n s i t i e s ; b r i g h t e r p i x e l s are s p a r s e ,  and  corresponding s u l t of having  the h i s t o g r a m  peaks at an i n t e n s i t y l e v e l of  to the s a t u r a t i o n r e g i o n at the femoral a l a r g e percentage of the 65536 p i x e l s  shaft.  63, The  concentrated  re-  55  around the d a r k e s t  and  the b r i g h t e s t p o r t i o n s o f the h i s t o g r a m  image w i t h l i t t l e v i s i b l e d e t a i l  [33].  i s an  Although i t i s g e n e r a l l y agreed  t h a t 64 q u a n t i z a t i o n l e v e l s are adequate to f a i t h f u l l y encode a radiogram  [34], the f a c t that i n our system these  apportioned  l e v e l s are  over the dynamic range of the system makes the  scheme i n e f f i c i e n t .  In a d d i t i o n to o b s c u r i n g  encoding  genuine c o n t r a s t  t h i s method of r e c o r d i n g i n f o r m a t i o n i s w a s t e f u l t h e o r e t i c sense.  uniformly  i n an  ratios,  information  T h i s w i l l be apparent when examining the r e s u l t s  c o n t r a s t enhancement.  One  p o s s i b l e way  to improve the q u a l i t y o f  of the  q u a n t i z e d p i c t u r e i s to r e f i n e the grey s c a l e ( i n c r e a s e the number of grey l e v e l s ) . limitations.  T h i s was  Another approach was  d i r e c t manipulation non  not p o s s i b l e i n our case due  to hardware  t h e r e f o r e f o l l o w e d , namely  of the grey l e v e l h i s t o g r a m  the  by p o s i t i o n - i n v a r i a n t  - l i n e a r p o i n t o p e r a t i o n s , as f o l l o w s : 1. L o g a r i t h m i c  conversion:  Software can be used to  convert  p i c t u r e b r i g h t n e s s f u n c t i o n to a d e n s i t y f u n c t i o n based upon the t h a t the eye The  responds l o g a r i t h m i c a l l y to v a r i a t i o n i n i n t e n s i t y  e f f e c t o f the l o g o p e r a t i o n i s to expand the range of the  s c a l e that i s h e a v i l y populated  and  The  r e s u l t i n g histogram  pixels  are n o r m a l i z e d  that  I f the o r d i n a t e s of the  define  histogram  w i t h r e s p e c t to the t o t a l number o f  (65536), then the r e s u l t i n g curve  f i r s t order d i s c r e t e p.d.f.  grey  i s shown i n F i g . ( 4 . 2 ) .  2. - Histogram E q u a l i z a t i o n : o f F i g . (4.1)  [35].  compress the range where the p i x e l s  are s p a r s e , which r e s u l t s i n expanding the c o n t r a s t r a t i o s edges.  fact  c o u l d be  Summing t h i s curve  considered  from l e f t  a f a i r l y monotone, n o n - d e c r e a s i n g Cummulative D i s t r i b u t i o n  as  a  to r i g h t Function  gives  F i g . ( A . 3 ) I d e a l and A c t u a l Cummulative D i s t r i b u t i o n Functions  Fig.  (4.4)  Histogram Equalization  57  (CDF)  as shown by curve  2 o f F i g . (4.3).  Had the number o f p i x e l s p e r  i n t e n s i t y l e v e l been the same throughout the h i s t o g r a m t a n g u l a r d i s t r i b u t i o n ) , t h e CDF would be r e p r e s e n t e d Fig. be  (4.3).  obtained  The  by curve  1 of  An approximation to t h i s r e c t a n g u l a r d i s t r i b u t i o n u s i n g techniques  quantiles i n s t a t i s t i c s The v e r t i c a l  (ideal rec-  could  s i m i l a r t o those based upon d i s t r i b u t i o n  [36] (Appendix A ) .  T h i s i s done as f o l l o w s :  a x i s i n F i g . (4.3) i s d i v i d e d i n t o 64 e q u a l  intervals.  o r d i n a t e s o f the CDF a t the v e r t i c a l a x i s increments a r e then ^ >  matched t o t h e i r c o r r e s p o n d i n g  abscissa values  z a t i o n l e v e l s f o r the p i x e l s .  The p i c t u r e elements a r e then  to those newly d e f i n e d v a l u e s .  to d e f i n e new q u a n t i -  The r e s u l t i n g h i s t o g r a m  reassigned  i s shown i n  F i g . (4.4) 3 - Gamma C o r r e c t i o n : r e f e r r e d to grey  Although gamma c o r r e c t i o n o r i g i n a l l y  s c a l e and c o n t r a s t adjustments i n t e n d e d  t o compensate  f o r uneven o r n o n - l i n e a r responses o f t h e image s e n s o r ,  t h e term can  be g e n e r a l i z e d to i n c l u d e any continuous  o f t h e grey  scale  [37].  The t r a n s f o r m a t i o n  a x i s o f t h e CDF i n t o 256 equal ordinates  transformation  c o n s i s t s o f p a r t i t i o n i n g the h o r i z o n t a l i n t e r v a l s , then u s i n g  to determine new q u a n t i z a t i o n l e v e l s .  the c o r r e s p o n d i n g  There w i l l  only 64 q u a n t i z a t i o n l e v e l s , b u t they w i l l be u n e q u a l l y s i g n a l s w i l l be compressed i n slow-slope and expanded i n h i g h s l o p e p o r t i o n s  s t i l l be  spaced.  The  p o r t i o n s o f t h e curve (CDF)  ( F i g . (4.5)).  4 - Smoothing and R e d i s t r i b u t i o n o f the p i x e l s over the grey s c a l e : Histogram e q u a l i z a t i o n (method 2) has the somewhat u n d e s i r a b l e of r e d u c i n g  the number o f non-zero q u a n t i z a t i o n l e v e l s .  l i m i t e d number o f o r i g i n a l q u a n t i z a t i o n l e v e l s  effect  Because o f the  (N=64), t h e p i x e l  58  200  2,0  •lKTEIISirr LEVELS  Fig.  (4.5)  Gamma C o r r e c t i o n  • • W H I t l LE¥EL5*  ca  TO  F i g . ( 4 . 6 ) Smoothing & R e d i s t r i b u t i o n  Fig. (4.7) O r i g i n a l D i g i t i z e d Radiogram  59  h i s t o g r a m and  CDF  i s composed of step  these s t e p s ,  the  quantization  levels.  per  functions.  fewer the number of u s e f u l I f one  The  more pronounced  (occupied) newly  i s t r y i n g to e q u a l i z e  defined  the number o f p i x e l s  l e v e l , the e f f e c t i v e n e s s o f the e q u a l i z a t i o n technique w i l l  upon the number of q u a n t i z a t i o n increases  i n the  Fortunately, noise  l e v e l s N and  the s i z e s of  the  depend  step  CDF. one  can  at the same time.  artificially  increase  T h i s i s done by  N and  convoluting  reduce the the  f u n c t i o n w i t h a c i r c u l a r l y symmetric low-pass f i l t e r  X-ray  picture  f u n c t i o n , whose  d i s c r e t e impulse response i s : h(i,j) = 26(i,j)+cS(i-l,j)+6(i+l,j)+6(i,j-l)+6(i,j+l) The  r e s u l t i n g p i c t u r e ' s histogram w i l l  contain  e n t r i e s from 0 to  Histogram e q u a l i z a t i o n i s then used to f i n a l l y o b t a i n of F i g . (4.6)  and  the  c o r r e s p o n d i n g p i c t u r e of F i g .  4.2.2- Results A first 64  and  (4.1)  the  histogram  (4.11).  Evaluation  o r d e r e n t r o p y measure was  computed f o r each o f  grey - l e v e l histograms o f the radiograms shown i n F i g s .  (4.11).  The  378.  computation i s g i v e n by  the  (4.7)  to  \  63 H(P)  The  = -E p i l o g i=o  Pi  P i v a l u e s were computed as  grey l e v e l i , to the v a l u e of H(P) The  2  bits/pixel  the r a t i o of the number of p i x e l s w i t h  t o t a l number of p i x e l s i n the image.  then c a l c u l a t e d .  as the d i f f e r e n c e between maximum and  therefore  The  i s s i x b i t s / p i x e l , which o c c u r s when the P i ' s are  t o t a l redundancy i n b i t s / p i c t u r e was  defined  (4.2)  i s given  by:  maximum equal.  Redundancy i s  a c t u a l entropy  [38],  and  60  R=  (6+Ep i  log  ±  2  v)  where 65536 i s the The  r e s u l t s are  * 65536  ±  bits/picture  t o t a l number of  tabulated  prixels  i n t a b l e 4.1.  the t a b l e t h a t each of the f o u r methods i n c r e a s e s with  respect  I t i s obvious  from  the e n t r o p y i n b i t s  to the number of non-zero q u a n t i z a t i o n  method 4 produces the  (4.3)  levels.  Although  g r e a t e s t number o f o c c u r r i n g q u a n t i z a t i o n  levels  a f t e r r e d i s t r i b u t i o n , i t does t h i s a t the expense of edge b l u r r i n g as can be (Fig.  e a s i l y seen i n the m i n u s c u l e o s s i f i c a t i o n c e n t e r (4.11)).  considering  One  can p a r t i a l l y  correct this undesirable  method 4.  f o r t h i s i s t h a t w h i l e method 2 t o t a l l y p r e s e r v e s method 4 has  better contrast  Each o f the linear operation Pre-filtering  by  f o u r techniques on  The  reason  edge s h a r p n e s s ,  investigated i s equivalent  to a non-  the i n t e n s i t y s c a l e , which i s p o s i t i o n - i n v a r i a n t .  c o n t r a s t enhancement i s p a r t i c u l a r l y  A uniform  toward one  end  impressive  f o r X-rays  o r the o t h e r o f the  d i s t r i b u t i o n of grey l e v e l s  use  of each q u a n t i z a t i o n l e v e l t h e r e b y e n h a n c i n g low  The  t e c h n i q u e can be  f o r which such changes o c c u r  grey-  tends to make e q u a l detail  information.  seen as making s u b t l e changes more e v i d e n t most f r e q u e n t l y , w h i l e  s u b t l e i n t e n s i t y changes i n l e s s f r e q u e n t l y o c c u r i n g [39].  effect  ratios.  with histograms h e a v i l y biased  regions  condyles  the output of the c o n t r a s t enhancement stage as a w e i g h t e d  average of the output p i c t u r e s o f method 2 and  s c a l e range.  i n the  in  the  lessening  grey s c a l e  regions  Logarithmic Conversion  Processed Histogram Gamma Correction Equalization  4.523542  4.379244  4.377023  4.483789  5.338506  96 761  106 217  106 363  99 366  43 351  34  52  Original  Radiogram  A c t u a l Entropy  (bits)  Smoothing and Redistribution  Redundancy w i t h r e s p e c t to 64 l e v e l s  (bits/picture)  Number of o c c u r r i n g quantization levels i n picture Max. Entropy  64  35  26  corresponding  to the number of non-zero l e v e l s A c t u a l Redundancy  6.0 96761  5.12928295  4.70043945  5.08746243  5.70043945  49154  21195  39562  23179  T a b l e 4.1 - Redundancy i n Radiograms a f t e r P r e f i l t e r i n g C o n t r a s t Enhancement  62  Fig.  (4.10) Gamma C o r r e c t i o n  Fig.  (4.11) Smoothing & Redistribution  63  To use any of the t r a n s f o r m a t i o n s d e s c r i b e d i n methods 2, 3 o r 4, one must: a)  compute the h i s t o g r a m  b)  compute the e m p i r i c a l d i s t r i b u t i o n f u n c t i o n ,  c)  use  d)  r e s c a l e and q u a n t i z e the r e s u l t i n g v a l u e s .  this distribution  of the image grey l e v e l v a l u e s ,  curve f o r the grey l e v e l t r a n s f o r m a t i o n ,  and  F i n a l l y , although these t r a n s f o r m a t i o n s are very e f f e c t i v e f o r enhancing  low  c o n t r a s t d e t a i l s , they do not d i s c r i m i n a t e between  low  c o n t r a s t i n f o r m a t i o n and n o i s e .  4.2.3  - Filtering  P r o c e s s e d p i c t u r e s w i t h r e d i s t r i b u t e d grey l e v e l s have b e t t e r c o n t r a s t r a t i o s and more v i s i b l e d e t a i l than the o r i g i n a l p i c t u r e . edges too appear somewhat s t r o n g e r because of low-pass f i l t e r i n g ) . can be  (except i n the case of method 4  The v i s u a l a c u i t y o f the x-ray image  f u r t h e r improved by p r o p e r m a n i p u l a t i o n  spectrum, however. quencies  The  of the image  frequency  T h i s i s i n t u i t i v e l y done by a c c e n t u a t i n g the  fre-  t h a t c o n t a i n edge or d e t a i l i n f o r m a t i o n , and a t t e n u a t i n g  those  f r e q u e n c i e s t h a t are p r i m a r i l y r e l a t e d to n o i s e . Two  approaches can be used to d e s i g n a r e q u i r e d d i g i t a l  namely the Z-trans form and was  the d i s c r e t e F o u r i e r t r a n s f o r m .  chosen because d e s i g n techniques  v e r s a t i l e and no  filter  i n the frequency  s t a b i l i t y problems have to be  d i s c r e t e , two-dimensional  Fourier transform  t i z e d p i c t u r e f(m,n), m,n=0,l,  >N-1,  (DFT)  The  filter,  latter  domain are more considered.  o f a sampled and  whose samples are  The quan-  equispaced  64  i n the x- and y - d i r e c t i o n i s g i v e n by N-1  N-1  „ 2. IT  F(u,v) = 1 m=0  £ f(m,n) e x p [ - j — n=0  u,v = 0,1,  (rau + n v ) ]  (4.4)  ,N-1  Where N i s the number of p o i n t s per r a s t e r i n the square p i c t u r e .  The  i n v e r s e t r a s f o r m o f F(u,v) i s g i v e n by:  N-1 N-1 f(m,n) = r^z E E F(u,v) exp [j ^ u=0 v=0  2 i t  (urn + vn) ]  (  Our concern i s t o determine high-emphasis produce p i c t u r e s which are s a t i s f a c t o r y  f i l t e r which  i n terms o f s u b j e c t i v e  w h i l e at the time t a k i n g i n t o c o n s i d e r a t i o n c o m p l e x i t y and time. of  However, f o r the moment we w i l l  a low-pass f i l t e r  high-emphasis  restrict  evaluation  computation  t r a n s f o r m space i s not o b t r u s i v e l y  can use- c i r c u l a r l y symmetric f i l t e r s  [42].  problem i s the p r o p e r c h o i c e of the f i l t e r  I t i s apparent  non-isotropic  T h i s b e i n g the case,we  roll-off  as to e l i m i n a t e as much as p o s s i b l e the o s c i l l a t i o n s put  caused by the Gibbs phenomenon  [40].  Figs  of the t r a n s f o r m c o e f f i c i e n t s  can c o n f i n e o u r s e l v e s to the d e s i g n o f a one-dimensional f i l t e r . first  )  o u r s e l v e s to the d e s i g n  the radiogram i n the u and v d i r e c t i o n s r e s p e c t i v e l y .  t h a t we  5  will  f i l t e r s can be d e r i v e d from the low-pass p r o t o t y p e .  t h a t the magnitude  >  s i n c e band-pass, b a n d - r e j e c t i o n , h i g h - p a s s and  (4.12) and (4.13) are p l o t s o f the magnitude of  4  f u n c t i o n so  i n the f i l t e r  Several r o l l - o f f  The  out-  functions  have been c o n s i d e r e d to e v a l u a t e t h e i r e f f i c i e n c y i n terms o f c o m p l e x i t y , computation time and f i l t e r i n g performance.  