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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.Sc, The University of Alexandria, Egypt, 1970 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of E l e c t r i c a l Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1974 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C olumbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department of £ L£ £ T l\ I CflL izLN G\ < NizlEfW N C, The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada i i ABSTRACT The problem of determining and correcting measurement errors i n r a d i o l o g i c a l estimates of the bone lengths and d i f f e r e n t i a l growth of children's legs i s discussed. Sources of possible measurement error are f i r s t c l a s s i f i e d as being p h y s i o l o g i c a l , psychophysical, or psychological. The extent of the contribution of each of the i d e n t i f i e d sources of er-ror to the o v e r a l l measurement error i s then estimated by experiments using a bone phantom and s p e c i a l l y constructed test f i x t u r e s . Procedures are s p e c i f i e d f o r reducing s i g n i f i c a n t contributors to the o v e r a l l e r r o r . In p a r t i c u l a r , the problem of radiolucency of bone c a r t i l a g e i s treated by combining a mammographic x-ray technique with computer processing of the radiogram. Also, suggestions are made as to how to reduce the human error. A description of the s p e c i a l purpose scanning system b u i l t for use i n the computer processing studies i s included.. The scanning system o f f e r s the unique advantage of d i g i t i z i n g an 11 by 11 inch radiogram, or smaller subsections, with v i r t u a l l y any pres p e c i f i e d r e s o l u t i o n . i i i TABLE OF CONTENTS PAGE ABSTRACT i i TABLE OF CONTENTS i i i LIST OF ILLUSTRATIONS . v l LIST OF TABLES i x ACKNOWLEDGEMENT x I. INTRODUCTION 1 1.1 Problem Formulation 1 1.2 Research Organization 6 I I . THE PHYSIOLOGICAL, PSYCHOPHYSICAL AND PSYCHOLOGICAL ASPECTS OF THE PROBLEM OF MEASUREMENT ERRORS OF LONG LEG BONES IN CHILDREN 8 2.1 Introduction 8 2.2 P h y s i o l o g i c a l Errors 9 2.2.1 Geometric and radiographic d e s c r i p t i o n of long l e g bones i n children 9 2.2.2 Trabecular patterns 15 2.2.3 Anatomical structure errors 16 2.3 Psychophysical Errors 18 2.3.1 Image c l a r i t y 18 2.3.1.a Contrast 21 2.3.1.b Image Quality 25 2.3.2 Properties of the HVS 35 2.4 Psychological Errors 37 I I I . AN ANALYSIS OF ERRORS IN THE RADIOGRAPHIC MEASUREMENT OF LONG LEG BONES 38 3.1 The Apparatus 38 i v 3.2 E f f e c t of Bone Rotation 42 3.3 E f f e c t of Beam Center Location 44 3.4 E f f e c t of 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 of Lufkin Ruler Orientation and Human V a r i a b i l -i t y 48 3.7 Conclusion 52 IV. ON .THE PROBLEM OF RADIOLUSCENCY OF UNOSSIFIED CARTILAGE IN CHILDREN 5 3 4.1 The Radiographic Imaging Technique 53 4.2 Image Processing ••• 54 4.2.1 P r e f i l t e r i n g contrast enhancement 54 4.2.2 Results and evaluation 59 4.2.3 F i l t e r i n g 63 4.3 Conclusion , 79 V. EDGE DETECTION AND CONTOUR TRACING 82 5.1 Introduction 82 5.2 Edge point: D e f i n i t i o n and Location, 84 5.3 The edge detection algorithm 85 5.4 Experimental r e s u l t s and discussion 92 VI. THE DATA ACQUISITION SYSTEM 96 6.1 Introduction 96 6.2 The image dissector camera 96 6.3 Noise removal system 99 6.4 Light source and movable stage 101 6.5 The computer in t e r f a c e 102 6.6 The software implementation 102 V 6.6.1 Axes alignment 102 6.6.2 Stage p o s i t i o n i n g control 105 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 transfer 107 VII. CONCLUSION AND SUMMARY 114 APPENDIX (A) THE TRANSFORMATION OF A GREY LEVEL HISTOGRAM TO AN APPROXIMATELY RECTANGULAR DISTRIBUTION 117 APPENDIX (B) UNDETERMINATE 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 v i LIST OF ILLUSTRATIONS FIGURE PAGE 1.1 Teleoroentgenographic and Orthoroentgenographic ex-posure techniques 4 2.1 A x i a l r e l a t i o n s h i p s of the shaft of the femur 10 2.2 A x i a l r e l a t i o n s h i p s of the hip j o i n t 10 2.3 Cartilage space at knee j o i n t of new born infant 12 2.4 Osseous changes i n the knee with age i n the male and female 14 2.5 Normal v a r i a t i o n s i n the s i z e and configuration of the anterior t i b i a l process 15 2.6 Trabecular patterns of the neck of the femur 16 2.7 Modelling the psychophysical error components 19 2.8 Parameters a f f e c t i n g image c l a r i t y 20 2.9 C h a r a c t e r i s t i c (H & D) curve 23 2.10 Film transmission x r e l a t i v e exposure 23 2.11 Diagrams for geometric analysis of 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 of the MTF 33 2.14 Mach phenomenon 36 3.1-J Photograph of the apparatus used to simulated leg p o s i -t i o n i n g errors 39 3.2 Top view of one end of p l e x i g l a s s bar showing the wire markers 40 3.3 Top view of x-ray tube cap frame 41 3.4 Measurements on the roentgenographic 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 plate 44 3.6 A x i a l r e l a t i o n s h i p s at the bone extremities 50 v i i 4.1 Histogram of o r i g i n a l d i g i t i z e d radiogram 56 4.2 Histogram af t e r logarithmic conversion 56 4.3 Ideal and actual commulative d i s t r i b u t i o n functions.... 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 correction 58 4.6 Histogram af t e r smoothing & p i x e l s r e d i s t r i b u t i o n 58 4.7 Picture of o r i g i n a l d i g i t i z e d femur's radiogram 58 4.8 Radiogram af t e r logarithmic conversion 62 4.9 Radiogram a f t e r histogram equaliz a t i o n 62 4.10 Radiogram a f t e r gamma correction 62 4.11 Radiogram af t e r smoothing & p i x e l s r e d i s t r i b u t i o n 62 4.12 Magnitude transform space i n u-d i r e c t i o n 65 4.13 Magnitude transform space i n v - d i r e c t i o n 65 4.14 R o l l - o f f functions of low-pass prototypes 67 4.15 The two functions G(f) & K(f) used to generate the pro-posed f i l t e r response Hg(f)....• 66 4.16 E f f e c t of high-emphasis f i l t r a t i o n on i d e a l edge 69 4.17 Comparison of the weight functions of f i l t e r s HlZ,H and H £ 69 6 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 af t e r Gaussian 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 s f i l t e r i n g ( f c = 0.1071, f = 0.357, a = 1.0) 72 4.21 Radiogram a f t e r H, f i l t e r i n g (f = 0.1071, f = 0.357, a = 4.0) 72 4.22 Histogram of radiogram a f t e r Gaussian f i l t e r i n g 73 4.23 Histogram of radiogram a f t e r H 5 f i l t e r i n g 73 4.24 Histogram of radiogram a f t e r non-linear f i l t e r i n g 73 v i i i 4.25 CDF of Gaussian, non-linear and H 5 f i l t e r e d images 73 4.26 Contrast enhanced version of F i g . (4.18) 75 4.27 Contrast enhanced version of F i g . (4.19) 75 4.28 Contrast enhanced version of F i g . (4.20) 75 4.29 Contrast enhanced version 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 f i l t e r i n g ( f c = 0.3213, f = 0.0714, a = 2.0) 77 4.33 Radiograms a f t e r H f i l t e r i n g (f = 0.2856, f = 0.0357, a = 4.0) c. 77 4.34 Block diagram of non-linear f i l t e r i n g process 78 5.1 Block diagram of p i c t o r i a l pattern recognition 82 5.2 Edge detector 83 5.3 T y p i c a l edge configurations 85 5.4 Intensity p r o f i l e s of 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 tracing without Gaussian weighing function 94 5.6.b Contour tracing using Gaussian weight with cr = 2.0 94 5.6.c False contour due to lack of edge points at condyles 94 5.6.d Complete trace of c h i l d ' s femur 94 6.1 Photograph of the data a c q u i s i t i o n system 9 7 6.2 Data a q u i s i t i o n system organization 100 6.3 Photograph of an out-of-focus edge t r a n s i t i o n 106 6.4 Photograph of an in-focus edge t r a n s i t i o n 106 6.5 Flow chart of the routine PIPLN9 112 i x LIST OF TABLES TABLE PAGE 2.1 Normal degrees of anteversion of the femoral neck 11 3.1 E f f e c t of r o t a t i o n on the femur radiogram 45 3.2 E f f e c t of beam center l o c a t i o n on the femur radiogram ... 46 3.3 E f f e c t of beam height on the femur radiogram 47 3.4 E f f e c t of Lufkin 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 i t y . 51 4.1 Redundancy i n radiograms a f t e r p r e f i l t e r i n g contrast enhancement 61 4.2 Gaussian High-Emphasis f i l t e r i n g parameters 78 4.3 H,. High-Emphasis f i l t e r i n g parameters 78 ACKNOWLEDGEMENT The i n t e r e s t , advice and encouragement that I have received from my supervisor, Dr. G.B. Anderson, throughout the research and w r i t i n g of this thesis i s greatly appreciated. I would l i k e to express my sincere gratitude to Dr. A.E. Burgess of the Department of Diagnostic Radiology, Faculty of Medicine, University of B r i t i s h Columbia for the time and e f f o r t he devoted to the preparation of the radiograms used i n this research, and for his h e l p f u l suggestions and comments. I would also l i k e to thank my f r i e n d Mr. M.E. Koombes for providing the software for d i s p l a y i n g p i c t u r e s , for designing and wiring part of the hardware and f o r his expert guidance and advice. I am indebted to Drs. G.E. Trueman and J.P. Gofton of the Faculty of Medicine, University of B r i t i s h Columbia for t h e i r help and encourage-ment, and to Dr. D. Ozonoff of the Department of Radiology, Harvard Medi-c a l School, Boston and Dr. E.L. H a l l of the Department of E l e c t r i c a l Engineering, University of Southern C a l i f o r n i a for t h e i r generous and stimulating correspondence. I would also l i k e to thank the following people for t h e i r c o n t r i -butions : Mr. G.E. Austin f o r many h e l p f u l discussions, Mr. H.H. Black f o r preparing many photographs and s l i d e s , Mr. G.F. Brocklesby for b u i l d i n g the mechanical stage 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 for her patient and e f f i c i e n t typing of the thesis. Many thanks to a l l my colleagues at the E.E. Department, par-t i c u l a r l y my friends Mr. J.A. McEwen and Mr. W.P. A l s i p for invaluable encouragement and assistance. x i TO MY PARENTS 1 CHAPTER 1  INTRODUCTION 1. 