The low-pass p r o t o t y p e s o f  ABSOLUTE VPLUES OF FOURIER C D E F F S . : PIU.01X100  ABSOLUTE VRLUES OF FOURIER C D E F F S . ! PI0.VIX100  rt  >J  1  fi1  c  9  66  and H2 are Ormsby and Martin-  these f i l t e r s are shown i n F i g . (4.14). Graham f i l t e r s , respectively; H3 and  are Taylo's f i l t e r s  [41], and  H5 i s related to the Ormsby f i l t e r by the equation H (f) - [Hi(f)]  (4.6)  2  5  i s our proposed r o l l - o f f  function.  The mathematical expression f o r  this f i l t e r i s derived by convoluting the two functions G(f) and K(f) in Figs (4.15.a) and (4.15.b). be elaborated here.  The steps of the convolution w i l l not  Rather, we w i l l  concern ourselves with the weight  functions or s p a t i a l responses of the s i x f i l t e r s . of  Again, the process  finding the inverse Fourier transform of these f i l t e r s w i l l not be  carried out because i t i s lengthy and straightforward.  The weight func-  tions are represented by equations (4.9) to (4.14), with AM  where and  Fig.  f  =  9uAf  =  9-rrCf  - f  'I  = termination frequency  (4.7)  ,  f  = cut-off frequency  Af = f_ - f T c  (4.15) The two f u n c t i o n s G ( f ) and K ( f ) used proposed f i l t e r response H , ( f )  (4.8)  t o generate the  t 'T  f  -c  H ^ f ) = <f H (f) = 2  H (f) 3  T  - f)/(f  T  - f ). c  (  [l+cos[rr(f-f )/(f -f )]]/2 c  T  = (1/2TT) s i n t 2 T r ( f - f ) / ( f - f ) ] + ( f - f ) / ( f - f ) T  c  T  H ( f ) = (9/16) c o s [ 7 r ( f - f ) / ( f - f ) ] - ( l / 1 6 ) 4  c  T  c  T  5  H (f) =1 6  [H^f)]  )  .  cos t 3 i r ( f - f ) / ( f ^ - i ) ] c  £  (4.12)' (4.13)'  2  - 2[(f-f )/(f -f )]  2  2[(f-f )/(f -f )]  2  c  T  Fig.  9  (4.11)'  c  + i H (f) =  >  (4.10)'  c  c  A  T  T  c  c  (4.14) R o l l - o f f  ,  f <f<  (f +f )/2  ,  (f +f )/2<f<f  c  c  c  T  T  T  f u n c t i o n s o f low-pass p r o t o t y p e s  (4.14)'  68  (2/TTAIOX )  [s!±n-(-Aaix/2) sin((co  (4.9)  -t- t o J x / 2 ) ] c T h ( x ) = [ r r / x ( T r - A t o x ) ] [cos(Acox/2) sin((a) + u_) x/2)] c 1 h ( x ) = [1/1-(AWX/2TT) ] h ^ x )  (4.10)  h ( x ) = [1/1-(AO)X/3TT) ] h ( x )  (4.12)  2  2  2  2  2  (4.11)  2  3  2  4  2  h ( x ) = (2/TTACOX ) [COS(CO X) - (2/Acox) sin(Acox/2) cos((co +co ) x/2)] c (4.13) 2  T  5  c  h ( x ) = [tan(Aux/4)/(Atox/4) ] h ^ x )  (4.14)  6  The. v a l u e s o f t h e s e f u n c t i o n s  at t h e i r undeterminate  points  are d i s c u s s e d i n Appendix B.  Filter  Parameter:  High-emphasis contrast  information  f i l t e r i n g o f a radiogram p a r t i a l l y r e t a i n s the  i n a r a d i o g r a m , w h i l e r e i n f o r c i n g the low-energy  high-frequency c o e f f i c i e n t s responsible  f o r d e t a i l sharpness [23]. I t s  t r a n s f e r f u n c t i o n can be w r i t t e n i n terms o f the low-pass f i l t e r  transfer  f u n c t i o n as: H (f) = 1 + aU-H^Cf)) R E  Where H ^ C f )  -,  a>0  (4.15)  i s the t r a n s f e r f u n c t i o n o f t h e low-pass p r o t o t y p e .  A schematic representation shown i n F i g . (4.16).  o f the e f f e c t of H  G i v e n H^p(,f) , the f i l t e r  f o l l o w i n g three parameters: 1 - the c u t - o f f f r e q u e n c y 2 - the t e r m i n a t i o n  frequency  3 - the m u l t i p l i c a t i o n f a c t o r 'a'  ( f ) on an edge i s  i s ^ s p e c i f i e d by the  69  ^E(x)  >h (x) HE  kQ(_x). oversnco_  hoc  corllrast  f  *  -vs. Pixels.  X  X  Convolution H-E F u n c t i o n Fig.  I d e a l Edge  (4.16) E f f e c t of High-Emphasis  -3.CD  Fig.  | Tr T  ' D.BO  | •i  1.63  Output P i c t u r e F i l t r a t i o n on I d e a l Edge  • i - M - r - r T T "* ' ' 1 ~r-f-i-T-T-r-t—t-i 1  T  2.-»  5.:D  r  4.CO  4.00  3.60  (4.17) Comparison o f t h e weight f u n c t i o n s o f f i l t e r s H^, H  5  and H  &  70  A high-emphasis f i l t e r processing.  This  filter  of the type H,. was  i s described  i n reference  initially [27] as:  of u)  images w i t h the g r e a t e s t v i s u a l a c u i t y r e g a r d l e s s  c  y i e l d e d no n e g a t i v e  s i d e lobes  ...  ui - . . . A l s o ".  Our  own  however, i n d i c a t e d t h a t at no p o i n t d i d t h i s than the o t h e r  filters.  Fig.  filters.  rowest p o i n t spread f u n c t i o n , w h i l e h^(x)  weight.  I f we  of 5.6  increase  f  mm, and  traces a long negative  and  f i l t e r perform any  h^(x) f  m  has  to 0.2  and  0.5  mm  of the  1/mm  to x = 3.8  the n a r roll-off.  central  Also  Taylo's  filters,  frequencies.  whose weight f u n c t i o n s Filter  can be  e l i m i n a t e d by  ( p o i n t spread f u n c t i o n ) has  no  In  of the s i d e lobes  u s i n g a Gaussian  side lobes.  A l s o , the  are  has  the s m a l l e s t s i d e l o b e s .  Gaussian t r a n s f e r f u n c t i o n i s the only simple f u n c t i o n whose  transform  r  mm.  p e r c e p t i b l e r i n g i n g to propagate from a s t r o n g edge as Ringing  h (x) 5  always performs b e t t e r  the same, are b e t t e r than the Martin-Graham.  the femoral s h a f t .  1/mm  respectively,  were t e s t e d over a wide range of  s p i t e of i t s s u p e r i o r performance, the e x i s t a n c e  The  has  an u n a c c e p t a b l e  i s s t i l l 0.148  the narrowest p o i n t spread f u n c t i o n and  s l i g h t , but  better  are p l o t t e d f o r f =0.0159 c  f , the Martin-Graham f i l t e r  than the Ormsby f i l t e r . very n e a r l y  function  findings,  s i d e l o b e from x = 1.7  six filters  Independent of f  the  T  c  The  the p o i n t spread  I t i s obvious from the graph t h a t h^(x)  At a r a d i a l d i s t a n c e  of  An example o f t h i s i s shown i n  (4.17), where h . ( x ) , h (x) and h^(x) 4 5 6 f^=o,156 1/mm.  other  In f a c t , i t s p o i n t spread f u n c t i o n i s the w i d e s t  when compared to the s i x o t h e r  and  i n d i c a t e d that  p o s s e s s e d a somewhat narrower spread f u n c t i o n than any  spread f u n c t i o n s f o r a g i v e n to^ and  "yielding  and co^ chosen.  E x a m i n a t i o n of the p o i n t spread f u n c t i o n f o r t h i s f i l t e r it  used f o r  causes at filter.  inverse low-pass  71  p r o t o t y p e i s t o t a l l y determined  by o n l y one parameter,  d e v i a t i o n " a " , so t h a t the weight mined.  This o f f e r s  the unique  namely i t s s t a n d a r d  f u n c t i o n ' s s p r e a d can be s i m p l y d e t e r -  advantage of s t u d y i n g a wide v a r i e t y o f  outputs w i t h the l e a s t m a n i p u l a t i o n s o f f i l t e r parameters.  A  disadvantage  can e x i s t , however, i n t h a t the e v a l u a t i o n of the Gaussian f i l t e r  transfer  f u n c t i o n i n a computational p r o c e s s i n v o l v e s e x p o n e n t i a l s as compared to l i n e a r f u n c t i o n s o n l y i n the cases o f  or H .  J  o  R e s u l t s and D i s c u s s i o n : Figures high-emphasis  (4.18) and (4.19) are t y p i c a l p i c t u r e s emerging from a  Gaussian  f i l t e r , while Figs.  same i n p u t radiogram a f t e r high-emphasis  (4.20) and (4.21) a r e f o r the  filtration  out-of-range p i x e l s a r e generated by f i l t e r i n g ,  through H,_.  the p i x e l s a r e r e s c a l e d  between 0 and 63 b e f o r e d i s p l a y i n g the p r o c e s s e d radiograms. b e f o r e , the c o n t r a s t r a t i o s i n the f i l t e r e d (4.22) and (4.23) c o n t a i n histograms filtered  p i c t u r e s u s i n g a Gaussian  the C.D.F.'s o f these histograms elements  of  w h i l e enhancing  Figures  o f the grey l e v e l s o f two t y p i c a l  and an H,. f i l t e r ,  r e s p e c t i v e l y , and  a r e g i v e n i n F i g . (4.25).  The p i c t u r e  o f the i n t e n s i t y  the p i c t u r e s a g e n e r a l grey appearance.  a l i m i t i n g o p e r a t i o n can be used  As mentioned  p i c t u r e s are reduced.  a r e d i s t r i b u t e d over a narrow range  thereby g i v i n g  Because  scale,  The i n t r o d u c t i o n  to e l i m i n a t e out-of-range p i x e l v a l u e s  c o n t r a s t i n the p r o c e s s e d p i c t u r e .  We note t h a t n e g a t i v e  p i x e l s and p i x e l s o f l a r g e p o s i t i v e v a l u e o c c u r due t o overshoot i n r e g i o n s of abrupt change i n i n t e n s i t y . d e t a i l s o r edges t h a t f i l t e r i n g scaling  the f i l t e r e d  These are t h e r e g i o n s o f f i n e  i s working  to emphasize.  Instead of r e -  image between 0 and 63, we can s e t t o z e r o a l l the  72  73  •WTUSITT L E V E L S '  Fig.  (4.22) Gaussian  Filter  (4.24) Non-Linear  (4.23) H  5  in « « i n  'imcnin LETELI'  Fig.  Fig.  Filter  Filter  IEVEU  F i g . (4;25) CDF o f Gaussian, NonL i n e a r and H,. F i l t e r e d Images  74  n e g a t i v e p i x e l s and to 63 a l l the p o s i t i v e p i x e l s which are out o f range, then l i n e a r l y map 0 and  the r e s t of the p i x e l s c o n t r a s t enhanced v a l u e s between  63. The r e s u l t s o f a p p l y i n g the l i m i t i n g o p e r a t i o n to the r a d i o -  grams shown i n F i g s .  (4.18) to (4.21) are shown i n F i g s .  (4.26) to (4.29).  Observe t h a t p o s i t i v e p i x e l s which were o r i g i n a l l y out o f range have been d r a m a t i c a l l y overemphasized i n F i g . (4.26). bright  The reason f o r the  " r i n g " c l o s i n g at the bottom o f the radiogram i s the assumed  p e r i o d i c i t y of the p i c t u r e f u n c t i o n , whereby t h e bottom o f the s h a f t i s i n t e r p r e t e d as an edge by the DFT.  F i g . (4.27) i s a tremendous  ment a t t a i n e d by i n c r e a s i n g a from 1 to 2.  F i g u r e s (4.28) and  improve(4.29)  demonstrate the u n p r e d i c t a b l e p a t t e r n s that one gets u s i n g f i l t e r because of e x c e s s i v e r i n g i n g around t r a n s i t i o n The c o r r e c t c h o i c e s i n f i l t e r  regions.  d e s i g n l e a d to s i g n i f i c a n t l y  improved p i c t u r e s a f t e r c o n t r a s t enhancement, as can be seen by (4.30) to (4.33).  H,.  inspect-  ing  Figs.  The radiograms on the r i g h t of the page  are  the r e s u l t o f a p p l y i n g n o n - l i n e a r c o n t r a s t enhancement to the c o r -  responding radiograms on the l e f t the  of the page.  t h a t even w i t h  b e s t c h o i c e of f i l t e r parameters, the radiograms f i l t e r e d  H,. always c o n t a i n a r t i f a c t and f a l s e c o n t o u r s . list  Observe  through  T a b l e s (4.2) and  (4.3)  the f i l t e r i n g parameters used to o b t a i n the p i c t u r e s i n F i g s .  (4.30.b), (4.31.b), (4.32.b), and (4.33..b).  75  F i g . (4.28) Contrast Enhancement of F i g . (4.20)  F i g . (4.29) Contrast Enhancement of F i g . (4.21)  76  a) F i l t e r e d Fig.  (4.31) Gaussian  b) Contrast Enhanced F i l t e r i n g with a = 6.162  , a = 2.0  a) F i l t e r e d Fig.  b) C o n t r a s t Enhanced  (4.32) H F i l t e r : 5  f  q  a) F i l t e r e d Fig.  (4.33) H  = 0.3213 , f = 0.0714 , a = 2.0 T T  c  b) C o n t r a s t Enhanced 5  Filter:  f  £  = 0.2856 , f  = 0.0357 , a = 4.0  78  Table  4.2 - Gaussian High-Emphasis F i l t e r  Figure Number  Standard Deviation  Parameter 'a'  4.30.b  5 .60  2.5  .11324  17.28%  4.31.b  6.16  2.0  10809  16.49%  Number o f -ve P i x e l s  Table 4.3 - High-Emphasis F i l t e r  f(m,n)  Fig.  o f type H  Figure #  f  4.32.b  0.0714  0.3213  2.0  6282  9.58%  4.33.b  0.0357  0.2856  4.0  10055  15.34%  f  c  F(u,v) = | F ( u , v ) | e  DFT  % Number o f -ve P i x e l s  a  T  j < ! ) ( f )  //of -ve Pixels  % # o f•-ve Pixels  F(u,v) = | F(u,v) | V *  NonLinear Filter  (4.34) B l o c k Diagram o f N o n - L i n e a r F i l t e r i n g  (  f  )  Inverse TransForm  Process  f(m,n)  79  Non-Linear  Filtering:  A property  o f the F o u r i e r spectrum o f the radiogram i s i t s  l a r g e dynamic range these  [42]. Only a few p o i n t s are h i g h l y e n e r g e t i c and  are c o n c e n t r a t e d  i n the low-frequency p o r t i o n o f the spectrum.  Because the HVS i s more r e s p o n s i v e  to the h i g h e r  can c o n s i d e r u s i n g a n o n - l i n e a r f i l t e r  frequencies  i n the t r a n s f o r m a t i o n  [31], we domain that  tends to suppress l a r g e - v a l u e d terms and n o n - l i n e a r l y enhance s m a l l v a l u e d terms. The  A b l o c k diagram o f such a f i l t e r  r e s u l t o f a p p l y i n g such a f i l t e r i n g process  gram i s shown i n Figu'. (4.35. a ) ; the grey a t y p i c a l output pectively. (4.35.a).  i s shown i n F i g u r e  l e v e l histogram  to our r a d i o and the CDF o f  p i c t u r e are p l o t t e d i n F i g s . (4.24) and (4.25),  Figure  (4.34).  res-  (4.35.b) i s the c o n t r a s t enhanced v e r s i o n o f F i g .  I t i s apparent t h a t n o i s e i n the d i g i t i z e d radiogram generates  a v e r y unpleasant  salt-and-pepper  e f f e c t i n F i g . (4.35.b).  Better r e -  s u l t s , u s i n g d i f f e r e n t parameter v a l u e s i n the p r o c e s s i n g , are shown i n Figs.  (4.36.a) and (4.36.b), the radiogram i n (4.36.b) b e i n g  obtained  from (4.36.a) a f t e r c o n t r a s t enhancement. 4.3 The  Conclusion radiogram  presented  here was p r o c e s s e d  with  the primary  g o a l of i n c r e a s i n g c o n t r a s t r a t i o s o f image edges and i n c r e a s i n g the visibility  o f the condyles.  The p r o p e r t i e s o f the human v i s u a l  system  were used as m o t i v a t i o n  and j u s t i f i c a t i o n  niques.  t e s t e d , the Gaussian high-emphasis f i l t e r y i e l d e d  Of the designs  images w i t h filter  the g r e a t e s t v i s u a l a c u i t y .  f o r v a r i o u s enhancement  The p o i n t spread  tech-  function of this  can be made as narrow as d e s i r e d to c r e a t e a more narrow and steep  over-response at an image edge thereby  increasing activity.  Also  this  80  a)  Filtered  Fig.  (4.35)  b) C o n t r a s t  Non-Linear F i l t e r i n g :  a) F i l t e r e d Fig. (4.36)  y = 0.5  b) C o n t r a s t  Non-Linear F i l t e r i n g :  Enhanced  y = 0.83  Enhanced  81  f i l t e r y i e l d e d no n e g a t i v e s i d e l o b e s which produce an under-damped , response bands.  at edges, and  as such would b e s t r e i n f o r c e the HVS  For high-emphasis d e s i g n , a was  between 5.0  and  7.0.  kept between 2.0  Non-linear f i l t e r i n g  good v i s u a l a c u i t y f o r y between 0.8  c r e a t e d Mach  and 4.0,  and  a  a l s o produced radiograms w i t h  and 0.9,  w i t h the  salt-and-pepper  e f f e c t d e c r e a s i n g and edge d e f i n i t i o n weakening as y i n c r e a s e d .  82  Chapter 5  Edge P e t e c t i o n and Contour T r a c i n g 5.1  -  Introduction  In r e c e n t y e a r s ,  t h e r e has  been an i n c r e a s i n g i n t e r e s t i n  developing  e f f i c i e n t edge d e t e c t i o n and  use  i n the  automatic p i c t o r i a l p a t t e r n  The  g e n e r a l p i c t o r i a l p a t t e r n r e c o g n i t i o n scheme i s d e p i c t e d  picturel  [ADAPTIVE"  1  ,  T  '  I  _  Fig.  (5.1) The  ues  are  J  Block  f e a t u r e e x t r a c t i o n element i s s i m p l y  c a l c u l a t e d from a d i g i t i z e d  and  (measures).  c h a r a c t e r i s t i c s o f the  Recognition a scheme whereby  preprocessed  attempting  to s e l e c t the s e t o f  data  features  c l a s s e s o f images under c o n s i d e r a t i o n .  t r a c t e d , f o r example, from a c h e s t d i s e a s e s would be  val-  picture for a pre-  T h i s i s done to reduce the  a l s o a p p l i c a t i o n dependent, i n the sense t h a t the  heart  DISPLAY  I  Diagram o f P i c t o r i a l P a t t e r n  used f o r d e c i s i o n making, w h i l e  is  ~^  1  I rpTeorocessina 1 TpTcTuTe class 1\ •-\MEASUREMENT\I techniques ;appli-i i features; picture • ^cation dependent^ dependent J  s p e c i f i e d s e t of f e a t u r e s  to be  (5.1)  FEATURE  EXTRACTOR  —  in Fig.  CLASSIFICATION  FEATURE  I  ! control i  for  r e c o g n i t i o n of m e d i c a l images.  [SUPERVISOR  PREPROCESSOR]  DIGITIZER  contour t r a c i n g a l g o r i t h m s  different  features  radiogram f o r d e t e c t i n g  to be  It ex-  congenital  from the ones needed f o r pulmonary  diseases. Edge d e t e c t i o n and  contour t r a c i n g i s an i m p o r t a n t  t r a c t o r f o r p i c t o r i a l p a t t e r n r e c o g n i t i o n of radiograms.  feature  ex-  S e v e r a l schemes  83  have been proposed i n t h i s c o n t e x t .  Campbell  [24] used two one-dimen-  s i o n a l edge d e t e c t o r s o f the form shown i n F i g . (5.2) t o enhance the edges o f a d i g i t i z e d  radiogram.  v a r i a n t d e t e c t o r by adding one-dimensional  He approximated the r o t a t i o n a l l y i n -  the a b s o l u t e v a l u e s o f the outputs  d e t e c t o r s to o b t a i n the output.  o f two  The output p i c t u r e was  kD(x)  -oc CC  -7 Fig.  (5.2) Edge  Detector  then t h r e s h o l d e d t o r e t a i n p o i n t s t h a t q u a l i f i e d g l o b a l contour of-Contour  t r a c i n g al pori trim fhe.n searched  as edge c a n d i d a t e s .  the m'r.t.ure f o r a S t a r t —  (SOC) p o i n t , f o l l o w e d by a s y s t e m a t i c s e a r c h  edge p o i n t s u n t i l the e n t i r e p i c t u r e i s canvassed. suggested  f o r subsequent  Chow and Kaneko [45]  a t h r e s h o l d method f o r boundary d e t e c t i o n i n a p i c t u r e .  s i m i l a r approaches have been taken by Harlow e t a l . [46, 4 7 ] . et  a l . [48] adopted a scheme whereby a m i d l i n e  determined  f o r subsequent use i n d e t e r m i n i n g  A  Other  Roellinger  i n a c h e s t radiogram i s  the h e a r t shadow.  In t h i s  scheme a maximum g r a d i e n t technique was a p p l i e d t o h o r i z o n t a l scan  lines  to l o c a t e edge p o i n t s o f the r i g h t - h a n d edge by making use o f the constraint  t h a t an edge p o i n t must n o t v a r y a p p r e c i a b l y i n p o s i t i o n  the p o s i t i o n o f the edge p o i n t l o c a t e d i n the p r e v i o u s l i n e . s t r a i n t was added to prevent as r i b s and e x c e s s i v e  the a l g o r i t h m from t r a c i n g such  from  This light  conareas  vascularity.  I t i s d o u b t f u l whether any o f the above-mentioned edge  detec-  84  t i o n and  contour t r a c i n g techniques would f u n c t i o n p r o p e r l y  radiograms.  the  "field  of v i s i o n " , or the  p i c t u r e focused on, i s l i m i t e d i n s i z e and f u n c t i o n as hoped because they are regions  the  Some schemes do  not  tis-  i n t u i t i v e d e f i n i t i o n s o f what con-  - Edge P o i n t : edge may  be  D e f i n i t i o n and  Location  c o n c e i v e d i n a d i g i t i z e d p i c t u r e as a r i d g e  a number of p o i n t s  ( d i g i t a l p i c t u r e elements) r u n n i n g  a l o n g a c e r t a i n pathway t h a t i s o f t e n monotone. edge would then be  i n terms of the edge p o i n t s  A d e s c r i p t i o n of that  form i t .  emphasized, however, t h a t u s i n g the word r i d g e does not  edge s h o u l d n e c e s s a r i l y be ity  a r e a of  edge.  c o n s t i t u t e d by  be  false  where edges are e x c e p t i o n a l l y b l u r r e d , w h i l e o t h e r proposed  5.2 An  texture.  S/N  i n a p p r o p r i a t e l y a p p l i e d to s o f t  schemes f a i l because of t h e i r ad hoc, s t i t u t e s an  low  They u s u a l l y r e s u l t i n d i s c o n n e c t e d s t r u c t u r e s and  contour d e s c r i p t i o n s , u n l e s s  sue  on  imply t h a t  a l g o r i t h m s as i n  What i t does mean, however, i s t h a t i f a f t e r edge d e t e c t i o n are i n t e n s i f i e d  and  an  intens-  In f a c t such an i m p l i c a t i o n i s the  of the i n e f f i c i e n c y o f c e r t a i n edge d e t e c t i o n  w h i l e edge p o i n t s  I t should  a r e g i o n a l [ or g l o b a l pathway through  peaks i n a g i v e n p i c t u r e .  an  cause  [24].  and  tracing,  a l l o t h e r p i c t u r e elements  are  a s s i g n e d t o zero i n t e n s i t y ( f o r c o n v e n i e n c e ) , t h e i r appearance i n a three-dimensional representation In the  as  ridges.  context of x-ray images, an edge u s u a l l y s e p a r a t e s ,  contours a r e g i o n evant d e t a i l s .  would be  of h i g h  Figure  information  (5.3)  content i n a background o f  irrel-  i s composed o f t y p i c a l segments o f scan  l i n e s from a radiogram o f a c h i l d ' s femur, each segment c o n t a i n i n g edge p o i n t marked by  or  a v e r t i c a l arrow.  Scan segments l i k e  an  those of F i g s .  85  (5.3.a) and (5.3.b) are commonly encountered i n t r a n s i t i o n s between r e gions o f s i m i l a r grey l e v e l v a l u e . the edge c o n f i g u r a t i o n s bony s t r u c t u r e s . high-emphasis  i n regions  The scan segment  Figures of soft  (5.3.c) and (5.3.d) tissues surrounding  represent strong  i n F i g . (5.3.e) has been s u b j e c t e d  to  filtering.  (e) Fig.  (5.3) T y p i c a l Edge  5.3 - The Edge D e t e c t i o n  Configurations  Algorithm  B a s i c a l l y , any edge d e t e c t i o n a l g o r i t h m  i s a canvassing  scheme  by which each p o i n t o f a p i c t u r e f u n c t i o n and i t s n e i g h b o r s are examined to see i f there qualify  is a sufficient  the p o i n t  the g r a d i e n t consideration  r a t e of change of t h e p i c t u r e f u n c t i o n to  as an edge p o i n t .  or the L a p l a c i a n  A p l a u s i b l e approach i s t o use e i t h e r  of the p i c t u r e f u n c t i o n at the p o i n t under  to determine whether or n o t i t i s an e d g e . p o i n t .  the b a s i s o f our edge d e t e c t i o n  algorithm.  This i s  86  In d e v e l o p i n g the a l g o r i t h m , care has been taken t o make i t as modular as p o s s i b l e . its  e f f i c i e n c y over a broad  two t o t a l l y and  I t i s hoped t h a t t h i s main f e a t u r e w i l l maximize  decoupled  a l o c a l one.  class of picture functions.  a l g o r i t h m s have been developed,  this,  a global algorithm  The f u n c t i o n o f each w i l l be apparant  the moment i t i s s u f f i c i e n t  To achieve  l a t e r and f o r  to know t h a t the g l o b a l a l g o r i t h m commands  the main s e a r c h s t r a t e g y , c o n t a i n s s t o p p i n g c r i t e r i a to p r e v e n t  the de-  t e c t o r from f o l l o w i n g f a l s e c o n t o u r s , s u p p l i e s the parameters used by the l o c a l a l g o r i t h m f o r edge d e t e c t i o n , d i s p l a y s t h e c o n t o u r , The l o c a l a l g o r i t h m i s c a l l e d by the main r o u t i n e and performs detection.  etc... the a c t u a l  The edge d e t e c t i o n a l g o r i t h m i n i t s e n t i r e t y may be found i n  Appendix E. The a l g o r i t h m ' s f u n c t i o n and f e a t u r e s can p r o b a b l y be b e s t understood  i n the context o f i t s o p e r a t i o n on the radiogram which was  used i n the development and t e s t i n g o f the a l g o r i t h m . is  This  radiogram  the enhanced v e r s i o n of the c h i l d ' s femur c o n s i d e r e d i n the p r e v i o u s  chapter.  A f u r t h e r reason f o r u s i n g t h i s approach to e x p l a i n the a l g o -  r i t h m i s t h a t t h e p r e s e n t implementation  r e q u i r e s c e r t a i n parameter v a l -  ues be s u p p l i e d by the user a f t e r v i s u a l examination be p r o c e s s e d .  of t h e radiogram to  I t i s p o s s i b l e , however, t h a t t h i s dependency on user  a s s i s t a n c e can be removed by e x t e n s i o n s to the s o f t w a r e . In b e g i n n i n g the development o f t h e a l g o r i t h m , h o r i z o n t a l and v e r t i c a l scan segments a c r o s s edges were v i s u a l l y examined i n o r d e r t o g a i n an a p p r e c i a t i o n f o r t h e r e q u i r e d software edge p o i n t s .  complexity  to r e c o g n i z e  As an example of the d a t a , F i g u r e (5.4) i s a p r e s e n t a t i o n  of scan segments taken from every e i g h t h row i n the lower h a l f of t h e  -1  "5*  I  Fig.  (5.4)  Intensity  P r o f i l e s o:  -j—,—:—,—i—|—i—i—i—i  the  |  i  i—i—•  Radiogram i n F i g .  |  i—i—i (4.7)  i  j  i  i  i  i—|—i—i—i—i—|—i—i  ' ' i  88  p i c t u r e and a s s o c i a t e d w i t h the edges o f the femur. each o f the r i g h t and l e f t visual  hand edges are d i s p l a y e d  Only 50 p o i n t s i n order  about  to s i m p l i f y  examination. I t was apparent from examination of t h e d a t a that i t would n o t  be  sufficient  to base the edge d e t e c t i o n upon a simple one-dimensional  d i f f e r e n c e c a l c u l a t i o n as was done i n [48]. gradient  or L a p l a c i a n  tends to vary Instead  slowly  seem a p p r o p r i a t e ,  Neither  d i d a two-dimensional  s i n c e the edge p o i n t l o c a t i o n  from one row to the next or from column t o column.  i t was r e c o g n i z e d  to be c o m p u t a t i o n a l l y  f a s t e r and to a l l o w  fewer e r r o r s to make use o f knowledge of the l o c a t i o n of the edge p o i n t in  the p r e v i o u s  l i n e , and to f o l l o w the contour from row to row o r c o l -  umn to column, u s i n g e i t h e r h o r i z o n t a l o r v e r t i c a l edge d e t e c t i o n . The  global algorithm  h o r i z o n t a l o r a v e r t i c a l search uses a l o c a l o p e r a t i o n before  o f f e r s the o p t i o n o f c o n d u c t i n g e i t h e r a f o r edge p o i n t s .  at each p o i n t  t e s t i n g the p o i n t  The l o c a l  algorithm  that minimizes the e f f e c t s o f n o i s e  f o r edge candidacy.  The l o c a l o p e r a t i o n  s i s t s of least-mean-square-error f i t t i n g of a f i r s t  con-  and a second degree  p o l y n o m i a l to s e t s o f p o i n t s s u r r o u n d i n g and i n c l u d i n g each o f p o i n t s i n the scan segment under c o n s i d e r a t i o n . c u l a t e d f o r each o f the f i t t e d  The f i r s t  d e r i v a t i v e i s then  cal-  f i r s t - o r d e r and second-order curves a t  the p o s i t i o n of the edge p o i n t c a n d i d a t e .  The maximum r a t e o f change o f  the d e r i v a t i v e s o f the f i r s t - o r d e r curves i s then compared to the maximum r a t e o f change of the d e r i v a t i v e s o f the second-order curves. is  greater,  order  the edge p o i n t i s chosen as the p o i n t whose f i t t e d  curve has the l a r g e s t magnitude f i r s t  Ifi t  first-  derivative; i f i t i s less,  then the edge p o i n t i s chosen t o correspond t o the f i t t e d  second-order  89  curve w i t h the second  d e r i v a t i v e o f l a r g e s t magnitude.  As mentioned b e f o r e , the g e n e r a l s t r u c t u r e o f the edge d e t e c t i o n a l g o r i t h m was  determined  on an ad hoc b a s i s a f t e r v i s u a l  examin-  a t i o n of scan segments taken from the enhanced radiogram i n F i g . ( 4 . 7 ) . For example, s i n c e edges i n the radiogram of F i g . (4.31.b) c o u l d be ilar of  to e i t h e r F i g . (5.3.e) o r F i g s .  