1 - Problem Formulation.: The measurement of children's bone lengths from roentgeno-grams of the extremities has been routinely used since 1935 to answer many questions about the pattern of long-bone growth; how growth d i f f e r s i n boys and g i r l s , what vari a t i o n s e x i s t i n bodily proportions, and how bodily proportions change with growth and age. Also, i n planning the correction of i n e q u a l i t y of growth i n the lower extremities, i t has proved h e l p f u l to observe s e r i a l changes i n the lengths of the patient's long bones r e l a t i v e to the t y p i c a l normal values for child r e n of the same age and sex {1}. Moreover, the assessment of past growth abnormality and of future growth p o t e n t i a l i n i n d i v i d u a l patients i s considerably enhanced by charting the ch i l d ' s progress against a reference standard. Maresh [2] determined the length of the tubular bones i n healthy subjects from age 2 months to 18 years. One should consult his tables published i n 1955 for comprehensive and d e t a i l e d s t a t i s -t i c a l treatment of normal growth i n length of the tubular bones. The roentgenographic technique i s as follows ([3^: In infancy and early childhood years measurements could not include u n o s s i f i e d and there- fore i n v i s i b l e epiphyses. Length measurements were made between the  epiphyseal plates i n the long axis of the bone. In the preadolescent and l a t e r years, i t seemed advisable to include the o s s i f i e d epiphyses, and again measurements were made i n the simplest possible manner -2 along the long axis of the bone from the proximal edge of the upper  epiphysis to the most d i s t a l edge of the lower epiphysis of that bone, to the nearest 0.5 mm with a Lufkin s t e e l r u l e r . There are, therefore, two sets of data: (1) measurements from the 1st x-ray examination at 2 months of age and ending at an a r b i t r a r y age of 12 years f o r the infancy and childhood years, and (2) those measurements which include the epiphyses and were measured from an a r b i t r a r y age of 10 years to f u l l bone growth i n length, usually to 16 or 17 years i n g i r l s and to 17 or 18 years i n boys. No cor r e c t i o n of the measurements has been made for image d i s t o r t i o n . Maresh calculated the magnification from roentgeno-grams of dried bone specimens of i n f a n t s , children and adults as between 1.0 and 1.5% of the t o t a l bone length at a f o c a l f i l m distance of 7 1/2 f t . (2.3 m) with the bone i n d i r e c t contact with the cassette surface. 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 distance i n the l i v i n g s tate, varies con-siderably from areas such as the femoral neck and head, where i n chubby adol-escents the distance my be. from as much as 10 cm to the cassette surface to as l i t t l e as 1 cm for the distance from the lower end of the radius to the cassette.' These measurements are, therefore, equivalent of s i z e , rather than true ana-tomical lengths. On the other hand, the use of high speed screens would s a c r i f i c e some of the f i n e r d e t a i l s of bone structure i n the i n t e r e s t of speed. Green and Anderson i [ l ] , {4 ] published tables for the average lengths of the femur and t i b i a f o r boys and g i r l s together with cer-t a i n figures which describe the d i s t r i b u t i o n of the observed values around the mean at each age. These tables are valuable i n determin-ing the r e l a t i v e length of the bones of a p a r t i c u l a r c h i l d i n r e -3 l a t i o n to the expected d i s t r i b u t i o n for h i s chronological age and ske l e t e c a l age, and they are of assistance i n estimating the future growth of the i n d i v i d u a l bone a f t e r a given age and as an ai d i n pre-d i c t i n g the e f f e c t from epiphyseal a r r e s t . I f the patient's bones are long f o r h i s age and a l l the other factors are equal, he may be expected to require more correction than an individual-with-shorter bones. As i n Maresh's tables, the roentgenograms of the younger chil d r e n i n th i s series were teleoroentgenograms, made with one ex- posure of an en t i r e bone on a sing l e f i l m at a 6 - f t . tube - to -f i l m distance. On the other hand, orthoroentgenograms were made of the lower extremities of the older c h i l d r e n employing a three exposure technique, focusing successively over h i p , knee & ankle: Femur length was recorded as the distance from the proximal a r t i c u l a t i n g surface of the c a p i t a l epiphysis to the most d i s t a l point on the l a t e r a l condyle. T i b i a length was recorded as the most d i s t a l mid-point of a l i n e drawn across the proximal condyles to the mid-point of the d i s t a l a r t i c u l a t i n g surface. The accuracy of these measurements i s discussed i n the following section. 4 Teleoroeritgeriograpliy arid Orthoroentgenography ( F i g . (1.1)): \ Length of X-ray shadow ' (a) Teleroentgenography (b) Orthoroentgenography F i g . (1.1) Teleoroentgenographic and Orthoroentgenographic Exposure Techniques Both t e l e o - and orthoroentgenography produce measurement inaccuracies. However, i n orthoroentgenography, because only perpendicular rays are direct e d at the ends of the long bones, magnification of length i s minimized, and v i s u a l i z a t i o n of each undistorted epiphyseal l i n e i s po s s i b l e . The two methods w i l l be compared s t r i c t l y to demonstrate two fac t s concerning magnification ( a l l other sources of er r o r ignored): (a) orthoroentgenography i s somewhat inaccurate, (b) teleoroentgenography as compared to the former method (considered f a i r l y accurate by r a d i o l o g i s t s ) proves to give very erroneous measurements. 5 (a) Some d i s t o r t i o n i n length can occur i n the orthoroentgenogram i f the tube i s not centered over the end of the bone. Even i f p e r f e c t l y centered, s l i g h t shortening would occur i f the bone were not p a r a l l e l to the f i l m . In the femur a minimal amount of shortening must occur due to the oblique p o s i t i o n of the bone. This could be corrected by elevating the knee and ankle to the same l e v e l as the head of the femur. Such a procedure, however, i s undesirable as i t would lead to loss of bone d e t a i l due to the increased distance of the target from the f i l m . (b) In teleoroentgenography the divergence of the rays from the tube produces considerable magnification. The amount of magnification i s v a r i a b l e , depending upon the length of the bone, the distance of the bone from the f i l m , and the centering of the tube. I f t e l e r o e n t -genograms are used for s e r i a l measurements of growth, then a v a r i a b l e d i s t o r t i o n arises which makes them unsatisfactory, since the magnifi-cation becomes greater with the growth of the i n d i v i d u a l . This i n -creased d i s t o r t i o n i s produced both by the increase i n the bone - to -f i l m distance, r e s u l t i n g from the thickening of the p o s t e r i o r s t r u c -tures, and by the increased length of the bones themselves, which places the bone ends nearer the periphery of the diverging roentgen-o g r aphs beam. As reported by Green & Anderson [4] the measurements from orthoroentgenograms show l i t t l e deviation from the r e a l length of bones. Orthoroentgenographic measurement of a dissected adult femur, 45.7 cms long, gave a length of 45.5 cms; that of an adult t i b i a , 37.0 cms long was 37.0 by orthoroentgenogram. The lengths of these 6 bones, as recorded on a teleoroentgenogram centered at the knee were 49.2 cms for the femur and 38.5 cms for the t i b i a ! 1. 