sim-  (5.3.a) and (5.3.b), the p o s s i b i l i t y  t e s t i n g an edge p o i n t c a n d i d a t e based upon e i t h e r the f i r s t - d e r i v a -  t i v e or the s e c o n d - d e r i v a t i v e i s i n c l u d e d .  F i g u r e s (5.3. a) and (5.3.b)  correspond to the i n d i s t i n c t edges of the condyles i n F i g . (4.31.b), w h i l e F i g . (5.3.e) corresponds  to an edge of the femur s h a f t i n F i g .  (4.31.b). If  the radiogram to be. p r o c e s s e d i s v e r y n o i s y , which was the  case i n F i g . (4.31.b), i t i s advantageous t o a l s o smooth the d a t a b e f o r e a p p l y i n g the edge d e t e c t i o n a l g o r i t h m . function  done u s i n g the f i l t e r  o f e q u a t i o n (4.14) w i t h a c u t - o f f frequency of 1.071  and a t e r m i n a t i o n frequency o f 1.428 of  T h i s was  1/mm.  1/mm  As an example o f the e f f e c t  t h i s smoothing, F i g . (5.5) i s a p r e s e n t a t i o n of the scan segments i n  Fig.  (5.4) a f t e r  filtering.  To b e g i n to t r a c e a contour the a l g o r i t h m must have a s t a r t i n g l i n e to scan. of  C u r r e n t l y the u s e r s p e c i f i e s t h i s l i n e and a l s o a subset  p o i n t s i n the l i n e to c o n s i d e r as edge c a n d i d a t e s .  the i n i t i a l  T h i s i s done s i n c e  d e c i s i o n on an edge p o i n t i s c r u c i a l to the l o c a t i o n of edge  p o i n t s o f subsequent  scan l i n e s which are c o n s t r a i n e d by the p o s i t i o n of  the edge p o i n t i n the p r e v i o u s l i n e .  In the case of F i g . (4.31.b) the  contour t r a c e was s t a r t e d h o r i z o n t a l l y at the bottom row o f the image s i n c e the bone edges there are s t r o n g enough to i n s u r e an i n i t i a l  correct  ^ ^ ^ ^ ^ ^  i  i i i  1—^  'I  Fig.  1  1  1  1  I  (5.5) Smoothed I n t e n s i t y  Profiles  91  decision. the  A s e t of f i f t y points  i n the bottom row and a s s o c i a t e d  l e f t - h a n d edge was s p e c i f i e d f o r c o n s i d e r a t i o n  with  i n l o c a t i n g the f i r s t  edge p o i n t . As the contour i s t r a c e d the edge may change from b e i n g a t i v e l y v e r t i c a l i n o r i e n t a t i o n to being versa.  The software i s able to d e t e c t  when d e t e c t e d ,  begins p r o c e s s i n g  r e l a t i v e l y h o r i z o n t a l , or v i c e  t h i s change i n o r i e n t a t i o n and,  vertical  i z o n t a l scan segments, o r v i c e v e r s a .  scan segments i n s t e a d o f h o r -  F o r example, when o p e r a t i n g  the l e f t edge o f t h e femur s h a f t and t h e l e f t continues  from row to row u n t i l  rel-  along  c o n d y l e edge the a l g o r i t h m  the edge p o i n t b e g i n s t o s h i f t  i n loca-  t i o n t o the r i g h t i n d i c a t i n g t h a t the r e g i o n o f the upper edge o f the condyles has been reached. vertical direction.  Detection  I t continues  there s t a r t s to operate i n the  u n t i l the edge p o i n t drops  signifi-  c a n t l y downward i n d i c a t i n g the s t a r t o f t h e r i g h t edge o f the c o n d y l e s , where h o r i z o n t a l d e t e c t i o n s t a r t s again  t o t r a c e down the r e s t o f the  bone contour. An o p t i o n  o f w e i g h t i n g the d e r i v a t i v e s c a l c u l a t e d from the f i t -  t e d p o l y n o m i a l s i s i n c l u d e d i n the s o f t w a r e , which weights edge p o i n t candidates to favor points  c l o s e i n p o s i t i o n to the p o s i t i o n o f the edge  p o i n t l o c a t e d i n the p r e v i o u s  line.  The w e i g h t i n g c o e f f i c i e n t s a r e c a l -  c u l a t e d as p o i n t s on a Gaussian c u r v e .  The standard  d e v i a t i o n of the  curve i s s p e c i f i e d by the user and the mean i s n o r m a l l y taken to c o i n c i d e w i t h the p o s i t i o n o f the p r e v i o u s l y was i n c l u d e d  condyles.  This  option  t o l e s s e n the l i k e l i h o o d of the a l g o r i t h m wandering away  from the t r u e edge i n r e g i o n s the  determined edge p o i n t .  of strong noise  and poor d e f i n i t i o n such as  92  5.4 - E x p e r i m e n t a l R e s u l t s I t was decided  and D i s c u s s i o n  to t e s t the a l g o r i t h m by attempting  the e n t i r e contour o f the radiogram i n F i g . (4.31.b).  to scan  Before  s e v e r a l parameters had to be s u p p l i e d to the software.  proceeding  The s t a r t o f  contour p o i n t was s p e c i f i e d i n the bottom row and t h e a l g o r i t h m d i r e c t e d to search  50 p o i n t s b e g i n n i n g  i n Column 80.  The second-order polynom-  i a l s were s p e c i f i e d t o f i t 11 p o i n t s and the f i r s t - o r d e r seven p o i n t s .  The numbers  polynomials  o f p o i n t s spanned by the p o l y n o m i a l s  were  chosen to correspond to t y p i c a l widths o f edge t r a n s i t i o n s a s s o c i a t e d with  uses o f the f i r s t and second d e r i v a t i v e s i n edge d e t e c t i o n .  program was s t r u c t u r e d t o b e g i n the edge p o i n t s h i f t the l e f t  The  v e r t i c a l search when the p o s i t i o n o f •  20 p o i n t s t o the r i g h t o f the maximum e x c u r s i o n to  attained i n h o r i z o n t a l search.  S i m i l a r l y h o r i z o n t a l search  was s e t to resume when the t r a c e dropped 20 p o i n t s beneath the edge p o i n t of maximum h e i g h t .  In moving from row to row o r column to column  the search was r e s t r i c t e d to o n l y 11 p o i n t s c e n t e r i n g on the p o s i t i o n o f the p r e v i o u s  edge p o i n t .  and minimize  computation.  In b e g i n n i n g  T h i s r e s t r i c t i o n was i n c l u d e d to reduce e r r o r s  along  the l e f t edge o f the bone i t was  recognized  t h a t human i n t e r v e n t i o n was n e c e s s a r y to p r e v e n t the a l g o r i t h m tracing  the edge o f the e p i p h y s e a l p l a t e .  Because of the c o n c a v i t y o f  the l e f t edge of the bone i n the r e g i o n of t h e e p i p h y s e a l was e a s i l y accomplished by r e s t r i c t i n g  the a l g o r i t h m  p o i n t s which moved p r o g r e s s i v e l y to t h e l e f t Initially  plate, this  to l o c a t e edge  f o r s e v e r a l rows.  the a l g o r i t h m was used w i t h o u t w e i g h t i n g  v a t i v e s i n f a v o r o f edge candidates  from  the d e r i -  c l o s e t o the edge p o i n t i n the p r e -  93  vious l i n e . Fig.  T h i s produced  the contour i n F i g . (5.6.a).  The  contour i n  (5.6.b) r e s u l t e d when the Gaussian w e i g h t i n g f u n c t i o n was  a s t a n d a r d d e v i a t i o n of two the two There  sample p o i n t s .  used w i t h  Note the d i f f e r e n c e between  contours at the s t a r t of the condyles i n d i c a t e d by the arrow.  are e r r o r s i n the contour of F i g . (5.6.a) due  edge of the condyles i n the r e g i o n of the arrow and n o i s e r a t i o o f the  t o the the low  indistinct signal-to-  radiogram.  The r i g h t edge of the condyles i n F i g . (4.31.b) i s v e r y p o o r l y d e f i n e d and i n some p l a c e s the edge appears  to be n o n - e x i s t a n t .  When  the a l g o r i t h m began to t r a c e down the r i g h t edge of the bone i t d i d not s e l e c t edge p o i n t s which m a i n t a i n e d the c o n t i n u i t y .of the contour. a l g o r i t h m was  r e s t a r t e d by s e a r c h i n g the next few rows to f i n d a reason-  a b l e s t a r t o f contour p o i n t f a l l i n g contour at t h i s p o i n t . until  The  The  a l o n g the a n t i c i p a t e d path o f the  a l g o r i t h m then proceeded  to t r a c e downward  the edge of the condyles became i n d i s t i n g u i s h a b l e j u s t p r i o r  to  the top of the s h a f t . The row  a l g o r i t h m was  then d i r e c t e d t o s t a r t anew from the bottom  and t r a c e the r i g h t edge o f the s h a f t .  This i t s u c c e s s f u l l y d i d ,  but upon e n c o u n t e r i n g the b e g i n n i n g o f the condyles the a l g o r i t h m wandered o f f on an erroneous  contour.  See F i g . (5.6.c) where the arrow  marks the s t a r t o f the c o n d y l e s . Fig.  (5.6.d) i s the completed  c l o s e d contour o b t a i n e d by i n -  t e r p o l a t i n g between edge p o i n t s where breaks i n c o n t i n u i t y o c c u r e d  due  to the l a c k o f d i s c e r n i b l e edge p o i n t s . , O b v i o u s l y t h e r e are many problems to be s o l v e d i f a r e l i a b l e contour t r a c i n g procedure  i s to be developed  f o r t r a c i n g the edges o f  94  Fig.  (5.6)  R e s u l t s o f T e s t i n g the C o n t o u r - T r a c i n g  Algorithm  95  the condyles i n radiograms  o f femurs i n i n f a n t s and c h i l d r e n .  from the p r e c e e d i n g e x p e r i m e n t a l r e s u l t s i t appears is  a possibility.  However,  such a development  96  CHAPTER 6 The Data A c q u i s i t i o n System 6.1-  Introduction  A c e r t a i n amount o f work preceded radiogram i n chapter IV.  the s c a n n i n g o f the  An image d i s s e c t o r scanner making use of a  computer c o n t r o l l e d m e c h a n i c a l stage was  c o n s t r u c t e d f o r the  following  reasons: 1 - To a l l o w image scanning w i t h a g r e a t e r S i g n a l - t o - N o i s e r a t i o than p r e v i o u s l y a v a i l a b l e u s i n g a l t e r n a t e equipment a v a i l a b l e a t U.B.C, i.e.  the f l y i n g spot scanner  (FSS)  [50].  2 - To e l i m i n a t e a n e c e s s a r y a d d i t i o n a l p h o t o g r a p h i c p r o c e s s i n g step i n photo r e d u c i n g an X-ray i n p r e p a r a t i o n f o r s c a n n i n g by 3 - To a l l o w f l e x i b i l i t y  the  i n s e l e c t i n g subsections of l a r g e  images f o r examination by computer a n a l y s i s ; t h i s to be  FSS.  X-ray  accomplished  w h i l e p r e c i s e l y s p e c i f y i n g s u b s e c t i o n l o c a t i o n to a l l o w a c c u r a t e measurements o f l a r g e image s t r u c t u r e s w h i l e not r a d i c a l l y scanning r e s o l u t i o n  increasing  requirements.  A d e s c r i p t i o n of the s t r u c t u r e o f the image s c a n n i n g  and  d i s p l a y system and i t s o p e r a t i o n i s the s u b j e c t o f t h i s c h a p t e r . photograph  o f the d a t a a c q u i s i t i o n system 6.2  i s shown i n F i g u r e  (6.1)  - The Image D i s s e c t o r Camera  An image d i s s e c t o r camera purchased Telephone  A  from  International  and T e l e g r a p h I n d u s t r i a l L a b o r a t o r i e s i s used as the i n p u t  l i g h t s e n s i n g d e v i c e f o r the system. maximum r e s o l u t i o n o f 1000  The  camera has a s p e c i f i e d  l i n e s over the u s e f u l diameter o f i t s  s e n s i t i v e f r o n t s u r f a c e (photocathode).  Twenty-five  foot candles i s  Figure  (6.1) - The Data A c q u i s i t i o n  System  98  the maximum s a f e i l l u m i n a t i o n at the photocathode, and f o r b e s t r e s u l t s the most t r a n s p a r e n t  p a r t s o f the f i l m b e i n g  c l o s e to t h i s amount o f l i g h t  to reach  the maximum number o f e l e c t r o n s reach  scanned s h o u l d  the cathode.  that  quantum e f f e c t s .  This  i n p u t X and Y c o n t r o l v o l t a g e s which a r e p r o p o r t i o n a l  to the c o o r d i n a t e s s i g n a l with  This insures  the p h o t o m u l t i p l i e r f o r a given  f i l m d e n s i t y and thus minimizes the u n d e s i r a b l e camera accepts  allow  o f a p o i n t to be scanned.  I t s output i s an analog  an average v a l u e p r o p o r t i o n a l to the i n t e n s i t y o f l i g h t at  the p o i n t b e i n g  scanned.  The d i s s e c t o r camera does n o t i n t e g r a t e the  l i g h t i n c i d e n t on i t s photocathode as do v i d i c o n s and s i m i l a r t e l e v i s i o n camera tubes.  As i n o t h e r  tubes the i n c i d e n t l i g h t knocks  l o o s e e l e c t r o n s from the photocathode. ated toward the r e a r .  These are immediately a c c e l e r -  A magnetic f i e l d whose s t r e n g t h i s p r o p o r t i o n a l  to the i n p u t X and Y v o l t a g e s moves the whole f i e l d o f e l e c t r o n s i n a d i r e c t i o n perpendicular  to the f r o n t to back a x i s o f the tube.  Only  those e l e c t r o n s coming from one s m a l l r e g i o n on the face o f the tube get  through a 5 m i l round a p e r t u r e  t h i s p l a t e i s a conventional  i n a p l a t e at the r e a r .  Behind  10 dynode p h o t o m u l t i p l i e r which  converts  incoming e l e c t r o n s i n t o a measurable c u r r e n t p r o p o r t i o n a l to the l i g h t at  the p o i n t b e i n g  scanned.  The bandwidth o f t h i s system i s  fairly  h i g h and because only a v e r y s m a l l r e g i o n of the s e n s i t i v e s u r f a c e i s b e i n g measured a t any i n s t a n t the quantum e f f e c t i s apparent. the a r r i v a l o f i n d i v i d u a l e l e c t r o n s i s e v i d e n t large voltage  That i s ,  and shows up as r a t h e r  s p i k e s a t the output o f the camera v i d e o a m p l i f i e r .  Consequently, the s i g n a l from the camera i s extremely n o i s y be smoothed i f i t i s to be u s e f u l .  and must  The d e s i r e d s i g n a l i s the average  99  v a l u e of the  camera output.  6.3As  N o i s e Removal Sys tem  a first  step,  a 250  KHz  used to smooth the v i d e o s i g n a l . is  The  adjustments o f the scanner system.  video i s s t i l l  quite noisy,  and  256x256 g r i d p o i n t s  sequentially, involved  are p r o p o r t i o n a l 2 - A -10 the  l i n e , and  X and  to the  following  6-2.  