2 - Research organization: The present study has been motivated by the above discus-s i o n . The length measurement of bones by radiography is. complicated, the outcome being influenced by many factors including the po s i t i o n i n g of a patient at the time the x-raying i s performed, the a b i l i t y of the technician to choose the correct x-ray exposure parameters, the c l a r i t y of the radiogram used for length evaluation, the psychophysics of v i s i o n and i t s influence on perceiving relevant d e t a i l s , etc.. . Our approach to the problem was to f i r s t i s o l a t e a l l the factors that would seemingly contribute to an error i n measurement, to assess the magnitudes of t h e i r respective contributions to e r r o r , and, f i n a l l y , i f pronounced enough, to suggest methods for correcting or eliminating these sources of er r o r . In chapter I I , a thorough discussion of the geometric structure and radiographic c h a r a c t e r i s t i c s of long l e g bones i s con-ducted. A x i a l r e l a t i o n s h i p s & patterns of growth are also i n v e s t i -gated. Part II of the same chapter i s an o v e r a l l review of the psychophysical factors i n f l u e n c i n g the outcome of the x-ray imaging system, while part I I I i s concerned with the e f f e c t of the search behaviour on accurate and consistant 'reading' of a radiogram. In chapter I I I , we inve s t i g a t e the e f f e c t of the patient's p o s i t i o n i n g with respect to the x-ray tube on the o v e r a l l length measurement. A phantom bone i s used to obtain a s e r i e s of exposures, 7 through which the bone i s rotated and i n c l i n e d , and the beam center and height are varied; 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 length. Also, i t i s shown how the placing of the measuring r u l e r underneath the c h i l d ' s leg to measure his bone length 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 located. In chapter IV we attempt to solve the problem of the radioluscency of the bony c a r t i l a g e a t t n e j o i n t s i n infants and i t s great e f f e c t on length measurement. This i s done by using a non-routine radiographic technique where very low energy x-rays are used to accentuate the contrast between the cartilage- , and the muscle and fa t . The r e s u l t i n g image i s then processed to enhance x-ray contrast r a t i o s and the v i s i b i l i t y of contours of the epiphyses. A f t e r processing for x-ray image enhancement, an edge detection - contour"tracing algorithm i s proposed i n chapter V to follow the borders of the bone, thereby accentuating the edges and s i n g l i n g out the bone from i t s noisy background. Chapter VI contains a general d e s c r i p t i o n of the data a c q u i s i t i o n system. This includes a block diagram of the system organization, a review of i t s resolving c a p a b i l i t i e s and noise l i m i -t a t i o n s , and f i n a l l y the software established to operate the system and to transf e r data between the PDP-9 and the IBM system 370/67, and the PDP-9 and the DATA GEN 840A for picture display. 8 CHAPTER 2 The P h y s i o l o g i c a l , Psychophysical and Psychological  Aspects of the Problem of Measurement Errors  of Long Leg Bones i n Children 2.1 - Introduction Many factors can a f f e c t the f i n a l estimate of a bone length, yet the i n d i v i d u a l contributions of each of these has been l a r g e l y unknown. There are many reasons for t h i s . The geometrical character-i s t i c s of the bone are far from being e a s i l y formulated mathematically and misalignments i n making a radiogram lead to varying radiographic patterns since we only see the projections of tissues of d i f f e r e n t den-s i t i e s on a two-dimensional sensor. Also the v i s i b i l i t y of d e t a i l s , borders and other features i n the image i t s e l f i s a function of parameters of 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 of processing by the peripheral human nervous system, each of which have a rather well-defined p h y s i c a l characterization that corresponds c l o s e l y to the experimental s i t u a t i o n [18]. F i n a l l y , the unconscious cognitive process and the conscious decision-making, affected by t r a i n i n g and other complex i n t e r a c t i o n between v i s u a l and non-visual f a c t o r s , w i l l ultimately have a f i n a l e f f e c t on the magnitude of the error i n the length estimation. Our approach to i s o l a t i n g the error contributors w i l l involve the following general aspects of the problem: a - P h y s i o l o g i c a l - the geometric modelling of the bone, i t s angular re l a t i o n s h i p s and i t s changing, radiographic pat-terns i n children due to growth. 9 b - Psychophysical - the factors a f f e c t i n g the 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 im-pose on the peripheral nervous system's cognitive c a p a b i l i t y . c - Psychological - t h i s r e l a t e s to the fac t that there i s prac-t i c a l l y no 'unbiased' estimation of the bone length from a radiogram. This i s b a s i c a l l y be-cause many percept formation rules are non-visual and include t h e o r e t i c a l deduction from c l i n i c a l h i s t o r y or previous experience with the same or s i m i l a r patients. The rest of this chapter i s dedicated to the discussion of the sources of the above-mentioned types of e r r o r s . 2.2 - P h y s i o l o g i c a l Errors 2.2.1 - Geometric and Radiographic Description of Long Leg  Bones i n Children i ) The Femur: The femur i s the largest and longest bone i n the skeleton. The head of the femur i s a smooth, hemispherical structure, and i t s shaft i s rather c y l i n d r i c a l . The a x i a l relationships of the femur are depicted i n Figs. (2.1) and (2.2) and are describable as follows: (a) The medio-lateral angle which the neck forms with the shaft of the femur measures about 160° at b i r t h ; i n the adult, i t varies between 110° and 140° (approximately-r125° on the average). (b) The neck i s anteverted with respect to the shaft, which l i k e -wise v a r i e s with the age of the i n d i v i d u a l as indicated i n Table (2.1). Axis of Femur Shaft Axis of •Neck of Femur Axis of the -Femora! Condyles u^'1000 I V-i/5"- 20' I *i\approx. 170' i Axis of the Lower Shaft F i g . (2.1) A x i a l Relationships of the Shaft of the Femur Fi g . (2.2) A x i a l Relationships of the Hip J o i n t 11 This angle may measure as much as 50 degrees at b i r t h and diminishes to about 8 degrees i n the adult. Table (2.1) Normal Degrees of Anteversion of the Femoral Neck (Average's''adapted from several investigators [5]) AGE ANTEVERSION (DEGREES) B i r t h to 1 Year 30 - 50 2 years 30 3 - 5 25 6 - 1 2 20 12 - 15 17 16 - 20 11 Greater than 20 8 (c) A l i n e drawn through the lowermost margins of the femoral condyles forms an angle of 10° with the perpendicular (or 100° with the axis of the s h a f t ) . (d) There i s a s l i g h t anterior bowing of the shaft of the femur, so that the axis of the upper two thirds of the shaft of the femur forms an angle of 170° with the axis of the lower one t h i r d of the shaft of the femur, and t h i s l a t t e r axis i s continuous with that of the l e g i n the extended p o s i t i o n . (e) A h o r i z o n t a l l i n e drawn perpendicular to the axis of the shaft of the femur through the uppermost margin of the greater trochanter should pass through through or below the fovea c e n t r a l i s of the head of the femur (Skinner's l i n e ) . F i n a l l y , an important remark concerning the femur i s that the 12 d i s t a l epiphysis of the femur during i t s development may take on a very  markedly i r r e g u l a r appearance. Also, t h i s epiphysis may appear ra d i o -lucent i n part. This i s a normal v a r i a n t . As pointed out i n references [7] and [2], i n infancy and c h i l d -hood years measurements could not include u n o s s i f i e d and therefore i n v i s -i b l e epiphyses. As shown i n the schematic diagram of F i g . (2.3), the c a r t i l a g e space between the ends of the opposing bones at the knee j o i n t of a new born i n f a n t i s radiolucent. This space i s occupied by a shadow of water density i n the roentgenogram. In the drawing, t h i s space i s shown to be f i l l e d completely by the epiphyseal c a r t i l a g e s and t h e i r overlying a r t i c u l a r c a r t i l a g e s . Tibial Epiphyseal Cartilage F i g . 2.3 Cartilage Space at knee j o i n t of new born i n f a n t 13 The osseous changes i n the knee with age i n the male and female are shown i n F i g . (2.4). i i ) The T i b i a : The upper end of the t i b i a contains the medial and l a t -e r a l condyles which a r t i c u l a t e with the corresponding condyles of the femur. A n t e r i o r l y , the condyles meet to form the tuberosity of the t i b i a . This snout-like t i b i a l tuberosity which projects from the anterior sur-face of the proximal epiphysis and hangs down i n front of the shaft i s an extremely v a r i a b l e structure 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 to degenerative changes during the- growth period [5].' Not infrequently, the tuberosity w i l l appear d i f f e r e n t on the two sides. The shaft of the t i b i a has a prominent crest (the anterior crest) a n t e r i o r l y i n i t s upper two t h i r d s , which gradually extends medi-a l l y towards the medial malleolus. The l a t e r a l border of the t i b i a forms the interosseous c r e s t . In a f u l l front 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 walls are approximately equal i n thickness. In a 10° and 15° ro t a t i o n r e s p e c t i v e l y , the l a t e r a l c o r t i c a l w a l l becomes progressively t h i c k e r . The thickening i s due to the f a c t that the ante-r i o r t i b i a l crest comes progressively more into p r o f i l e on the l a t e r a l edge of the shaft as the t i b i a i s rotated e x t e r n a l l y . This phenomenon cannot be demonstrated roentgenographically during the f i r s t years of l i f e , however. [Roentgenograms are shown i n F i g . 