image are  sampled  steps i n d i c a t e what i s  point: PDP-9 computer sends  Y v o l t a g e s to the d i s s e c t o r camera.  c o o r d i n a t e s o f the p o i n t  v o l t s i g n a l i s sent out  switched u n i t s .  a m p l i f i e r and  the  D i g i t a l Equipment C o r p o r a t i o n (DEC)  appropriate  during  filtered  combination shown i n F i g .  form the r a d i o g r a p h i c  i n scanning a s i n g l e  1 - The the  l i n e by  that  device  display unit  However, t h i s  is  f u r t h e r smoothing i s performed w i t h  the s w i t c h e d a m p l i f i e r - i n t e g r a t o r  out  s i g n a l from t h i s analog  f e d to the i n t e n s i t y i n p u t o f a T e k t r o n i x 602  various  The  pass-band, low-pass f i l t e r  on  the  C a l l t h i s time t=0.  i n t e g r a t o r to t u r n on.  sampled.  c o n t r o l l i n e going  This  The  to be  These  causes both  i n t e g r a t o r now  to  the  begins  to  average the v i d e o s i g n a l . 3 - At t = l m i l l i s e c o n d changed to -5 the  the v o l t a g e  v o l t s c a u s i n g the  i n t e g r a t o r on.  Although the i n t e g r a t o r  condition  l o n g enough f o r the A/D  is  leaving  c o n t i n u e s to o p e r a t e , i t s  zero.  i n step 3 continues f o r 50 microseconds o r c o n v e r t e r to sample the i n t e g r a t o r  5 - At t=1.05 m i l l i s e c o n d , the  the c o n t r o l l i n e i s  a m p l i f i e r to s w i t c h o f f but  output h o l d s c o n s t a n t s i n c e i t s i n p u t 4 - The  on  output.  a zero v o l t s i g n a l i s sent out  c o n t r o l l i n e which turns o f f the i n t e g r a t o r  and  on  r e s e t s i t s output  adjustable \heght ~  i  H  r  I D  'swftched' amplifier offset gam  camera control  C  lowpass filter  switched integrator  0H>  '-{scope  0)  0>  o o  film d-c  O  a  ~1  tektronix display, unit  light  source  -1 Q  a/d  offset  fmSile 'stage  video output -i-<x stooe position syyiiiuaun matron control control •vcontrol W  y  control for switched units  p p.g DIGITAL COMPUTER  digital output  D  v  v  OD TTY Fig.  CRT  (6.2) Data A c q u i s i t i o n System O r g a n i z a t i o n  DEC TAPES  o o  101  to  zero v o l t s .  The  c y c l e i s complete and a new  p o i n t can now  be  scanned. T h i s analog s i g n a l i s then f e d to an A/D to  6 b i t s , and s t o r e d on a DEC  magnetic  converter, quantized  tape.  6.4  - L i g h t source and movable stage  The  radiogram  to be scanned i s i l l u m i n a t e d  from behind by  a  l i g h t box which p r o v i d e s a f a i r l y homogeneous i l l u m i n a t i o n w i t h i n 4 or 5% over an area of 11x11  inches.  stage t h a t i s f r e e to move on two  The l i g h t box  i s mounted on a  p e r p e n d i c u l a r racks i n the X & Y  d i r e c t i o n s under computer c o n t r o l , or u s i n g a manual j o y s t i c k . maximum-excursion a l o n g any d i r e c t i o n i s 6 i n c h e s .  This provides  freedom to expose any p a r t i c u l a r a r e a i n the radiogram The  The  to the  the  dissector.  s i z e of the a r e a t h a t i s b e i n g scanned depends on the h e i g h t of  the d i s s e c t o r w i t h r e s p e c t to the t r a n s i l l u m i n a t e d radiogram.  This  h e i g h t c o u l d be v a r i e d between. The programmable motion o f the stage and the a d j u s t a b l e d i s s e c t o r h e i g h t p r o v i d e the f l e x i b i l i t y  of d e c i d i n g upon the system's  r e s o l u t i o n or scanning frequency over a f a i r l y  l a r g e range, y e t w i t h -  out b e i n g r e s t r i c t e d to a p a r t i c u l a r p i c t u r e s i z e .  I t s h o u l d be  noted  however t h a t the h i g h e r the s c a n n i n g r e s o l u t i o n the s m a l l e r the p i c t u r e s i z e scanned, or the l a r g e r the number of r a s t e r p o i n t s needed to r e p r e s e n t the scanned p i c t u r e . The h o r i z o n t a l motion of the stage was  rendered  as smooth  as p o s s i b l e by u s i n g t h i r t e e n s u p p o r t i n g columns capped w i t h bearings.  The accuracy o f p o s i t i o n i n g  the stage a f t e r any  e x c u r s i o n i s w i t h i n one s t e p displacement  ball  complicated  of the s t a g e , t h a t i s  102  0.0015 i n c h e s . diagonally.  The e x c u r s i o n can be  D i a g o n a l motion i s accomplished  a l t e r n a t i v e displacements. e f f e c t e d by  i n the X o r Y d i r e c t i o n , o r b y ^ a c c a d e s o f X and  The motion of the stage on the racks i s  two p o w e r f u l SLO-SYN s t e p p i n g motors, a c t i v a t e d by  p u l s e s under software command o r a manual j o y s t i c k  w i t h 16K  computer  control.  6.5  - The  Computer I n t e r f a c e  The  computer used i n t h i s system i s a DEC  o f memory and  t h r e e Dectape u n i t s .  d i s s e c t o r and the d i g i t a l [51],  Y  PDP-9  equipped  The i n t e r f a c e f o r the  c o n t r o l used w i t h i t i s w e l l documented  [52], although a few hardware m o d i f i c a t i o n s have been made.  Appendix C summarizes the software i n s t r u c t i o n s used to c o n t r o l hardware.  the  These d e s c r i p t i o n s s h o u l d adequately e x p l a i n the p o s s i b l e  hardware f u n c t i o n s from the u s e r ' s p o i n t of view. 6.6  - The  Software  Implementation  F i v e g l o b a l r o u t i n e s have been implemented to c o n t r o l  the  stage p o s i t i o n i n g w i t h r e s p e c t to the d i s s e c t o r , t o f o c u s the image, to d i g i t i z e the image, to read the image onto DEC t r a n s f e r the data e i t h e r to the DATA GEN u s i n g the FSS,  t a p e , and  to  840A computer f o r d i s p l a y  or to the IBM system 370/67 f o r p r o c e s s i n g .  The  f o l l o w i n g s e c t i o n s are a b r i e f d i s c u s s i o n of these r o u t i n e s . 6.6.1  - Axes  Alignment  I t i s i m p e r a t i v e to determine of t r a v e l of the stage i n the Y-  ( o r X-)  o r i e n t a t i o n of the d i s s e c t o r axes and  v e r y a c c u r a t e l y the  direction  d i r e c t i o n r e l a t i v e to the  to make t h i s d i r e c t i o n e x a c t l y  c o i n c i d e n t w i t h the d i s s e c t o r Y- axis'. (X- a x i s ) .  To a c h i e v e t h i s ,  t r a n s p a r e n c y o f a v e r y s t r a i g h t edge ( b l a c k to b r i g h t  transition)  the  103  is  taped on the i l l u m i n a t i o n box, so t h a t the edge i s a p p r o x i m a t e l y  along  the stage Y- a x i s .  The r o u t i n e EDGTST i s c a l l e d , and through  c o n v e r s a t i o n a l made on the t e l e t y p e w r i t e r (TTY), t h e u s e r s p e c i f i e s whether he i n t e n d s  t o a l i g n the edge w i t h the Y- d i r e c t i o n o f stage  t r a v e l o r w i t h the d i s s e c t o r Y- a x i s . s t a r t w i t h the s t a g e .  The e a s i e s t procedure i s to  The f o l l o w i n g steps  describe  the program oper-  ation. 1 - The r o u t i n e i n s t r u c t s the d i s s e c t o r t o s c a n the h o r i z o n t a l l i n e whose Y- c o o r d i n a t e  i s 512 ( m i d l i n e i n the 1024 p o s s i b l e e n t r i e s  i n t h e r a s t e r ) and to t r y to d e t e c t  an edge p o i n t .  2 - I f the h o r i z o n t a l l i n e ;3s scanned and no edge p o i n t i s detected,  c o n t r o l returns  to the u s e r who then r e p o s i t i o n s the t r a n s -  parency and r e s t a r t s the program. 3 - Upon d e t e c t i o n of an edge p o i n t , i t s X e n t r y i s s t o r e d i n a b u f f e r and the stage i s i n s t r u c t e d to move along 100 steps  the Y- d i r e c t i o n  (0.15 i n c h e s ) .  4 - The program goes to a 30 second w a i t i n g l o o p until  any p o s s i b l e mechanical j i t t e r  are repeated u n t i l  32 edge p o i n t s a r e l o c a t e d .  i n t e r f a c e d t o the computer. to c o n s t r u c t  on the d i s p l a y u n i t  The f i r s t edge p o i n t i s used as a  a v e r t i c a l l i n e , and subsequent edge p o i n t s  are d i s p l a y e d i n p o s i t i o n s r e l a t i v e to t h i s v e r t i c a l l i n e . d i s p l a y u n i t has a r e s o l u t i o n of 1024 p o i n t s and  three b i t s o f b r i g h t n e s s  the stage Y- a x i s .  time  fades away, and s t e p s 1 to 4  5 - The 32 edge p o i n t s a r e then d i s p l a y e d  reference  to s c o r e  control.  I f any d e t e c t e d  along  The  the X and Y axes,  The v e r t i c a l l i n e  represents  edge p o i n t appears on the d i s p l a y  104  s c r e e n other than on the v e r t i c a l l i n e , parency  then the s t r a i g h t edge t r a n s -  i s r e p o s i t i o n e d and steps 1 through  5 are repeated.  6 - Sometimes the d i f f e r e n c e between a l o c a t e d edge p o i n t and the v e r t i c a l l i n e i s o n l y one b i t p o s i t i o n which might n o t be d e t e c t a b l e on the d i s p l a y s c r e e n . Accumulator  To a v o i d t h i s , the f o u r most s i g n i f i c a n t  b i t s on the o p e r a t o r c o n s o l e are used  t o accentuate the  d e v i a t i o n from the v e r t i c a l l i n e by as much as 128 times. l e a s t s i g n i f i c a n t AC b i t s a r e used  The t h r e e  to c o n t r o l the b r i g h t n e s s on the  screen. 7 - A f t e r p o s i t i o n i n g the t e s t edge along the stage Y- a x i s , t h e user r e q u e s t s , through with  the TTY, an alignment  o f the d i s s e c t o r Y- a x i s  the stage Y- a x i s (which i s c o i n c i d e n t w i t h the t e s t edge).  routine followed i s e s s e n t i a l l y  The  the same as used when a l i g n i n g the  t e s t edge w i t h the stage Y- a x i s .  Minor changes i n the program occur,"  however, when i n c r e m e n t i n g the Y- c o o r d i n a t e of the h o r i z o n t a l to be examined f o r edge d e t e c t i o n .  line  The s t a r t i n g h o r i z o n t a l l i n e i s  taken a t the bottom o f t h e p i c t u r e , and every subsequent l i n e i s 32 e n t r i e s above the p r e v i o u s  line.  8 - I f the d i s s e c t o r axes a r e n o t c o i n c i d e n t w i t h the stage the user c a l l s DISEDG t o e f f e c t the alignment.  The s t r a t e g y o f  s e a r c h f o r edges i s the same as i n EDGTST, except is  axes,  t h a t the t e s t edge  c o n t i n u o u s l y scanned, and the edge l o c a t i o n s on the d i s p l a y  are c o n s t a n t l y updated as t h e i r e n t r i e s a r e s p e c i f i e d .  screen  Each edge  p o i n t i s d i s p l a y e d f o r 3 seconds b e f o r e i t s l o c a t i o n i s updated, t o allow the o p e r a t o r s u f f i c i e n t time to manually o r i e n t a t i o n w h i l e r e f e r r i n g t o the d i s p l a y .  a d j u s t the d i s s e c t o r  105  6.6.2  - Stage P o s i t i o n i n g C o n t r o l  The  r o u t i n e STAGE, when invoked,  r e q u e s t s the u s e r , v i a  t e l e t y p e c o n v e r s a t i o n , to e n t e r t h e s i g n and magnitude o f the X and Y displacements  he wants the stage t o undertake.  a d j u s t s i t s i n s t r u c t i o n s to execute the displacement X-  The program  the r e q u i r e d e x c u r s i o n .  along the Y- d i r e c t i o n i s l o n g e r than  then I f , say,  along the  d i r e c t i o n , t h e stage f i r s t moves a d i s t a n c e Y-X a l o n g the Y - d i r e c -  t i o n and then moves d i a g o n a l l y to i t s d e s t i n a t i o n . 6.6.3  - Focusing  F o c u s i n g i s a c h i e v e d by a program c a l l e d SCANLN which c o n t i n u o u s l y scans  a h o r i z o n t a l l i n e whose Y- c o - o r d i n a t e i s e n t e r e d  v i a t h e TTY. A scope i s used to d i s p l a y the i n t e n s i t y  variations  along t h a t l i n e and the user attempts t o maximize t h e d e t a i l s as seen on the scope. calls  When the b e s t s u b j e c t i v e f o c u s i n g i s a t t a i n e d the user  the r o u t i n e FOCUS.  software  Here again t h e u s e r i n t e r a c t s w i t h the  and the f o l l o w i n g message i s prompted on the TTY: ATTN! FLAG FOR FOCUSING SET BY BIT 9 NEED FOCUSING? Y OR N — > I f the answer i s N ( n o ) , e x e c u t i o n t e r m i n a t e s ; i f Y (yes)  the next message on the TTY i s : DETECTION DIRECTION: X OR Y? Here the user s p e c i f i e s to be used by FOCUS. response  the d i r e c t i o n of the l i n e he wants  The program w i l l s t a r t a f t e r r e c e i v i n g a  t o t h e f o l l o w i n g f i n a l message: ENTER COORD. VALUE — > The  'COORD. VALUE" i s the Y- c o o r d i n a t e o f a h o r i z o n t a l  106  F i g u r e (6.3) - Radiogram Out-of-Focus  Figure (6.4) - Radiogram i n P e r f e c t Focus  107  r a s t e r o r the X- c o o r d i n a t e o f a v e r t i c a l r a s t e r along which f o c u s i n g i s attempted.  A s e a r c h s t a r t s along t h i s l i n e f o r an edge p o i n t . I f  no edge p o i n t i s d e t e c t e d , t h e program r e s t a r t s and r e q u e s t s inputs.  user  Upon d e t e c t i o n of an edge p o i n t , t h e f i v e p o i n t s p r e v i o u s  to the edge p o i n t and t h e next c o n s e c u t i v e n i n e p o i n t s a r e d i s p l a y e d on the d i s p l a y u n i t , t o g e t h e r w i t h the l o c a t e d edge p o i n t .  The d i s p l a y  i s c o n t i n u o u s , and the s c r e e n i s r e f r e s h e d every 2 seconds.  The user  attempts  F i g . (6.^3)  to maximize the edge s l o p e as seen on the d i s p l a y .  i s a photograph from Fig.  the d i s p l a y o f an out o f focus s i t u a t i o n , w h i l e  (6..4) i s o f an edge i n a p i c t u r e p e r f e c t l y i n f o c u s .  