8-186, Ref. 6, p. 934]. The upper margin of the i n t e r o s s e a l crest i s frequently of a le s s e r density than the remainder of t h i s ridge and simulates a p e r i o s t a l elevation or thickening. This appearance i s normal. There i s a s l i g h t normal curvature 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 MOS. O, 7.5 MOS. 9, I YR. 9,15 MOS. y r \7 [ if <J,Z Y K o . C f , ci Y K S . O " , 3.5 Y ' H S . 0\4.5 Y R S . O" , 5.b Y K i i . 9,1.8 YRS. 9, 2.3 YRS. 9, 2.7 YRS. 9, 3.5 YRS. 9, 4.6 YRS. i l l ' ' ' l l I 1 1 ) ' ' ! !_!_! ! i U ! _ J 1 d\9YRS. C>\ 13 YRS. d\ 18 YRS. 9,7 YRS. 9 , 10 YRS. 9, 15.5 YRS. F i g . (2.4) Osseous changes i n the knee with age i n the male and female (Ref. [5]) . 15 F i g . (2.5) Normal Variations i n the Size and Configuration of the A n t e r i o r T i b i a l Process amongst Individuals 2.2.2 - Trabecular Patterns In any bone there are two major groups of trabeculae: the r e l a t i v e l y broad t r a j e c t o r y trabeculae or primary trabeculae which are concerned with support, weight bearing and r e s i s t i n g s t a t i c d i s t o r t i o n along major l i n e s or torce and s t r e s s ; and tne intervening f i n e mesh trabeculae (secondary trabeculae) which add further strength to the main trabeculae and permit absorption of complex stresses i n terms of changing dynamic pressures applied through mobile j o i n t surfaces. In areas where major d i r e c t i o n a l stresses can be w e l l defined, such as the c a l c a r fem-o r a l , major t r a j e c t o r y trabeculae can be observed. Where stresses of weight bearing and muscle p u l l are constantly subjected to changing f o r c e s , such as at j o i n t surfaces and bone ends, f i n e trabeculae predominate. Since both the coarse t r a j e c t o r y and the f i n e cross bracing trabeculae are concerned with the same basic supporting function, dynamic a l t e r -ations i n both represent responses to mechanical demands and metabolic v a r i a t i o n s i n health and disease [8]. The appearance of the trabeculae i n an antero-posterior 6 roentgenogram of the neck of the 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 trabeculae, Area 2 i s the secondary transverse group, and Area W i s the Ward's t r i a n g l e . F i g . (2.6) Trabecular Patterns of the Neck of the Femur 2.2.3 - Anatomical Structure Errors From the above b r i e f d i s c u s s i o n , we can conclude that there are mainly two anatomical factors that a f f e c t accurate bone measurement; these are: 1 - The radioluscency 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 anatomical structure of the l e g bones. The f i r s t f a c t o r i s accentuated by the f a c t that as the c h i l d grows, more osteoblasts are formed adding length to the opaque c a l c i f i e d s haft. In assessing the c h i l d ' s bone elongation a f t e r s e v e r a l months, an inescapable e r r o r w i l l occur due to the f a c t that the d i f f e r e n c e i n 17 length between the two measured bones w i l l be the sum of two e n t i t i e s : the natural bone growth, and the extra length that i s no longer radio-luscent i n the radiogram due to 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 anatomical bone stru c t u r e , could a f f e c t the measurement i n many ways. The neck anteversion, for example, would ne c e s s a r i l y a l t e r the measurement because i t s magnitude changes over the years, hence disturbing the perspective relationships i n the bone and consequently changing the magnification r a t i o s that ultimately control the measured length. The same e f f e c t w i l l occur i f the leg i s s l i g h t l y rotated with respect to a previous p o s i t i o n i n g when taking the radiogram. On the other hand, the measurement could be af-fected at the femoral d i s t a l epiphysis and the t i b i a l proximal epiphysis, for example, due to t h e i r highly i r r e g u l a r development pattern i n early childhood. From the above dis cuss ion, we _are le.dw t^o. investigate the follow-ing : 1 - The p o s s i b i l i t y of r e g i s t e r i n g and accentuating the contrast between the unossified epiphyses and the surrounding medium (muscle and f a t ) . This i s done i n Chapter IV with considerable success. 2 - The magnitude of the error caused by varying the r e l a t i v e p o s i -tions of the x-ray tube and the bone. The res u l t s of such an i n v e s t i g a -t i o n are discussed i n Chapter I I I . 3 - The implications of subjective estimation of the bone axis l o c a -t i o n when producing a radiogram on the angular r e l a t i o n s h i p s described above and on the o v e r a l l bone length. This i s also treated i n Chapter I I I . 18 2.3- Psychophysical Errors In order to be useful to the r a d i o l o g i s t , c l i n i c a l l y s i g n i f i c a n t features i n the patient must be transformed into corresponding two dimen-s i o n a l projections i n the x-ray image. The "x-ray imaging system", com-prised of the x-ray source, relevant p h y s i c a l properties of the patient, recording medium, and viewing mode, a f f e c t s t h i s transformation. C l e a r l y , any technical inadequacy i n the system which r e s u l t s i n the nonregistra-t i o n of useful information w i l l adversely a f f e c t the performance of the r a d i o l o g i s t . The imaging system cannot be considered i n i s o l a t i o n from i t s i n t e r f a c e with the human observer. O p t i c a l properties of 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 parameters of the perip h e r a l and low-level c e n t r a l nervous system a f f e c t perception.of.the image. Thus, i f a good radiograph i s transilluminated with u l t r a - v i o l e t l i g h t , the information recorded on the f i l m w i l l remain i n a c c e s s i b l e to the r a d i o l o g i s t . What i s at stake, then, i s not only the passing of the desired information over a l l the l i n k s i n the x-ray imaging system i t s e l f , but also to and through the human v i s u a l receiver (see Fi g . (2.7)) The psychophysical error w i l l be studied then i n the context of i t s following two general sources: image c l a r i t y , and properties of the human v i s u a l system (HVS). 2.3.1 - Image C l a r i t y The term 'image c l a r i t y ' i s used to describe the v i s i b i l i t y of 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 radiograph. Two basic factors determine the c l a r i t y of the radiographic image: contrast and image qu a l i t y . Figure (2.8) i s a d e t a i l e d tree structure of the parameters X-RAY FILM TRANSILLUMINATION PERIPHERAL NERVOUS SYSTEM 1 ~1 1 adaptive \ ! ! 1 brightness \ characteristics of retinal receptors, optical properties of the eye r~ - i poor contrast unsharpness limited resolution I _ ] Brightness Levels , Contours TO CNS X-RAY IMAGING SYSTEM Fig. (2.7) Modelling the psychophysical error components IMAGE CLARITY I CONTRAST r T SUBJECT CONTRAST FILM CONTRAST 1- Thickness Differences 2- Density Difference 3- Atomic Number Difference 4- Radiation Quality 1- C h a r a c t e r i s t i c Curve 2- Density 3- Screen or Direct Exposure 4- Film Processing FOG AND SCATTER 1 IMAGE QUALITY r RADIOGRAPHIC MOTTLE SHARPNESS Screen Mottle Structure Mottle Quantum Mottle Film Graininess RESOLUTION I MTF PTF 1- Geometric Unsharpness 2- Motion Unsharpness 3- Absorption Unsharpness 4- Screen Unsharpness 5- Parallax Unsharpness Fi g . (2.8) Parameters Affecting 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 following i s a b r i e f discussion of the most important of these parameters. 2.3.1.a - Contrast The term radiographic contrast r e f e r s to the difference i n density between areas i n the radiograph and depends on subject contrast, f i l m contrast and fog and s c a t t e r . 1 - Subject Contrast: Subject contrast i s the difference i n x-ray i n t e n s i t y transmitted through one part of the subject compared to that through another part. I t depends upon thickness d i f f e r e n c e , density 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) and atomic number di f f e r e n c e . The f i r s t three of these factors are c l a s s i c a l . The fourth f a c t o r , however, w i l l be further elaborated because of i t s importance to our work i n Chapter IV. In diagnostic 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 contribution to sub-j e c t contrast. Photoelectric absorption i s increased i n substances with high atomic•.numbers, e s p e c i a l l y when low-KVp x-rays are used. The ap-proximate atomic numbers of bone, muscle and f a t are: Bone 13.8 Muscle 7.4 Fat 5.9 Muscle and f a t , with l i t t l e difference i n t h e i r atomic number, show l i t t l e difference i n t h e i r a b i l i t y to attenuate x-rays by the pho-t o e l e c t r i c absorption process. Use of very low KVp (below 30) x-rays produces the greatest possible difference i n p h o t o e l e c t r i c x-ray ab-sorption between muscle and f a t . S o f t - t i s s u e radiography, such as mam-22 mography, requires the use of very low KVp x-rays because the small d i f -ferences i n atomic number between breast tissues produce no subject con-t r a s t unless maximum photoelectric e f f e c t i s used. 2 - Film Contrast: The information content of the i n v i s i b l e , latent x-ray image ( the pattern of varying i n t e n s i t y of the x-ray beam caused by d i f f e r e n t i a l attenuation of x-rays by the subject ) i s "decoded" by the x-ray f i l m into a pattern of v a r i a t i o n s i n o p t i c a l density which determine f i l m contrast. This pattern depends on four f a c t o r s ; s e n s i t -ometric properties of the f i l m , exposure (MAS) , the use of i n t e n s i f y i n g screens, and f i l m processing. The l a s t three factors w i l l not be elaborated here because they were not taken into account i n our work. The sensitometric properties of the f i l m , on the other hand need be considered. The r e l a t i o n s h i p between the density produced on a f i l m and the exposure i t receives i s p l o t t e d as a curve known as the c h a r a c t e r i s t i c curve, F i g . (2-9). Observe that x-ray films w i l l c h a r a c t e r i s t i c a l l y generate harmonic d i s t o r t i o n since the transmitted l i g h t of an exposed and processed f i l m i s quite non-linear with respect to the i n t e n s i t y of the film's exposing r a d i a t i o n [21]. Some inve s t i g a t o r s ( f o r example [12]) have taken this into account and produced radiographs with peak densities between 0.5 and 1 density units for research purposes. I f any n o n - l i n -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 observed, they would correct den-? sitometric readings to those which would have been obtained with a l i n e a r response. In our research t h i s was not done, mainly because of a lack 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 D curve experimentally. However, i t was necessary to l i m i t our work on radiograms to those where 23 density v a r i a t i o n s were within 0.5 and 2.0 density u n i t s , so as to be able to adequately quantize the radiograms using a 64 l e v e l grey s c a l e . Relative Exposure Relative Exposure F i g . (2.9) Fig.(2.10) 3 - Fog and s c a t t e r : Fog i s s t r i c t l y defined as those s i l v e r h a l i d e grains i n the f i l m emulsion which are developed even though they were not exposed by r a d i a t i o n . This produces unwanted f i l m density, which lowers radiographic contrast. The fog e f f e c t could be eliminated by subtracting i t s density l e v e l from the density of every point on the radiogram. ,A simpler approach was adopted and consists of adjusting an o f f s e t during image quantization to assign to zero i n t e n s i t y any i n t e n s i t y l e v e l de-s i r e d . 24 The e f f e c t of scattered r a d i a t i o n (Compton Scatter) on contrast r a t i o s i n radiograms can be estimated by a simple procedure: Let 1^ be the average r a d i a t i o n i n t e n s i t y of a very narrow beam of r a d i a t i o n emerging from a small segment of a body part and AI^ be the reduction i n this primary i n t e n s i t y as this beam passes through an adja-cent structure of greater density. The r a d i a t i o n contrast CL^  (N s i g n i -f y ing narrow beam) between the two adjacent areas i s then given by the equation: A I. [ P Let us now replace the narrow beam by a broad beam, large enough to cover the ent i r e area of i n t e r e s t ; Let I be the i n t e n s i t y of the scattered r a d i a t i o n reaching the f i l m . The new r a d i a t i o n contrast C L (B s i g n i f y i n g broad beam) w i l l then be given by the equation: a AI CB I + I (2.2) P s and hence CL = B 1 + I /I (2.3) s p The r a t i o I /I depends on the body thickness, tube p o t e n t i a l s p J and f i e l d s i z e , but to a l e s s e r extent i s also influenced by such factors 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 distances between the f o c a l spot, the body part and the f i l m . Seeman [19] has shown that i n the case of chest examination, I /I i s of the order of 2. Morgan s p [20] has shown t h i s r a t i o to range from 4 to 9 f o r s k u l l and abdominal examinations. I t follows that the contrast CL obtained with the f i e l d B 25 sizes normally encountered i n routine chest radiography w i l l be about 35% of the narrow beam contrast C„ and only about 10 - 20% of C, i n the N N case of s k u l l and abdominal procedures. To our knowledge I /I has not been calculated f o r leg radio-° s p grams. However, the s i z e of the beam needed i n teleoroentgenography suggests a poor contrast r a t i o and hence poor feature perception. 2.3.1.b - Image Quality The second basic factor determining image c l a r i t y i s image q u a l i t y . The q u a l i t y of the radiographic image may be defined as the a b i l i t y of the f i l m to record each point i n the object as a point i n the f i l m . Image q u a l i t y i s affected by radiographic mottle, unsharpness and l i m i t e d r e s o l u t i o n . 1 - Radiographic Mottle D e t a i l 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 associated with bone edges, i s reduced by radiographic mottle. Radiographic mottle i s mainly due to quantum mottle, which i s manifested by coarse density fluctuations instead of the i d e a l uniform background on a radiogram, and f i l m graininess, which i s due to the b u i l t - i n random d i s t r i b u t i o n of exposed grains i n the emulsion. Quantum mottle 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 disturbing e f f e c t due to s p a t i a l f l uctuations of x-ray. quanta absorbed i n i n t e n s i f y i n g , screens. 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-t l e . Rossman [22] presented an a n a l y t i c expression for the standard deviation from average density C D ) of a radiogram, taking into account the e f f e c t of the o v e r a l l MTF (Modulation Transfer Function) on l i m i t i n g 26 transmission of high-frequency components. Assuming the average number of x-ray quanta h i t t i n g a unit area i s IT (hence the number absorbed i n some area element 'a' i s n a) and follows a Poisson's d i s t r i b u t i o n , then x the mottle standard deviation w i l l be given by: a(D) = [a 2(D) . + ( . 4 3 G ) 2 = ^ F 2 ] > 0 gram n x a J . (2.4) !0 system unsharp 1 system sharp and G i s the f i l m gradient. We can e a s i l y conclude then that, since i s proportional to the exposure time, any attempt to decrease the exposure time to lessen the e f f e c t of the patient's leg motion w i l l only increase the radiographic mottle. The noise r e s u l t i n g from t h i s mottle i n the radiogram i s not concentrated at the high-frequency end of the spectrum as might be as-sumed from the salt-and-pepper e f f e c t . Rather, the noise i s somewhat evenly d i s t r i b u t e d over a l l frequencies passed by the system. Con-sequently, a simple LPF (Low pass F i l t e r ) cannot remove noise i n many cases and may even r e s u l t i n a poorer image than the o r i g i n a l by pro-ducing a clumping or mottled e f f e c t [23]. 2 - Sharpness Sharpness i s the a b i l i t y of the x-ray f i l m to define an edge. Edge unsharpness may be caused by any or a l l of the following f a c t o r s : a - Absorption Unsharpness b - Screen Unsharpness c - Parallax Unsharpness 27 d - Geometric Unsharpness e - Motion Unsharpness • The f i r s t three factors are commonly understood [49] and w i l l not be • described here/ Geometric and motion unsharpness however are i n t e r e s t i n g to consider. • 0 h e 4 H F i g . (2.11) Diagrams for geometric analysis In the diagrams of F i g . (2.11), the source of r a d i a t i o n i s the target, at l o c a t i o n T, with e f f e c t i v e f o c a l spot s i z e 'a'. The x-ray absorbing object i s at l o c a t i o n 0 and has diameter 'd'. The perpendicular distance from T to 0 i s TO. The shadow image cast on the f i l m at l o c a t i o n F has o v e r a l l s i z e 's' and may be divided up i n t o two segments: ' i ' . i s the width of the magnified image of the object due to a point source of r a d i a t i o n at T, and 'e' the s i z e of the geometric error due to the d e v i -ation of the f o c a l spot from a point source. This geometric d i v i s i o n 28 can be generalized to high magnification more meaningfully than the v i s u a l separation into umbra and penumbra. The magnification f a c t o r , m, i s defined as the r a t i o of the s i z e of the magnified image, i , to the object s i z e , d, or m = i / d i = md If 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 evident that: i / d = TF/TO m = TF/TO e/a = OF/TO Substituting OF = TF - TO and solving f o r 'e' gives e = a(m - 1) (2.5) Since s== i + e, therefore s = md + a(m - 1) (2.6) One, of course, can write down these two equations automatically by considering a pinhole 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 of correction needed i n conjunction with teleoroentgenography due to