As i n  EDGTST and DISEDG, the AC b i t s on the o p e r a t o r c o n s o l e c o n t r o l the s c a l e and b r i g h t n e s s on the d i s p l a y . When f o c u s i n g i s accomplished, AC  the user s e t s b i t 9 o f t h e  to one. T h i s w i l l i n t e r r u p t the program, and a l l o w the user t o  c a l l the r o u t i n e LINTST which p r i n t s f o r i n s p e c t i o n the i n t e n s i t y v a l u e s along any p a r t i c u l a r l i n e whose c o o r d i n a t e i s e n t e r e d v i a the TTY. Note:  I t was found t h a t the p h o t o m u l t i p l i e r and the output  from  the p r e a m p l i f i e r on the d i s s e c t o r do n o t s a t u r a t e a t any o f t h e camera F- s t o p s .  The d.c. output v o l t a g e from the p r e a m p l i f i e r v a r i e s w i t h  the l e n s opening  as f o l l o w s :  F - stop  22  15  -.11  8-11  Pream  .22  .29  .42  .52  Output(v)  8 .78 .  5.6-8 1.17  5.6  4  1.55  2.2  Hence F-4 was always used i n scanning ;the maximum RMS d i s s e c t o r n o i s e was  found  to be 54mV.  T h i s would i n s u r e a s i g n a l - t o - N o i s e r a t i o o f  2.2/0.054 = 40.7 b e f o r e i n t e g r a t i o n and smoothing.  108  6.6.4 - Data A c q u i s i t i o n The stage.  radiogram s c a n n i n g and q u a n t i z a t i o n i s performed a t t h i s  Before a c t u a l l y reading  get i n f o r m a t i o n  the p i c t u r e on DECtape, the u s e r can  about the i n t e n s i t y d i s t r i b u t i o n i n any subsquare o f  the p i c t u r e by c a l l i n g  the r o u t i n e AVERAG.  When c a l l e d , t h i s  routine  echoes the f o l l o w i n g message on the TTY: SIDE OF SQUARE TO BE SCANNED & the u s e r e n t e r s TTY  >  a number t h a t s p e c i f i e s t h e s i d e o f the square.  echoes: PLEASE ENTER STARTING COORDINATE  The  s t a r t i n g coordinate  of the square.  i s the c o o r d i n a t e  The  >  o f t h e lower l e f t  corner  The program then outputs on the TTY the maximum,  minimum & average i n t e n s i t i e s w i t h i n t h a t  square.  r o u t i n e PICTUR reads the e n t i r e p i c t u r e onto DECtape,  This routine also provides  the u s e r w i t h the f a c i l i t y  of i n t e r r o -  g a t i n g each p i c t u r e p o i n t two, f o u r o r e i g h t times as d e s i r e d . would s i m u l a t e  reading  This  a v e r a g i n g m u l t i p l e c o p i e s o f the same p i c t u r e and  reduce the n o i s e .  in  The  I n t e r r o g a t i n g a p o i n t 4 times and a v e r a g i n g the  i s adequate t o achieve a reasonable s i g n a l - t o - n o i s e  a r e a s o n a b l e amount o f time.  ratio  In t h i s case, the p i c t u r e s c a n n i n g  time i s 5 min. 50 sees. 6.6.5 - Data  Transfer  Data i s t r a n s m i t t e d ,  e i t h e r f o r processing  o r f o r d i s p l a y on the NOVA 840A, v i a the DATA LINK. t i o n of important l i n k ' s  features  follows:  o p e r a t e s on a l i n e - at - a - time b a s i s .  on the IBM 370 A brief  descrip-  The d a t a l i n k system At the end o f a l i n e , the  109  Transmitting  computer r e v e r t s to the r e c e i v e mode and w a i t s  for a  s p e c i a l message from the r e c e i v i n g computer to i n d i c a t e whether o r not  the message was  received correctly.  r e c e i v e d , then an ACK  ( p o s i t i v e acknowledgement 006)  t r a n s m i t t e d i n d u p l i c a t e and proceed to the next l i n e . message, a n e g a t i v e  acknowledgement (NAK  025)  a r e - t r a n s m i s s i o n of the l a s t l i n e or a new  i s s e n t , and  A SEL  line.  To achieve 61  f o r each  I f the r e c e i v i n g computer d e t e c t s a l i n e w i t h  s e l e c t c h a r a c t e r as i n the p r e v i o u s  original  character  l i n e , i t w i l l i g n o r e the  this, sucthe same current  [53]. B i n a r y mode was  first  attempted f o r data t r a n s m i s s i o n .  b a s i c c h a r a c t e r s i z e f o r the data correspond was  the  transmitted i s e i t h e r  the s e l e c t c h a r a c t e r i s a l t e r n a t e d between 41 and  line  another s p e c i a l  f o r b i n a r y mode)) i s used to communicate  to the r e c e i v i n g computer t h a t the l i n e b e i n g  cessive l i n e .  character i s  r e - t r a n s m i t the l a s t l i n e .  (41 or 61  correctly  the o r i g i n a l t r a n s m i t t i n g computer w i l l  I f an e r r o r i s d e t e c t e d ,  t r a n s m i t t i n g computer w i l l (select character  I f the message was  l i n k i s e i g h t b i t s , s i x o f which  to a t r a n s m i t t e d s i x b i t b i n a r y c h a r a c t e r .  s e t to 42 words (126  characters).  4800 b i t s / s e c , which i n BIN e i g h t e e n words/sec.  The  The  line  Unfortunately,  length  data r a t e f o r the l i n k i s  mode corresponds to approximately  s u c c e s s f u l , the reasons b e i n g  The  200  t h i s mode o f t r a n s m i s s i o n was  not  the f o l l o w i n g :  1 - As mentioned above, at the end o f each t r a n s m i t t e d l i n e ,  the  PDP-9 ( t r a n s m i t t i n g computer) expects the IBM-370 ( r e c e i v i n g computer) to check f o r p a r i t y e r r o r s and l i n e i f any  to ask  e r r o r s are d e t e c t e d .  f o r a r e t r a n s m i s s i o n o f that  Otherwise a p o s i t i v e acknowledgement  110  is  sent  rectly  to i n d i c a t e to the PDP-9 that the l a s t l i n e was r e c e i v e d corrand the next l i n e i s d e s i r e d .  happening was  that a f t e r  However, what appeared to be  a NAK requested  the l i n e was n o t r e c e i v e d by the 370. promptly sent lost.  a r e - t r a n s m i s s i o n of a l i n e ,  In s p i t e  of t h i s , an ACK was  t o the PDP-9 to resume t r a n s m i s s i o n , and the l i n e  The sequence o f l o s t l i n e s was completely  was  random and was de-  t e c t e d i n one of two ways: a - A counter was s e t up i n the d a t a l i n k h a n d l e r count the number o f t r a n s m i t t e d l i n e s NAK i s r e c e i v e d the h a n d l e r  up to the f i r s t  o f data a c q u i s i t i o n  370 checks the f i r s t lines  and p r i n t s  but  lines  to d e t e c t  missing  serially.  c o u l d then be read from the o r i g i n a l  the p o s s i b i l i t y o f s t i l l  extremely t e d i o u s way  missing l i n e s  t h a t i s incremented by  number o f each l i n e i n the f i l e  on DEC tape and w r i t t e n onto another f i l e the l i n k , w i t h  so f a r .  A f t e r the data i s w r i t t e n on a d i s c f i l e , the  t h e i r numbers  The m i s s i n g  When a  from the d i s s e c t o r , each  42nd data word was r e p l a c e d by a l i n e number one f o r each new l i n e .  NAK.  causes a t r a n s m i s s i o n i n t e r r u p t and out-  puts on the TTY the number of t r a n s m i t t e d l i n e s b - In the p r o c e s s  (DPH.) t o  to achieve  t o be t r a n s m i t t e d  other l o s s e s .  file  through  A less  t r a n s m i s s i o n was to p r i n t  expensive out the  from the DECtape f i l e , punch them on cards and read  them i n t o a d i s c  file.  2 - The second handicap of the b i n a r y mode o f t r a n s m i s s i o n i s its  inefficiency.  then 12 b i t s y e t are s t i l l  S i n c e the o r i g i n a l  data i s d i g i t i z e d  to s i x b i t s ,  o f a PDP-9 e i g h t e e n b i t word c o n t a i n no i n f o r m a t i o n and transmitted.  T h i s i n c r e a s e s the f i l e space requirements  Ill  s i g n i f i c a n t l y , slows the r a t e of u s e f u l i n f o r m a t i o n  t r a n s f e r hence  i n c r e a s i n g used CPU time o f t h e IBM-370, and f i n a l l y r e q u i r e s a s p e c i a l packing routine  (called  (BIC 09) to arrange the three s i x b i t words  i n t o an "A4" format. 3 - The t h i r d major drawback i n b i n a r y present play)  transmission  i s that a t  communication between the PDP-9 (scanning) and the 840A ( d i s -  i s o n l y i n SRC MODE.  d i s p l a y e d by f i r s t  Therefore  a scanned image can o n l y be  t r a n s m i t t i n g i t to the IBM-370, then  reformating  the d a t a and then r e t r a n s m i t t i n g i t to the NOVA-840A. Because o f these major d i s a d v a n t a g e s , a P e r i p h e r a l - I n t e r change - Program f o r the L i n k between the Nova 840 and t h e PDP-9 (PIPLN9) has been w r i t t e n . fig. be  A flow  c h a r t o f the program i s shown i n  ( 6 . 5 ) , and the complete l i s t i n g i s i n Appendix D.  aware o f the f o l l o w i n g p r o v i s i o n s c o n c e r n i n g 1 - The maximum s i z e of a DEC tape b u f f e r  words.  t h i s program: (always even) i s 252  Each ASCII l i n e can a t most be 126 c h a r a c t e r s  by a c a r r i a g e r e t u r n .  One should  long,  terminated  T h i s corresponds to a maximum o f 63 data words  /ASCII l i n e , o r 4 ASCII l i n e s p e r DT b u f f e r . 2 - When u s i n g  the DEC macro .INIT, no d i s t i n c t i o n need be made  as t o whether the DPH. h a n d l e r w i l l be used f o r i n p u t both transmit  or output as  and r e c e i v e f u n c t i o n are used i n e i t h e r c a s e .  3 - The Word - P a i r - Count (WPC) i n the .WRITE macro i s r e p l a c e d by  a l i n e count and i s used as an End - Of - T r a n s m i s s i o n (EOT) f l a g .  A f t e r each b u f f e r i s t r a n s m i t t e d , where another b u f f e r i s b u i l t is transmitted,  control returns  f o r transmission.  from DPH. to PIPLN9 A f t e r the l a s t  buffer  t h e l i n e count i s s e t t o zero i n the .WRITE macro and  112  ^START  OPEN  ^  l/P  FILE yes  USE  A.!. REGS  AT  1st  DT  DATA  l/P  READ DATA  TO POINT WORD  IN  BUFFER  A  MAX  OF  252  CLOSE l/P FILE  WORDS N l/P BUFF.  GIVE  no  GET ti  ERROR  MESSAGE  OF  ibWlQDS N Ft fl no  4  COMPLETE  LINES \SET  ASCII  TO BE  XMITTED  UP COU\  INTERS FOR )LAST ASCII LINES TO BE XMITTED  5/7 DATA  ASCII IN  PACKING 0/P  OF  BUFFER  no  TERMINATE  LINE  C.R. a TRANSMIT  no  Fig.  BY  A  IT  yes  (6.5) Flow Chart o f PIPLN9  SET  EOT  FLAG  113  the h a n d l e r  i s re-entered.  The h a n d l e r  then s e t s the EOT f l a g and r e -  t u r n s to PIPLN9 which c l o s e s the a c t i v e i n p u t f i l e and w a i t s f o r subsequent t r a n s m i s s i o n . 4 - A f t e r t r a n s m i s s i o n to t h e IBM-370, the ASCII data can be read i n t o a l i n e a r a r r a y u s i n g the f o l l o w i n g program INTEGER*2  DO  10  READ 2  ARRAY(65536) , DATA(126)  I = 1, 1041 (1,2)  DATA  FORMAT (12611) DO  11  J = 1, 125, 2  11  ARRAY(63*(I-l)+(J+l)/2) = DATA (J)*8+DATA(J+l)  10  CONTINUE  114  Chapter 7 C o n c l u s i o n and The human and length  purpose of t h i s t h e s i s was  the  tibia  are not  o r i e n t a t i o n with respect  a x i a l r o t a t i o n and  and  I t was  the  shown that  knee i n c l i n a t i o n , as w e l l  The  t e s t f i x t u r e and  as x-ray beam c e n t e r i n g  making a s e r i e s of  I t was  due  i n c l i n a t i o n t o g e t h e r was  to r o t a t i o n and  found t h a t  of a femur 43.00 cms.  of e i g h t  long.  0.9  mm.  spe^  the  error  i n the measured  V a r y i n g the beam h e i g h t o v e r a range  nounced e r r o r , however, i s caused by v a r y i n g  of 1.9  mm.  Changes i n p o s i t i o n i n g of the L u f k i n  A more p r o -  the beam c e n t e r over  Here the maximum r e a s o n a b l e e r r o r was  i n measured l e n g t h which could  a  and  orthoroentgeno-  a r e a s o n a b l e bound on  i n c h e s caused a measurement d i f f e r e n c e  femur p r o x i m a l end.  the  e f f e c t s of  were e x p e r i m e n t a l l y determined f o r a phantom femur u s i n g constructed  the  hence v a r i a t i o n s i n t h e i r  e s t i m a t e s from a radiogram.  g r a p h i c exposures.  length  correct  i n determining  children.  e a s i l y modelled and  and  to the x-ray tube when r a d i o g r a p h i n g a p a t i e n t  l e a d to changes i n l e n g t h  height,  to i n v e s t i g a t e  t e c h n i c a l sources o f measurement e r r o r s  of l o n g l e g bones i n i n f a n t s  femur and  cially  Summary  7.75  the mm.  r u l e r were found to cause v a r i a t i o n s  reasonably extend up  to 2.375 cms.  Com-  p u t e r automated schemes to c o r r e c t f o r v a r i a t i o n s i n the placement of Lufkin  r u l e r and  l o c a t i o n of the beam c e n t e r might be  of the  contributions  to o v e r a l l e r r o r of v a r i a t i o n s o f the  meters can perhaps h e l p c l i n i c i a n s for  the p r o d u c t i o n of  useful.  to d e v i s e b e t t e r  Knowledge  above p a r a -  c l i n i c a l procedures  radiograms.  P s y c h o p h y s i c a l s o u r c e s of measurement e r r o r s were c o n s i d e r e d and  the  difficulty  the  of m a t h e m a t i c a l l y m o d e l l i n g these c o n t r i b u t o r s  to  115  e r r o r was  discussed.  We  concluded t h a t d e g r a d a t i o n of the radiogram by  the x-ray imaging system c o u l d not be scheme.  On  the  countered by  other hand, the v i s i b i l i t y  a simple r e s t o r a t i o n  of the d e t a i l s i n a radiogram  and  the d e f i n i t i o n of the edges t h e r e i n c o u l d be  was  demonstrated by  g r e a t l y enhanced.  This  the a p p l i c a t i o n of image enhancement techniques to a  t e s t radiogram o f a c h i l d ' s femur. The  most s e r i o u s  c h i l d r e n i s the  radioluscency  This problem was investigated.  source of e r r o r i n measuring the l e g bones o f  studied  The  and  of the u n o s s i f i e d c a r t i l a g e i n i n f a n t s . a p o s s i b l e s o l u t i o n proposed and  proposed s o l u t i o n c o n s i s t s o f f i r s t  u n o s s i f i e d condyles on  then d i g i t i z e d and p r o c e s s e d on the IBM  success.  techniques are  Prefiltering  methods (histogram  The  r e s u l t i n g radiogram i s  370/67 computer.  c o n t r a s t enhancement u s i n g  any  provements i n o v e r - a l l v i s u a l q u a l i t y .  Several  filters  ance over p r e v i o u s l y c o n s i d e r e d smaller  side lobes.  processed using a non-linear edges sharpness.  gamma c o r r e c a p p l i e d to  i n entropy and  the im-  F i l t e r i n g s u c c e s s f u l l y enhanced  u s i n g a high-emphasis Gaussian f i l t e r or a nonwere s t u d i e d  i s proposed f o r p i c t u r e enhancement.  f u n c t i o n and  dig-  of f o u r d i f f e r e n t  r e d i s t r i b u t i o n of the p i x e l s ) was  radiogram of a c h i l d ' s femur and y i e l d e d i n c r e a s e s  the edge v i s i b i l i t y  Various  then a p p l i e d to the radiogram, some w i t h  e q u a l i z a t i o n , logarithmic conversion,  t i o n or smoothing and  linear f i l t e r .  r e g i s t e r i n g the  the radiogram u s i n g very-low-energy monochromatic  x-rays generated from~.a molybdenum t a r g e t .  i t a l processing  briefly  The  This  filters The  and  t e s t e d and  f i l t e r has  a new  filter  improved perform-  i n terms o f narrower p o i n t  filtered  spread  radiograms were f u r t h e r  mapping technique which g r e a t l y enhanced  p r o c e s s e d radiogram was  seen to be  sufficient  to  116  be e a s i l y used f o r l e n g t h measurement, which i s t o t a l l y r o u t i n e l y radiographed c h i l d ' s  i m p o s s i b l e i n any  femur.  An e d g e - d e t e c t i o r i - c o n t o u r - t r a c i n g a l g o r i t h m was developed to t r a c e the edge of the c o n d y l e s .  The a l g o r i t h m can p o s s i b l y be used i n  o t h e r r a d i o g r a p h i c a p p l i c a t i o n s and i s e f f i c i e n t both i n computation and i n o v e r a l l performance.  The f e a s i b i l i t y o f human a s s i s t e d  t r a c i n g o f the condyles by computer has been demonstrated. c e r t a i n i n i t i a l i z a t i o n parameters  contour  At p r e s e n t  must be d e f i n e d by the user based on  examination of the x-ray to be p r o c e s s e d . done w i t h a l a r g e r d a t a base.  time  Future experiments  s h o u l d be  A l s o , e f f o r t s might be made to f u r t h e r  automate the procedure. Comprehensive i n t e r a c t i v e software was e s t a b l i s h e d to operate a s c a n n i n g and d i g i t i z i n g offers  system w i t h g r e a t f l e x i b i l i t y .  the f a c i l i t y o f d i g i t i z i n g  lution. digitized  radiograms  The system  o f v a r i a b l e s i z e and r e s o -  I t a l s o p r o v i d e s the o p t i o n o f i n e x p e n s i v e l y t r a n s m i t t i n g the radiogram to the IBM 370/67 f o r p r o c e s s i n g o r to the DATA GEN  840A f o r p i c t u r e d i s p l a y u s i n g a f l y i n g  spot scanner.  In summary, t h i s , study has accomplished many objectives-; much work remains  to improve  the t e c h n i q u e s and a l s o t o develop an o n - l i n e  computer system which i s u s a b l e and economical i n the c l i n i c a l e n v i r o n ment of the h o s p i t a l .  117  Appendix (A) The T r a n s f o r m a t i o n o f a G r e y - L e v e l to an Approximately  Rectangular  Histogram  Distribution  I f the grey l e v e l s were c l o s e enough so as to approximate the x^'s by a continuous v a r i a b l e X, d e f i n e d on (a,b) : p . d . f . f (x) , then the summation  a < x < b , w i t h the  Z f(x -) would be r e p l a c e d by the n  integration  F (x) x  = Pr { X * x } = '  X  a  f ( x ) dx  (A.l)  x  where F (x) i s the CDF. A.  Now  let  Z = F(X)  and  F(X) = 0 = a  ;  (A. 2)  f ( x ) dx v  = 1 The t r a n s f o r m a t i o n z: 0 ^ z < 1  X < a a < X < b  (A.3)  b < X Z = F(X)  maps the s e t  x: a < x ^ b  onto  the s e t  ; the J a c o b i a n o f the t r a n s f o r m a t i o n b e i n g  dx. dz  Since dz _ f ( x ) , a < x < b, then the p . d . f . of z, p„(z) w i l l be dx Z  e q u a l to P (z) z  = f(x)  = f(x)  dx' dx = f(x) dz dz 1 dz/d X  f(x)  = 1  1 f(x) a <  That i s the p . d . f . of Z = F(X) i s P (z) z  = 1  0 <. z < 1  = 0  elsewhere  118  Appendix Undeterminate  B Points  of the S i x L i n e a r F i l t e r s  of Chapter IV  The undeterminate p o i n t s are those p o i n t s at which weight f u n c t i o n s : value  ( s p a t i a l response) of the f i l t e r s  l i k e °°/°° , 0 x  00  o r 0/0.  L'Hospital's  the  assume an undeterm-? rule i s  a p p l i e d at  o f the undeterminate p o i n t s and the r e s u l t s are as f o l l o w s :  c  (B. 1)  f T + fc  (B. 2)  1 - h (0) = h (0) = f 1  3  2 - h (0) 2  = h (0)  =  4  T  +  f  3 - h  (Tr/Aoo) = ( A f / 2 )  4 - h  (2-ir/Ato) = -(Af/2rr) s i n ( 2 T r f  c  5 - h (3Tr/Aco) = (Af/16) c o s ( 3 i T f 4  6 - h (0) = 2 ( f + 5  7 - h (0) « f 6  8 - h^(2Tr/Aco) = o  +  f  /Af) JM)  c  (B. 5)  (B. 7)  c  (2Af/rr3)  (B. 4)  (B. 6)  2f )/3  T  T  (B. 3)  cos(irf /Af)  sintirCf^1  I  + f )/Af] c  (B. 8)  119  Appendix C The  IOT i n s t r u c t i o n s f o r the s p e c i a l hardware o f t h e data ac-  q u i s i t i o n system  are l i s t e d below. Description  Mnemonic  Code  SSNS  702201  Skip i f stage needs s e r v i c e  RSSC  702202  Read s c a n n i n g stage code  SLAS  702221  Skip i f l i m i t  STCL  707042  S t a r t remote scan of d i s s e c t o r  SPCL  707021  Stop remote scan o f d i s s e c t o r  LDX  707002  Load X - c o o r d i n a t e of d i s s e c t o r from AC (10 b i t s )  LDY  707022  Load Y - c o o r d i n a t e o f d i s s e c t o r from AC (10 b i t s )  ADCV  707041  S t a r t A/D c o n v e r s i o n on d i s s e c t o r signal  ADSF  707061  Skip i f d i s s e c t o r A/D c o n v e r s i o n i s done  ADRB  707076  Read r e s u l t o f the d i s s e c t o r A/D c o n v e r s i o n i n t o the AC (6 b i t s )  SSXP  707242  Step the stage i n the X - p o s i t i v e direction  SSXM  707204  Step the stage i n the X-negative direction  SSYP  707241  Step the stage i n the Y - p o s i t i v e direction  SSYM  707202  Step the stage i n the Y-negative direction  SSKP  707201  Skip i f s c a n n i n g stage step i s done  alarm s e t  120  APPENDIX' (D)  cTITLE  PIPLN9  /  n  B I N A R Y D A T A .T.NTO 5 / 7 A S C I I F R O M AM l / P F I L E ON TRANS"! I T I E D E I T H E R TO T H E N O V A 8-A0A OR TO T H E / I B M S Y S T E M . .370/67 F O R D I PSL A Y OR P R O C E S S I N G , R E S P E C T I V E L Y . T H I S ' • /ROUT I [IF. C A L L S T H E D A T A P H O N E H A N D L E R D P H . . / „ 1 9 9 5 .IODEV G E T F I L , DPH. .GLOBL ;S P R O G R A M P A C K S DATA I S THEN /DT2  /  2,0,1MIT 5,0, INIT INIT GETFIL  . INIT . INIT LAC J MS* n  INIT  / R E S E T A L L SOFTWARE F L A G S IM D P H . / I N I T I A L I Z E D T 2 FOR l / P & L I N K FOR 0 / P O P E N l/P FILE /  HLT /  / A . I , R E G . 10 U S E D (BUF10+1 / DT2 B I N DATA.INTO CUTO 2 , 1 , B U F 1.0,25A  LAC DAC* .READ .WAIT LAC AND SZ A JMP DZ M  START  9  B U F 10  L HC D AC . LAC AND SAD SKP JMS LAW D AC LAW D AC D AC D.AC D.AC A /GET /  D; TA  ERROR 1 FORI.. IN' ( B u F C ri T FORCMT B U F 10 (377000 ( 177000 BUPTAR -A FORLIN -77 BUFCNT 3UFCNT+1 BUFCNT+2 BUFCMT+3  WORDS R E A D Y F O R  /  NOEROR  / /START / /  LAC DAC* JMS DZM LAC DAC ASCII  LAC D.AC*  FOR R E A D I N G BUF10  ( B U F ! 1-1 DUTO PREPAC PNTER (OPBUF+2 BUFPNT PACKING  / S A V E V A L I D I T Y B I T S OF / 1ST H E A D E R WORD / DATA CORRECT ? G I V E ERROR MESSAGE / MO;r PARAMETERS / Y E S ? I N I T I A L I Z E PROGRAM  / CHECK / ./ / / / / /  W.P.C.  BIN.  DATA  WORDS  t  THIS  IS LAST  NO  BUFFER  .  YA ES S CO TO . T R A N S F E R A C; I I SLEITN EAS -A/ D TU NBTUEFRF E R EACH ASCII. L I N E HAS A D I F F E R E N T COUNTER I N I T I A L I Z E D AT - S 3 . -  ASCII  PACKING  --->  / I N I T I A L I Z E P O I N T E R TO R E A D I N T O B U F 11 / F.ROM B U F 10 S 3 B I N A R Y D A T A WORDS ( OR / LESS I F LAST BUFFER ) / I N I T . P N T E R AT Z E R O TO P A C K C H A R A C T E R 1 / I N 5 / 7 , & B U F P N T TO P O I N T AT 1ST / CHARACTER .  --->  (BUF11-1 DUTO  = 252 ?  '  / RE I N I T . /  POINTER  AT T O P OF  .  BUF1 ! .  -  ELECTRICAL ENGINEERING Us Be C « LAC* JMS ISZ JMP LAC JMS  1 1 PACK OPCNTR o-3 (15 PACK  121  PIPLMQ SRC  / / /  0/P A S C I I L I M E READY ? NO : K E E P ON . YES ? T E R M I N A T E BY A CR  /  /TRANSFER  ASCII LINE  / /  CHECK  LAC D AC DZM .WRITE .WAIT LAC SNA JMP ISZ J MP CLC SAD JMP DZM LAC  TO L I N K -•  / SET HEADER WORDS 0 & 1 (33032 OPPU.F 0P3UF+1 / A L I N E COUNT P ARAMETE 5,2,0PBUF » 1 / S P E C I F I E D RATHER THEN A WORD COUNT 5 / IN THE .WRITE MACRO CHECK+3 / CHECK+3 I S ZERO AT EOT . / END-OF-TRANSMISSION ? / YES: CLOSE I / P F I L E CLOSE / NO : D T 2 B U F F E R EMPTY ? FORLIM / NO : R E F I L L 0/P P U F F E R MOEROR / Y E S : WAS I T L A S T B U F F E R EOT / TO BE T R A N S M I T T E D ? START / MO : READ MORE R I N . DATA I N .WRITE MACRO TO CHECK+3 / Y E S : S E T EOT F L A G ( 1005 A D n i | r  .FORCE D P H . TO END T R A N S M I S S I O N  JMP  CHECK  .WRITE .WAIT  - 12,2,ERMSG1,3 4 - 12  .CLOSE CLC D AC JMP  2  /  / /  ERROR 1 / CLOSE  / / / /  / EOT IMIT  R E I N I T . EOT  PARAMETER  / RESTART  * * * * * PROGRAM S U B R O U T I N E S * * * * * ;  /  BUFPAR 0 / T H I S • S U B R O U T I N E C A L C U L A T E S THE 9 OF R I M DATA I N THE L A S T B U F F E R /TO B E P A C K E D & T R A N S M I T T E D . THE # OF L I N E S ( M A X . 4 ) I N I T I A L I Z E S /THE COUNTER FORL I'M THE 4 L O C A T I O N S AT BUFCNT ARE USED TO COUNT /THE L A S T DATA TO BE T R A N S M I T T E D . / GET WORD COUNT = 10 LRS (776 / (W.P.C„*2)-2 AND (-2 TAD (-77 / TEST I F # OF WORDS I S L E S S THAN 6 3 TAD. / STORE WORD COUNT - S3 I N . T M R A R Y . DAC TMRARY / L E S S THAN 63 ? SPA / YES : S E T COUNTER FOR # OF WORDS • ONE JMP (-77 / & TERMINATE TRANSMISSION . TAD D.AC / NO : TMRARY  ELECTRICAL U.B.C. .  ENGINEERING  SPA JMP TAD D AC SPA JMP TAD  THREE  TWO  ONE  DAC LAW DAC IS?. ISZ LAW DAC ISZ ISZ LAW DAC ISZ ISZ LAC TAD CM A TAD DAC* LAC DAC LAC DAC DZ M L.AC DAC JMP*  / / P R E P AC  0 ' LAC* CLL RAL D.AC LAC* LRS AND TAD D.AC* LLS AND TAD DAC* ISZ* JMP ISZ  JMP*  P I PL N 9 SRC /  TWO (-77. TMRARY THREE (-77 TMRARY -77 BUFCNT+ FORCMT FORLIN -77 RUFCNTiFORCNT FORLIN (-77 BUFCNT FORCMT FORLIN TMRARY (77  / L E S S THAN / Y E S ... / / LESS / YES  THAN  -122 •  •  1 2 6 .?  I B S '?  I F THE L A S T L I N E I S P A R T I A L L Y F U L L THEN S E T T H E C O U N T E R S F O R L I N E S 1, 2 , 3 AT - 6 3 , & I N C R E M E N T F O R C M T T 0 P O I N T AT R U F C N T - f 1 , AT T H E E N D O F T H E S U B R O U T I N E I T W I L L P O I N T AT R U F C N T + 3 TO R E A D I N T H E C H A R A C T E R S COUNT FOR•THE L A S T I N C O M P L E T E ASCII LINE F O R L I N W I L L B E S E T AT 3 , 2 , 1 OR 0 AT S U B R . E N D D E P E N D I N G ON T H E A S C I I L I M E ! # ( W H E T H E R 4 , 3 , 2 OR 1) T H E N I 3 T O N E ' S COM• P L E M E M T WLL B E T H E # - O F - L I N E S C O U N T E R /  S E T CNTR  FOR L A S T  ASCII  LINE  ( 1 • FORCMT FORLIN FORLIN (BUFCNT FORCMT EOT (NOEROR  BLIFPAR  / L E T F O R C M T P O I N T A G A I N TO 1 S T A S C I I / WORDS C O U N T E R . / S E T EOT F L A G / SET SUBROUTINE RETURN ADDRESS .  LINE  BUFPAR  FORCMT  OPCNTR 10 3  (7 (260 I I 3  / / /  GET # OF B I N D A T A W O R D S / A S C I I L I N E ( I N TWO'S C O M P L E M E N T ) & M U L T I P L Y B Y 2 TO C O U N T # OF C H A R A C T E R S /LINE  / READ B I N DATA / 3 M.S.3. S A V E THEM / A S C I I CODE / A S C I I DATA / SAME FOR 3  FROM  DT2 BUFFER  BUF1 1  (7 (260 1 1 FORCMT PREPAC+5 . FORCMT PREPAC  / 6 3 (OR L E S S ) B I N D A T A W R I T T E N / NO : C O N T I N U E / Y E S ; P O I N T AT N E X T A S C I I LINE  INTO  BUF 11?  ELECTRICAL  12 3  PIPLN-9 S R C  ENGINEERING  U.B.C.  / PACK C H A R A C T E R S INTO / 0 PACK (177 AND T EMP DAC PNTER LAC SAD (5 NEWORD JMP SAD (.A JMP * FIFTH SAD (3 FOURTH JMP (2 SAD THIRD JMP ( ! SAD SECOND JMP /  FIRST  / TAG  DZM* LAC CLL ALS  BUFPNT TEMP  ND  (774000  TAD* DAC* ISZ n.  BUFPNT BUFPNT PNTER  I M  13  i -\ o  ;\  /  Ul'M  SECOND  LAC CLL ALS AND J MP  TEMP  LAC CLL LRS AND TAD* DAC* DZM* LAC CLL. ALS AND JMP  TEMP  T  h (3760 TAG  /  THIRD  / FOURTH  3 ( 17 BUFPNT BUFPNT BUFPNT TEMP 17 (700000 TAG  L.AC CLL ALS AND JMP  TEMP  LAC RCL AND  TEMP  10 (77400 TAG  /  FIFTH  (37S  5/7  ASCII.  / SHORTEN  TO S E V E N  BITS  ELECTRICAL U.B.C.  / ME WORD  / / / /. /  ENGINEERING  JMP  TAG  DZM S7 DZM* JMP  PNTER BUFPNT BUFPNT FIRST  ****  ERi'lSG 1  0420C2 0 • .ASCII  PROGRAM  ' ERROR  PIPLNS  SRC  124  / RESET POINTER / INCREMENT BUFFER POINTER / Z E R O OUT N E X T B U F F E R LOCATION  CONSTANTS  IN R E A D I N G  ****  BINARY  DATA  *<15><12>  /  CUTO DUTO FORLIN  FOR C U T BUFPNT  OPCMTR TEMP PMTER  TMRARY EOT BUF! 0 n u r  i (  OPBUF  BUFCNT  / / A . I . P O I N T E R TO D T 2 B U F F E R // ............... P R E P A C A S C I I BUFFER /./ C O U N T E R F O R # OF A S C I I L I N E S / DT B U F F E R / / P O I N T E R TO L O C A T I O N O F A S C I I L I M E S C H S . C O U N T E R S / / P O I N T E R TO O/P A S C I I L I N E S / / C O U N T E R F O R # OF A S C I I C H S . TO B E PACKED // USED IN PACK SUBROUTINE //.................  