penumbral shadows alone. Also, we observe that i f 'd' i s much smaller 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 ( Fig. (2.11.c)). This e f f e c t might show at the knee j o i n t radiogram, because of the markedly i r r e g u -l a r shape at the proximal end of the t i b i a . Here, the intercondyloid eminence together with the l a t e r a l and medial condylar surfaces w i l l be projected into a rather b l u r r e d region. The f o c a l spot may even appear on a double penumbra and hence propose f a l s e contours. These contours are enhanced, or rather contrast i s enhanced at these penumbral regions of the f o c a l spot because of 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 target. We w i l l reconsider t h i s l a t e r i n conjunction 29 with the l i n e spread function. The nature and configuration 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 explained as follows: Effective J^_J Focal Spot *- sail F i g . (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-ray beam Fig. (2.12) shows the rectangular d i s t r i b u t i o n of r a d i a t i o n emission from e l e c t r o n bombardment of a t y p i c a l r o t a t i n g anode. Note that the cup surrounding the filament focuses the electrons so that there i s a zone of decreased e l e c t r o n density i n the middle. This 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, preventing the development of a central hot spot. The o v e r a l l width of the r a d i a t i o n zone i s also due to the focusing c h a r a c t e r i s t i c s of the cup and i s the e f f e c t i v e width of the f o c a l spot i t s e l f . Since the anode surface angle i s considerably l e s s than 45°, the rectangular r a d i a t i o n zone i s foreshortened; the e f f e c t i v e shape i s designed to be as nearly square as possible. The dimension of the e f f e c t i v e f o c a l spot i n the cathode-anode axis i s therefore a function of the length of the filament and the angulation of the anode surface. How uniformly r a d i a t i o n i s d i s -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 of anode angulation 30 (heel e f f e c t ) and whether there i s any focusing of the electrons by the ends of the cup, j u s t as the sharpness of the two bands of high r a d i a t i o n i n t e n s i t y depends on the focusing by the sides of the cup. A pinhole image of the f o c a l spot, i f not overexposed, w i l l c l e a r l y show the double source of r a d i a t i o n [26]. Motion Unsharpness: Subject motion af f e c t s both the sharpness of image edges and the o v e r a l l system r e s o l u t i o n . Morgan [13] has shown that the MTF (see next section) due to object motion i s given by the equation: s i n T f 0 v t MTF = T T T f D V t where f (cycles/mm) i s the s p a t i a l frequency of a t e s t object of s i n u -s o i d a l transmission, v (mm/second) i s the v e l o c i t y of motion and t (sec-onds) i s the time of exposure. I f the product vt i s less than 0.1 mm, we can s a f e l y neglect motion unsharpness. 3 - Resolution The resolving power of a system can be defined as i t s a b i l i t y to record separate images of close objects. Resolution i s most conven-i e n t l y expressed i n terms of the system modulation transfer function (MTF). In the following we b r i e f l y explain t h i s e n t i t y . A s i n u s o i d a l t e s t object i s defined as one whose x-ray trans-mission varies s i n u s o i d a l l y with distance along one axis and i s constant i n a d i r e c t i o n perpendicular to t h i s axis. I f a beam of r a d i a t i o n , a r i s -ing from a point source, i s transmitted through the test object, the var-i a t i o n of i n t e n s i t y I(x) on an "image plane" may be described by the equation: 31 I(x) = I Q + l£ cos(2Trf ±x) (2.7) Where I 0 i s the mean i n t e n s i t y of the r a d i a t i o n , I* i s the modulation amplitude, x i s the distance from some reference point on the image plane i n the d i r e c t i o n of the axis of the test object, and f ^ i s the s p a t i a l frequency of the test object when projected onto the image plane. The x-ray beam diverges uniformly; therefore, the frequency on the image plane, f ^ , i s re l a t e d to the frequency of the tes t object, f Q , by the expression f. = f Q d 1 / ( d 1 + d 2) (2.8) where d 1 i s the focus-to-testr-object distance and d 2 i s the object-to-image distance. In p r a c t i c e , x-rays do not a r i s e from a point source but from an extended source with highly i r r e g u l a r emission. Therefore, the:; r a -d i a t i o n transmitted by the t e s t object 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 that given by equation (2.7) and may be described by the equation I(x) = I 0 + I* M(f) cosUTrf-iX - <f>(f)] ( 2.9) where M(f) i s the modulation transfer function. The term (f>(f) indicates that the maximum and minimum i n t e n s i t i e s may occur at points other than those corresponding to the points of maximum and minimum transmission of the test object. <f>(f) i s c a l l e d the phase transf e r function (PTF)[12]. The MTF has become a widely accepted concept f o r the s p e c i f i -cation of the re s o l u t i o n c a p a b i l i t i e s of e n t i r e r a d i o l o g i c systems, groups of components of a system, and i n d i v i d u a l components i n a system. 32 Morgan [13] derived a t h e o r e t i c a l expression for the MTF of a square f o c a l spot with uniform emission. However, x-ray fo c a l spots are not perfect squares or perfect rectangles, nor do they have uniform emission. Takenaka et 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 of the roentgen f o c a l spot into symmetric and antisymmetric components using a basis of rectangular functions. They standardized the parameters of i t s d i s t r i b u t i o n by i t s MTF and cut-off frequency. However, since x-ray f o c a l spots are generally designed on the line-focus p r i n c i p l e , the s i z e and shape of the projected f o c a l spot vary with the angles of p r o j e c t i o n . Hence the MTF or radiographic r e s o l u t i o n also 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 plane normal to the d i r e c t i o n of the beam. This e f f e c t i s further accentuated by the fa c t that the shape of the f o c a l spot i s quite i r r e g u l a r . Doi [15] indicated that, because the point spread function i s not i s o t r o p i c , one-dimensional MTF's should be determined f o r every d i -r e c t i o n . He also discussed the fact that since the target plane of the x-ray tube i s positioned at an angle a with both the object plane and image plane because of the geometry of the x-ray tube (see F i g . (2.13)), the point spread function of the f o c a l spot on the image plane strongly depends on the f i e l d p o s i t i o n of the image plane. This property i s referred to as the ' f i e l d c h a r a c t e r i s t i c s ' as i n o p t i c s . The MTF of the f o c a l spot which depends on the f i e l d c h a r a c t e r i s t i c s can be determined at some s p e c i f i e d positions by a geometric method. Depending on the values of a and 3, the f i e l d c h a r a c t e r i s t i c s can manifest themselves to a considerable extent. A c t u a l l y , the change i n MTF with a and B i s so 33 pronounced that the question automatically a r i s e s whether there i s an optimal 'target angle that i s x^orth being determined f o r f l a t t e r MTF and better r e s o l u t i o n [25]. The experimental c a l c u l a t i o n of the MTF using o p t i c a l Fourier transformation by Doi [15], and the MTF and PTF using Perrin's equations [16] (Equations (2.10) and (2.11))* by Rao and Bates [12] leads us to * I f the l i n e spread function l(x) of an image-forming system i s known, the MTF, M(f) , and the PTF, <j>(f) can be evaluated using the equations: y X <"? . 1 F T P I H fJiflrflrt-p.ristip.fi o f thp WVV M(f) cos<f>(f) -°°J l(x) cos(2-rrfx) dx -«>;°°l(x) dx (2.10) M(f) sin<J>(f) -<*•' l ( x ) sin(2Tffx) dx -°°J l(x) dx (2.11) 34 the following important conclusions: 1 - The net b l u r r i n g i n a radiogram depends on several b l u r -causing parameters ^ i n .the "image-forming-chain. Part of the.blurring i s 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 (40 1/mm) or the film-screen combination. Another part i s due to the f i n i t e s i z e and shape of the f o c a l spot. 2 - The PTF i s zero only i n the [1.1] d i r e c t i o n (with respect to anode-cathode a x i s ) , where the MTF i s approximately given by a Gaussian function rather than a sampling function. In the other 2 d i r e c t i o n s ([0.1] and [1.0]), the MTF could be neglected below f - 0.4 lines/mm, but the PTF would lead to spurious re s o l u t i o n and interference patterns at higher frequencies. 