10 11 0 0 0 0 0 0 0 -1 o BLOCK  // END-OF-TRANSMISS'IOM /-'00  .BLOCK .BLOCK  70 4  .END  IN IT  / '  '  FLAG  125 APPENDIX (E) MICHIGAN TERMINAL SYSTEM FORTRAN GI41336I  EDGE OET ECTION ALGORITHM  OOOl 0002 0003 0004 OOOS  ' » « * . >  > » • > > > 0006 0007 000 8 0009 0010 0011  >  REAO IN ORIGINAL PICTURE DO 10 J - l , 2 5 6 CALL R E A D ( T E M P ( 1 J , L £ N . O , L N R , 1 . C 9 9 1  >  ARRANGE THE PICTURE IN MEMORY THE SAME ORIENTATION « « 00 11 1=1,256 JJJ-TEMPIII OARRAYI1257-JI,(257-1)I-JJ4 CONTINUE •  • >  ' 0016 0017 0018  002 5 0026  RCA0 VALUE DF STANDARD DEVIATION OF THE WEIGHING FUNCTION C THE LAST ENTRY IN BOTTOM ROW AFTER WHICH EOGE DETECTION SHOULD BEGIN RE AO 15,1001 SO.INIT W R ! T E ( 6 , 1 0 1 I SO OENO=SD»(SORT 12.»3.1415931 I S0S0=2.»IS0*«2I  0014 0015  001 9 002 0 0021 002 2 002 3 0024  REAL 0ARRAYI256,256) LOGICAL FIRST.NOME 1T DIMENSION RCW(50) DIMENSION SCRATC (101,21 1NTEGER-2 T EMP(25M .LEN/51 Zl ROW IS A LINEAR ARRAY CONTAINING ALL THE POINTS USED IN EDGE DETECTION . INIT IS THE ENTRY AFTER WHICH SEARCH FOR AN EDGE SHOULD START . F U S T WHEN SET TO . T R U E . INDICATES THAT-THE 1ST LOCAL EDGE U ILL BE DETECTED . NORPOS TAKES THE VALUE *1 OR - 1 , DEPENDING ON WHETHER DETECTION IS ALONG AN INCREASING ( » l l DR A DECREASING (-11 MATRIX INDEX . SOSO £ OENO ARE PARAMETERS OF THE GAUSSIAN WEICHING FUNCTIUN • HIOPNT SPECIFIES THE ENTRY IN A SEOUENCE OF EDGE CANDIOATES WHERE THE GAUSSIAN WEIGHING FUNCTION IS MAX . FOR E . G . . IF SEARCH IS OVER 6 POINTS AND THE FIRST IS TO BE EMPHAS1ZE0 THEN MIOPNT = 1 NOWEIT ASSUMES A WEIGHT OF 1 FOR EACH EDGE CANOIOAT E WHEN SET TO .TRUE. LOC IS THE DETECTED EDGE LOCATION . LOCEOG SPECIFIES THE LOCATION OF THE PREVIOUS EOGE U . R . T . THE ENTRIES TESTED FOR A NEW EDGE . USUALLY LOCEDG « MIDPNT . I FIT IS THE DEGREE CF THE POLYNOMIAL . NPOINT » OF POINTS INVOLVED IN CURVE FITTING . LSRCH * OF ENTRIES OPTIMIZED FOR AN EDGE .  O I .UUU  START AT ROW 1 FORM THE BOTTOM WHERE THE EOGE IS THE STRONGEST FIRST-.TRUE. COC« 1 NOWEIT".TRUE.  «  FIRST EDGE OETECTION BEGINS AT COLUMN 81 00 1 J - 1 , 5 0 ROW(Jl-OARRAY(256,<INIT«J)) CALL E D G E ( R O W , I N I T , F I R S T , 1 , S 0 S Q , D E N 0 , 6 , N O W E I T , L 0 C , 6 * 2 , l l , 6 ) Y = 0. X-LOC WRITE(8,1CS) X.Y  • • '  ON RETURN FROM THE SUBROUTINE THE IMPORTANT PARAMETER IS THE ENTRY AT WHICH THE SECOND DERIVATIVE OF THE FITTED CURVE IS MAX• CONTINUE ECGE OETECTION UP TO ROW 129 FIRST*. FALSE. 00 3 1=2, 128  '  SEARCH FOR AN EDGE NOW IS OVER ONLY THE NEIGHBORHOOD OF PREVIOUS •EDGE LOCATION . THIS NEIGH3DRH000 IS THE IMMEDIATE 5 ENTRIES ' • BEFORE L C C . READ IN THESE 5 ENTRIES * 5 OTHERS IMMEDIATELY PRECEDING THE FORMERS FOR CURVE FITTING . 002 7 002 8 002 9 0030 0031 0032  DO 2 J - 1 , 1 6 R0W(J)=0ARRAYU257-I1,(L0C + J - U I > CALL EDGE I ROW,IN I T , F I R S T , 1 , S D S 0 , D E N O , 6 , N 0 W E I T , I O C , 6 , 2 , 1 1 , 6 ) Y»l-1 X-LDC WRITEIS.IOS) X.Y 123 EDGES HAVE BEEN LOCATED : CONTINUE HORIZONTAL EDGE OETECTION Bur ALLOW FOR THE POSSIBILITY OF THE NEW EDGE POINT TO BE EITHER SIDE OF THE PREVIOUS ONE . SAVE THE LOCATION OF THE LAST EOGE POINT IN RCH 129  003 3 0034 0035 0036 0037 003 8 003 9 0040 0041 0042 004 3 004 4 004 5 004 6  LL 12 9 LOC REAMS, 105IINSID1 NOkEIT=.FALSE. WRIIE 16,104) WRIIE<6,1021 1-128  1  a  DO 5 J - 1. 21 ROWIJl-OARRAY((257-1 I . I L O C » J - l 1 ) ) CALL EOGE(ROW,INIT,FIRST,I,SDSQ,DENO,6,NOWE Y.I-1 X*LOC WR1IFIB.IOSIX.Y IF I ( L a C - L L 1 2 9 ) . L T , 1 N S I 0 1 ) GO TO 4  IT,LOC,6,2,11,11)  *  START DETECTION IN VERTICAL DIRECTION . D1IR1NG THIS LCCAIE THE MAX, HEIGHT THAI THE OEUCTOR REACHES , IF IT EVENTUALLY FALLS BY AN AMCUNV INSID2 , STOP VERTICAL OETECTION . IROW-256.-Y  5.000 6.OOO 7.000 8.000 9.000 10.000 11.000 12.000 13.000 14.000 15.000 16.000 17.000 18.000 19.000 20.000 21.000 22.000 23.000 24.000 25.000 26.000 27.000 28.000 29.000 30.000 31.000 32.000 33.O0O 34.000 35.000 36.000 37.000 38.000 39.000 40.000 41.000 42.000 43.000 44.000 45.000 46.000 47.000 48.000 49.000 50.000 51.000 52.000 53.000 54.000 55.000 56.000 58.000 59.000  60.000 61.000 62.000 63.000 64.000 65.000 ' 66.000 67.000 68.000 69.000 70.000 71.000 72.000 73.000 74.000 75.000 76.000 77.000 78.000 79.00 0 8C.000 81.000 82.000 83.000 84.000 85.000 86.000 87.000 83,000 89.000 90.000 91.000 92.000 93.000 94.000 95.000 96.000 97.000 98.000 99.000 ICO.000 101.000 102.000 1C3.000 104.000 ICS.000 1C6.000 107.000 10t».000 1C9.000 110.000 U1.000 112.000 113.000 114.000  126  MICHIGAN  TERMINAL  SYSTEM  FOR I R A N  MAIN  C(41336)  115.000 116.000 117.000  WRITE 16,1041 WW I ( 6 . 1 0 3 1 IROW.LOC REA.'M5, 1 0 5 I I N S I 0 2 Rl TMAX-O.  004 8 004 9  0050 00', 1 0052 0053 0054  lie.ooo  10C-1R0W I-K-1.  1-1*1  00 8 L " 1 . 1 6 ROW! L l = O A R R A Y I U O C U - 1 1 I.I I C A L L E D G E I R 0 W . I N 1 T , F I R S T , 1 , S D S Q • D E N O . 6 , N O U E I T , I O C . 6 , 2 . 1 1 , 111 Y-256-L0C  005 5 005 6 005 7 005 8 0051 0060  X-I  NR1TEI8,108)X,Y IF I Y . G T . R I T M A X I RITMAX-Y IF 1 ! R I T M A X - F L O A T ( ) N S I D 2 ) ) . L T . Y )  .0061 0062  CO T O 7  T H E D E T E C T O R H A S NOW F A L L E N S U F F I C I E N T L Y OVER T H E R . H . S . CONOYIE. D E T E C T O R N O J O P T I M I Z E S T H E S L O P E TO A 1 S T O E G R E E P O L Y N O M I A L . WRIT E C 6 ,  006 3  W R I T E 1 6 , 1 0 6 ) 1 ,  006 5  F I R S T - . T R U E .  0066  L L 1 2 9 - L 0 C  19  0057 006 3  20  00  J - 1 ,50  2 0  E O G E ( R O W , 2 5 7 , F I R S T , - l , S D S 0 . 0 E N 0 , 4 , N O W E I T , l O C , 4 , l , 7 , 7 l  0070  IF  0071  L L 1 2 9 - L L 1 2 9 » 1  0072  GO  0073  21  0074  1 L O C . G E . I  GO T O  21  Y = 2 5 6 - L L 1 2 9 X-LOC WRIT E O . 1 0 8  0076  Fl R S T - .  0077  L L 1 2 9 » L L 1 2 9 » 1  CO  0078 0079  ooeo ooal  12  1 3  K=LL129,149  00 1 2 J - 1 , 1 3 ROW!JI-0ARRAY1K,IL0C+7-JI) CALL  EOGEI  0032  Y - 2 5 6 - K X - L O C  13  DO  14  T  Y  CONTINUE  FIRS  0037  e  ROW,257,FIRST,-1,SDSO,DENO,4,NOUEIT,LOC,4,1,7,71  W R I T E ( 8 , 1 0 3 ) X  003 4 003 5  IX,Y  F A L S E .  003 3  0036  T - . T R U E .  1 4 . J - 1  , 5 0  RO WI J I = n ; R R A Y I 2 5 6 , U 4 0 * J I I  0G3 9  CALL  005 0  SCRATC  11  0071  SCRATC  11,1)-LOC  E O G E I R O a . 1 4 0 , F I R S T , 1 , SO  SO,OENO,6,NOUE!T,LOC,6,2,11,6)  , 2 1 = 0 .  F I R S T " . F A L S E .  00=2 ' 009 3  0094  00  1 6  I =2 . 1 0 1  DO  1 5  J - 1 , 1 6  15  ROW( J ) = OA R R A Y ( ( 2 5 7 — 1 ) , U O C * J - 6 ) ) CALL E O G E I R O U , 1 4 0 , F I R S T , 1 , SDSO,DENO,2,NOWEIT,LOC,1,2,11,6)  16  CONTINUE  0101  17  DO 1 7 L - l , 1 0 1 WR I T E i 8 , 1 0 8 I S C R A T C  0102  100  0103  101  0104  102  0105  103  0106  104  009 5 0096 009 7 009 3 0099 0100  SCRATC  II,1)-L0C  SCRATC  ( I , 2 1 = 1 - 1  F O R M A T ! ' 1  7  105 1 06  * , / / / / / / , 2 0 X » *  WI-TH  1 ( 1 0 2 - 1 1 , 2 )  13)  STANOARO  EOGE  DETECTION  DEVIATION DETECTION  USING  A  GAUSSIAN  WEIGHING  FU  - - > ' , F 8 . 4 / I STARTS  NOW  IN  UPPER  L E F T  HALF  OF  T  R A D I O G R A M ' / , 4 0 X , 6 1 1 ' - ' ) , / / >  F O R M A T ! / / / / , 4 0 X , ' E D G E C01NT  010 8  171.000 1 ( 1 0 2 - L 1 , 1 1 , S C R A T C  F O R M A T ( / / / / , 4 0 X , • E D G E  CHE  010  170.000  •  F 0 R 1 A T ( F 1 0 . 0 ,  CNCTION  AT  FORMAT!  ! ' , 1 4 , '  , ' • 1 4 , '  DETECTION  IN  VERTICAL  )* , / , 4 0 X , 6 7 ( . ' - •  ),  DIRECTION  :  STARTING  P  //)  M M  F O R*1 A T 1 1 3 ) F O R M A T ! / / / / , 4 0 X , ' S L O P E CTING  POINT  AT  1 • ,1 4 , '  O P T I M I Z A T I O N , • , 1 4 , '  IN  ) ' , / , 4 0 X , 7 3  HORIZONTAL (' - '  )  DIRECTION  ,//)  :  STAR  172.000 173.000 174.000 175.000 176.000 177.000 178.000 179.000 180.000 •181.000 182.000 183.000  0109  108  F O R M A T ( 2 F 1 0 . 0 1  184.000  0110  109  F O RMA T 1 ' S E N D ' 1  0111  99  185.000 186.000 187.000  0112  NO  1  19  T O  0075  003  LOC  ROW! J l - 0 A R R A Y I L L 1 2 9 , ( 2 5 7 - J ) 1  CALL  0069  .  1041  0064  119.000 120.000 121.000 122.000 123.000 124.000 125.000 126.000 127.000 128.000 129.000 130.000 131.000 132.000 133.000 134.000 135.000 136.000 137.000 138.000 139.000 140.000 141.000 142.000 143.000 144.000 145.000 146.000 147.000 148.000 149.000 150.000 151.000 152.000 153.000 154.000 155.000 156.000 157.000 158.000 159.000 160.000 161.000 162.000 163.000 164.000 165.000 166.000 167.000 16S.0OO 169.000  STOP END  • O P T I O N S IN E F F E C T * ID,EBCDIC,SOURCE,NOLIST,NOOECK,LOAO,NOMAP • O P T I O N S IN E F F E C T * NAME - M A I N , L I N E T NT a 57 • STATISTICS* SOURCE STATEMENTS 1 1 2 , PROGRAM S I Z E • 267594 •STATISTICS* NO D I A G N O S T I C S G E N E R A T E D ERRORS I N M A I N  MICHIGAN TERMINAL  SYSTEM  FORTRAN  GI4D36)  S U B R O U T I N E EDGE I R O W , I N I T , F l « S T » N D R P O S , S D S 0 , D E N O , M I O P N T » N O K E I T , L O C , CIUCEDG.IFIT,NPOINT,LSRCH)  »•  A G I V E N ARRAY D F D A T A IS S E A R C H E D . F O R AN EOGF . T H E C R I T E R I O N I S O P T I M I Z I N G E I T H E R THE S L O P E OR T H E S E C O N D O E « ! V A T I V E T O A P O L Y N D M I A L O F F I R S T OR 2ND D E G R E E F I T T E D TO A P R E S P E C I F I E D « OF P N T S D I M E N S I O N X I 1 1 I , Y ( 1 1 ) , P ( 3 1 , R O W ( 5 0 1 , P P I 401 01 M r N S I ON SI 3 I » S I G M AI 2 I , A ( 2 I , B I 2 I , Y F ( 1 1 1 , Y D 1111 • U T I 111 LOGICAL F1RSI.LK.NOWEIT  000 2 0003 0004  WEIGHTIKI•(EXPI-(HIOPNT-KI**2/SOSOII/DENO •» *» •• • •  • * **  • • »• •* *. *• •» •» 0006 0007 000 B 0009 0010 0011 OD12 0013 0014 0015 0016  A L I N E A R A R R A Y C O N T A I N I N G A L L THE P O I N T S U S E D I N E O G E DETECTION . I N I T I S TH? E N T R Y A F T E R W H I C H S E A R C H FOR A N SHCULO START , F I R S T WHEN S E T TO . T R U E , I N O I C A T E S T H A T T H E 1 S T L O C A L EDGE W I L L BE OETECTEO . N O R P O S T A K E S T H E V A L U E , 1 OR - 1 , OE PE NO I N G ON WHETHER OETECTION I S A L O N G AN I N C R E A S I N G t . l l OR A D E C R E A S I N G ( - 1 1 MATRIX I I10EX . S D S O C DENO A R E P A R A M E T E R S OF THE G A U S S I A N W E I G H I N G F U N C T I O N . MIOPNT S P E C I F I E S T H E ENTRY IN A S E Q U E N C E O F EDGE C A N D I D A T E S WHERE T H E G A U S S I A N W E I G H I N G F U N C T I O N IS MAX . FOR E.G. , I F S E A R C H IS OVER 6 P O I N T S A N O T H E F I R S T I S TO BE E M P H A S I Z E O T H E N MJDPNT • 1 N O W E I T A S S U M E S A W E I G H T O F 1 FOR E A C H E D G E C A N D I D A T E WHEN S E T 7 0 .TRUE. t O C I S T H E D E T E C T E D EOGE L O C A T I O N . LOC EDO S P E C I F I E S T H E L O C A T I O N OF THE P R E V I O U S E O G E H . R.T. T H E E N T R I E S T E S T E D FOR A NEW EDGE . U S U A L L Y L O C E D G » M I O P N T . I F 1 T I S THE D E G R E E OF THE P C L Y N O M I A L . NPOINT t O F P O I N T S INVOLVED IN C U R V E F I T T I N G • L S R C H ( CF E N T R I E S O P T I M I Z E O FOR AN E O G E .  ECGE  INITIALIZE LK «, T R U E . SECDER-O.  L . S . FIT  PARAMETERS  NWT'O  10 «*  0017 0018 '0019 0320 072' 0022 0023 0024 0025 002 6 002 7 0028  RCW IS  LPLSl»LSRCH»l tPLSl«LSRCH»LSRCH 11*IFIT,1 K.|.(NP0INT«I>/2 KF-51-KI KMINl»[NP0INT-ll/2 DO 1 0 L " l , N P O I N T XI L l — K 1 » L  .  . .  .  '  • •  •  -  '  F I R S T E D G E TO B E D E T E C T E D ? I F I . N O T . F I R S T ) GO TO 1 6 00 12 l.KF 00 1 1 I " l . N P O I N T Y(I)-ROWIJ.l-KI I C A L L 01.OF < I F I T , N P O I N T , X , Y , YF , Y O , W T , N W T , S , S I G M A . A , B , S S « I K . P )  J'<  11  PP I J - N M I N 1 | . P ( I D I F I PI I I ) . L E . S E C O E R ) CO TO 12 SECOER-PlI11 LOC-INIT+J.NORPOS 12 CONTINUE IENTRYMNIT.KI.NORPOS WRIT E ( 6 , 1 10 I LOCIENTRY 002 9 W R I T E ( 6 , 1 1 1 I PP 0030 GO T O 2 0 00 3 1 16 LOCl'LOC 0032 W R I T E I 6 . U 4 I LOC 0033 00 1 7 H * 1 , I S R C H 0034 DO 18 l - l , N P O I N T 18 V I L l « R 0 W ( I ' 003 5 CALL O L Q F I I F I T , N P O I N T , X , Y , Y F , Y D , W T , N W T , S , S I GMA,A,8,SS,IK,PI 0036 PP(NI«P(11I 003 7 I F I N O W E I T l GO TO 1 9 0038 PI I I l = P ( I 1 1 . W E I G H T I H I 0039 PPIM.LSRCHl-PI11 I 004 0 19 I F I PI U l . L T . S E C D E R ) GO TO 1 7 0041 SECDER'Plll) 0042 LOC"LOCI.(M-LOCEOGI.NORPOS 0043 0044 17 CONTINUE 0045 W R ! T E I 6 , U S I LOCEDG 0046 WRIT 5 ( 6 , 1 12 I ( P P ( I ) , I - l , L S R C H ) 004 7 I F ( N O W E I T ) GO TO 2 0 004S WRIT E ( 6 , 1 1 3 K P P I 1 ] , I - L P I S I . L P L SI) 004 9 F O R M A T ! / / , - 0 ' , 4 X , ' F I R S T EDGE L C C A T E O AT E N T R Y * , 1 4 , • , T H E VALUES OF 110 C THE D E R I V A T I V E S S T A R T I N G F R C M E N T R Y * , 1 4 , • FOLLOW...«/) FORMAT('0 • . 1 0 F 1 0 . 6 I 111 005 0 C O R R E S P O N D S TO TH F O R M A T ! / / / / , ! ? * , ' IN T H E F O L L O W I N G . E N T R Y ' , 1 5 . 115 0051 CE P ' E V I O U S EOGE'/I F O R M A T ( * 0 • , S X , ' D E R I V A T IVES O F THE N E I G H B O R I N G P O I N T S -->',/, 0052 112 C11FI1.6/1 F O R I AT I ' 0 - , 4 X , • W E I G H E D D E R I V A T I V E S OF THE N E I G H P C R 1 N G PCINTS - - > • 113 005 3 C/.11F11.6/I F 0 R M A I I / / / / , 4 X , ' C H E C K : P R 6 V I C U S E O G E L C C A T E C AT E N T R Y : ',14/1 114 0054 RETJRN 20 0055 ENO 0056 .OPTIONS IN E F F E C T * I 0 , E B C O I C , S O U R C E , N O L 1 S T , N O O E C K , 1 0 AO,NOMAP • O P T I O N S I N E FF EC I* NAME • t O C E , LINECNT • 57 •STATISTICS* SOURCE S T A T E M E N T S • 56,PROGRAM S I Z E " 2734  NO  •STATISTICS* NO D I A G N O S T I C S ERRORS IN EDGE  NO  STATEMENTS  »SIG  F LAGGED I N  GENERATEO  THE A B O V E  COMPILATIONS.  188.000 169.000 190.000 191.000 192.000 193.000 194.000 195.000 196.000 197.000 198.000 199.000 200.000 201.000 2C2.000 203.000 2C4.000 2C5.000 206.000 207.000 2C8.000 209.000 21C.000 211.000 212.000 213.000 214.000 215.000 216.000 217.000 218.000 219.000 220.000 221.000 222.000 223.000 224.000 225.000 226.000 227.000 228.000 229.000 230.000 231.000 232.000 233.000 234.000' 235.000 236.000 237.000 238.000 239.000 240.000 241.000 242.000 243.300 244.000 245.000 246.000 247.000 " 248.000 249.000 25C.C00 251.000 252.000 253.000 254.000 255.000 256.000 257.000 258.000 259.000 260.000 261.000 262.000 263.000 264.000 265.000 266.000 267.000 268.000 269.000 27C.000 271.000 272.000 273.COO 274.000 275.000 276.000 277.000 278.000 279.000 280.000 231.000  128  REFERENCES  1.  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