3 - Relative focal-object and o b j e c t - f i l m distances (or i n other words, magnification) dramatically change the cut-of f frequency. The best r e s o l u t i o n i s obtained with non-magnification imaging [16]. The reader may r e a l i z e at t h i s stage that i t i s impossible for us to compensate for the net image b l u r r i n g caused by unsharpness and l i m i t e d r e s o l v i n g power. Much of the blur i s caused by manufacturing tolerances and the other contributors of technical o r i g i n and hence not measurable. This means that no accurate mathematical model can be constructed that encompasses a l l the image degrading fa c t o r s . Therefore no mathematical scheme can be used to restore the degraded radiographic image, and any attempt to enhance the v i s i b i l i t y of the d e t a i l s therein w i l l be purely experimental and h e u r i s t i c . On the other hand, three p o s i t i v e conclusions can be drawn from the above i n v e s t i g a -t i o n . The v i s u a l cut-off frequency (0.4 1/mm) should be taken i n t o 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 frequency a l i a s i n g . The f i e l d c h a r a c t e r i s t i c s of the f o c a l spot imply minimizing the deviation-from-normal angle 3 as a measure to a t t a i n f l a t t e r MTF. F i n a l l y , as mentioned e a r l i e r , the problem of optimum target angle remains to be investigated. 2.3.2 - Properties of the Human V i s u a l System (HVS) As mentioned before, the x-ray imaging system cannot be consi-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 with the human observer. 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 that forms a pattern of brightness var i a t i o n s and contours that i s recognizable by the peripheral nervous system. The degree of i l l u m i n a t i o n of the x-ray f i l m when viewed for length measurement should be based on a comprehen-sive knowledge of the contrast s e n s i t i v i t y of the eye. Much psycho-phys i c a l research has been directed to measurement of the contrast s e n s i -t i v i t y of the eye. It has been shown that the eye's dynamic range i s about 2.2 log u n i t s , centered about the adapting brightness [31]. This means that varying the adapting brightness over a wide range can make a ce n t r a l target appear to change from completely white to completely black. Other properties of the HVS w i l l be b r i e f l y reviewed, because of t h e i r importance to our work i n Chapter IV. The subjective e f f e c t known as "sharpness" i s more c l o s e l y related to the rendition of edges and objects much larger than those barely v i s i b l e , than i t i s to object o r i e n t a t i o n , l o c a t i o n and texture. The s e n s i t i v i t y of the observer to d i f f e r e n t s p a t i a l frequencies i s also important. Measurements by Lowry and de Palma [32] have shown t h i s 36 s e n s i t i v i t y to peak at middle frequencies (around 10 1/mm). A r e l a t e d e f f e c t i s the subjective enhancement of edge t r a n s i t i o n s due to the so-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 receptors. F i g . (2.14) Mach Phenomenon Along with subjective accentuation of edges goes a remarkable acceptance of a wide range of edge r e n d i t i o n . Edge (c) i n F i g . (2.14) i s also acceptable, but seems l e s s sharp and of lower contrast than edge (a). The best subjective- response i s attained by high-frequency accen-tuation, with a r o l l - o f f slow enough to prevent underdamped overshoot i n the transient response. This property i s used as an important c r i -t e r i o n i n the design of a d i g i t a l f i l t e r f o r edge enhancement i n Chapter IV. A f i n a l aspect of human v i s u a l response f o r us to consider i s the v i s i b i l i t y of radiographic noise. Radiographic images are character-i z e d by t h e i r low Signal to Noise Ratio (S/N) . Takenaka [28] studied S/N r a t i o s and v i s u a l c u t - o f f frequencies i n bones by o p t i c a l and d i g i t a l simulations. S/N was 7.4 db on the average f or acceptable v i s i b i l i t y of d e t a i l s . Selected features were completely obscured at 4.4 db and t o t a l l y 37 discernable at 16.7 db. He estimated by o p t i c a l simulation the average v i s u a l cut-off frequency of complicated radiograms to be 0.53 1/mm. Trabeculations had the highest cut-off frequency (3.8 1/mm). The pres-ence of noise reduces contrast and sharpness i n pictures very s i g n i f i -cantly. Also noise i s generally more v i s i b l e i f i t i s correlated with the picture than i f i t i s random. 2.4- Psychological Errors As mentioned before, "seeing" a radiographic image i s a complex i n t e r a c t i o n between v i s u a l and nonvisual f a c t o r s . The nature of the v i s u a l data has a very strong influence on the ease with which the per-cept formation rules may be applied and the accuracy of the r e s u l t i n g percept. One's a b i l i t y to derive meaning, from raw data ( l i k e ) estimating a bone contour location) can be studied i n the context of the c l a s s i c a l phenomenon of "set" i n psychology and indicates that the expectation of the observer determines, to a much greater extent than he thinks, the possible percepts that may r e s u l t from a given stimulus [18], and hence ultimately influences h i s f i n a l bone measurement accuracy. The mechanism by which the stimulus i s reduced to the- r e s u l t i n g percept i s not.well understood,and hence i t i s - d i f f i c u l t -to construct-s u f f i c i e n t models for analyzing the psychological e f f e c t s on measurement. For a comprehensive study on the nature of these e f f e c t s , the reader i s re f e r r e d to [18], [29], [30], [43] and [44]. 38 Chapter 3 An Analysis of Errors i n the Radiographic Measurement  of Long Leg Bones .....As..mentioned i n Chapter I, the accurate measurement of long leg bones i n children i s of paramount importance when assessing the amount of bone growth over a s p e c i f i e d period. The seriousness of any e r r o r i n d i f f e r e n t i a l length measurement can be put i n perspective by recognizing that i t may lead to a wrong decision as to whether a bone should be allowed to grow normally without intervention or whether i t s growth should be stopped or accelerated. I f the o r i e n t a t i o n of the bone r e l a t i v e to the x-ray tube i s d i f f e r e n t when taking the two radiograms to be used i n making a d i f f e r e n t i a l measurement, then we would expect that a certain amount of measurement error would consequently occur. In addition, since the bone length i s measured from the radiogram by matching the bone extremities positions on a Lufkin r u l e r , we can expect that the o r i e n t a t i o n of the r u l e r and human v a r i a b i l i t y would also a f f e c t the e r r o r . To assess the magnitude of the measurement error due to the above-mentioned f a c t o r s , a phantom bone was used i n a series of experiments to simulate var i a t i o n s i n leg p o s i t i o n i n g . The manner i n which t h i s was done i s the subject of the next section. 3.1 - The Apparatus Figure (3.1) i s a photograph of the apparatus used. I t consists of a rectangular wooden frame(a) whose legs are 0.9 inches high, or j u s t high enough to allow for i n s e r t i o n of an x-ray f i l m cassette underneath. F i g . (3.1) The Apparatus Used to Simulate Bone P o s i t i o n Variances 40 The h o r i z o n t a l plate (b) i s made of s t e e l to hold the magnetic stand (d) i n a f i x e d p o s i t i o n . The p l e x i g l a s s bar (c) has a t h i n wire stretched along i t s length and imbedded i n i t s lower surface. Near i t s ends, the wire i s crossed by other wires which together with markers play a part i n allowing precise r e g i s t r a t i o n of the x-ray beam center during the experiments; see F i g . (3.2). plexiglass marker r wire un 1 ( U-7. Figure (3.2) Top View of One End of P l e x i g l a s s Bar Showing the Wire Markers When the cassette i s inserted underneath the frame, the wire i s very close to the cassette surface. The markers can then be used to locate the beam center of the x-ray beam r e l a t i v e to the phantom bone. This i s done by using 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 over the p l e x i g l a s s p l a t e . This frame s l i d e s h o r i z o n t a l l y into the cap of the x-ray tube. I t consists of a p l e x i g l a s s bar which can s l i d e along one d i r e c t i o n i n a square aluminum frame as shown i n F i g . (3.3). The p l e x i g l a s s bar i s s l o t t e d and holds a small p l e x i g l a s s piece which can s l i d e along the bar's length. This small p l e x i g l a s s piece i s attached to a t h i n s t r i n g which hangs down from the frame and :> i n turn i s attached to a fuselage-shaped plumb bob of p l e x i g l a s s . By a l i g n i n g the plumb bob t i p to coincide with one of the points where a marker and wire cross, the x-ray beam center may 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 of X-ray Tube Cap Frame The magnet i n the magnetic stand can be turned on or o f f by an external switch. Fixed i n the stand i s a v e r t i c a l rod, along which a p clamp(e) can s l i d e smoothly to an adjustable height. This clamp holds a transverse rod (f) that can be rotated about i t s axis to any desired . angular p o s i t i o n . A hollow c y l i n d e r (g) i s f i x e d perpendicular to the end of the transverse rod and houses a second c y l i n d e r (h), which i s also hollow and c o a x i a l to*the f i r s t c y l i n d e r . The outer radius of the inner c y l i n d e r equals the inner radius of the outer c y l i n d e r . The inner cy l i n d e r clasps the c e n t r a l part of the shaft of an adult femur 43.0 cms long. The gap between the smooth c y l i n d r i c a l surface and the i r r e g u l a r bone shaft i s f i l l e d with an adhesive cement, so that the bone and the inner cylinder rotate as a unit about the c y l i n d e r axis. The L u f k i n r u l e r i s held i n f i x e d p o s i t i o n i n two grooves ( i ) , (j) by two powerful s t e e l springs. The l o n g i t u d i n a l axis of the r u l e r i s p a r a l l e l to the long wire embedded i n the p l e x i g l a s s p l a t e . Any leg o r i e n t a t i o n can be simulated using t h i s apparatus, an x-ray taken, and the femur length as i t appears on the radiogram measured. 42 The r e s u l t s of such measurements as a function of various parameters are discussed i n the rest of t h i s chapter. 3.2 - E f f e c t of Bone Rotation It i s intended here to estimate the var i a t i o n s i n radiograph-ically-measured length due to rot a t i o n of the femur about i t s axis. We assumed the zero-rotation p o s i t i o n to be where the lowermost points i n the medial and l a t e r a l condyles at the d i s t a l end of the femur are at the same height from the cassette ( r a d i o l o g i s t s acknowledged t h i s as a reasonable assumption). The distance from the cassette to ei t h e r of these points was 4.60 cms. i n t h i s p o s i t i o n . The distance from the lowermost part of the hemispherical femoral head to the cassette was 10.90 cms. At these heights, the bone was i n a po s i t i o n above the cas-sette simulating an i n vivo s i t u a t i o n . A serie s of orthoroentgenographic exposures were taken. A l l exposures were made with a s e t t i n g of 70 KVp, 5/6 mAs and a nominal beam height of 40 inches, f o r a l l experiments d i s -cussed i n t h i s chapter in c l u d i n g t h i s one. From these exposures, the following measurements were made (see F i g . (3.4)): 1 - The r u l e r reading corresponding to the tangent to the femoral head (H). This tangent, as well as others at the medial and l a t e r a l condyles are normal to the r u l e r , 2 - the r u l e r readings corresponding to the medial and l a t e r a l con-dyles (MC, LC), 3 - the maximum width at the proximal end (PW), 4 - the maximum width at the d i s t a l end (DW). 5 - The angle between the tangent to the femoral head and the greater 44 trochanter and the r u l e r , "0". Table (3.1) l i s t s the measurements taken from radiograms of the rotated femur. A p o s i t i v e r o t a t i o n angle i s considered to cause the femur head to move farth e r away from the cassette surface. From table (3.1) we can conclude that the r o t a t i o n of the bone has a s l i g h t ejffect on the o v e r a l l measured length of the femur. The maximum dif f e r e n c e i n the measurements of length over the range of r o t a t i o n angle considered i s 0.9 mm. Observe that the angle 0 increases approximately l i n e a r l y with the angle <of r o t a t i o n , and could be used, i f desired, to determine bone r o t a t i o n . 3.3 - E f f e c t of Beam Center Location The marker system used on the p l e x i g l a s s p l a t e allows precise the femur for orthoroentgenographic exposure (see Figure (3.5)). The markers were placed at the corners of three inch squares, since a v a r i -ation i n beam center l o c a t i o n of three inches i s not uncommon i n sets d i f f e r e n t combinations of beam center l o c a t i o n s at the proximal and d i s t a l ends of the bone. The r e s u l t s of these measurements are presented i n table (3.2). r* rs •*-»+- r\ -v of- f T no A -t F •£ o T* o r» t" r\ r\n of radiograms. Measurements were made from radiograms produced f o r Proximal End Distal End F i g . (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 Plate 45 Table 3.1 The E f f e c t of Rotation on the Femur Radiogram Rotation (degrees) H (cms) MC (cms) LC (cms) PW (cms) DW (cms) e (degrees) Femur Length(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 46 Table 3.2 The E f f e c t of Beam Center Location on the Femur Radiogram ( A l l entries i n cm.) PROXIMAL END DISTAL END • BONE * „** ^ l\ LENGTH B • C • L • H B. C. L. MC LC A 1 70.60 70.025 43.00 B 1 70.68 70.19 43.08 A 27.60 C 1 70.58 70.01 42.98 D 1 70.465 69.89 42.865 . O 1 70.60 70.05 43.00 A 1 70.60 70.025 43.185 B 1 70.68 70.19 43.265 B 27.315 C 1 70.58 70.01 43.165 D1 70.465 69.89 43.05 O 1 70.60 70.05 43.185 A 1 70.60 70.025 43.56 B 1 70.68 70.19 43.64 C 27.04 C 1 70.58 70.01 43.54 D 1 70.465 69.89 43.425 O 1 70.60 70.05 43.56 A 1 70.60 70.025 43.30 B 1 70.68 70.19 43.38 D 27.3 C 1 70.58 70.01 43.28 b 1 70.465 69.89 43.165 o 1 70.60 70.05 43.30 A 1 70.60 70.025 43.29 B 1 70.68 70.19 43.37 0 27.31 C 1 70.58 70.01 43.27 D 1 70.465 69.89 43.155 O 1 70.60 70.05 43.29 * B.C.L. = BEAM CENTER LOCATION ** H, MC, LC = Ruler Readings at Head of Femur, Medial Condyle and L a t e r a l Condyle respectively 47 The results i n the rightmost column of table (3.2) in d i c a t e a maximum difference i n length measurements of 7.75 mm. The shortest length recorded i s 42.865 cms and the longest 43.64 cms. Observe that when the beam center has a fi x e d p o s i t i o n at the proximal end and i s allowed to vary i n p o s i t i o n at the d i s t a l end, differences i n measured length tend to be s i g n i f i c a n t l y less than the differences which r e s u l t i f the beam center i s varied at the proximal end. 3.4 - E f f e c t of Beam Height A seri e s of orthoroentgenography exposures of the phantom bone were taken to study the e f f e c t of va r i a t i o n s i n the beam height on measured length. The bone was positioned as explained i n section (3.2), with zero degree r o t a t i o n . The r e s u l t s are summarized i n table (3.3). Table 3.3 The E f f e c t of Beam Height on the Femur Radiogram BEAM H MC .LC BONE HEIGHT (cms) (cms) (cms) LENGTH(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 The r e s u l t s i n column H in d i c a t e that the greatest v a r i a t i o n s i n the measured length occur due to changes i n the measured p o s i t i o n of the proximal end of the femur with changes i n the beam height. As expected, the higher the x-ray tube the closer the measurement i s to the actual 48 bone length. The measured length varied over a range of 1.9 mm as the beam height was reduced from 42 to 34 inches. 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 The length measurement error due to i n c l i n a t i o n at the knee can be roughly estimated by considering the bone as a cylinder. I f the beam center i s d i r e c t l y overhead the end of the bone, then the error i s the actual length of the bone times the sine of the i n c l i n a t i o n angle. For our phantom bone of length 43 cm. and assuming an i n c l i n a t i o n of as much as three degrees, the error i s les s than 0.6 mm, c l e a r l y n e g l i g i b l e r e l a t i v e to the error from other contributors. 3.6 - E f f e c t of Lufkin Ruler Orientation and Human V a r i a b i l i t y A teleoroentgenographic exposure of the phantom bone was made. The x-ray prepared from the exposed f i l m was then used to estimate the magnitude of length measurement changes due to 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 Lufkin 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 simulate possible placements of the r u l e r by a r a d i o l o g i c a l technician. Tangents to the extremities of the bone were drawn as normals to each of these l i n e s and length measurements thus determined. 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 of the bone at one end and a lengthening at the other end due to trans-l a t i o n s of the intersections of the tangents with the r u l e r , measurement errors at the ends of the bone due to improper angular o r i e n t a t i o n of the r u l e r tend to cancel one another. A more s i g n i f i c a n t factor i n causing error i s human v a r i a b i l i t y i n constructing tangents at the ends of the bone. 49 The r u l e r placement which gave the maximum length measurement using tangents at the extremities normal to the r u l e r was found to form an angle of 109° with .the tangent to both the condyles at the d i s t a l end of the bone as shown i n F i g . (3.6.a). This o r i e n t a t i o n was therefore considered to be p a r a l l e l with the axis of the bone. Placing the r u l e r so that i t also b i s e c t s the tangent to the condyles at the d i s t a l end of the bone r e s u l t s i n a po s i t i o n i n g of the r u l e r with respect to the femoral head as shown i n F i g . (3.6.b). The length measured along the r u l e r i n this p o s i t i o n with properly constructed tangents i s 47.80 cms. In a routine radiogram, due to the x-ray image degradation, low contrast 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 'read' the r u l e r anywhere between points a and b (see F i g . (3.6.a)). The d i s -tance a-b i s 0.685 cms. along the axis. At the proximal end, a deviation from the normal-to-the-ruler by +9° was considered an upper l i m i t to the erro r i n estimating the tangent to the femur head (see Fi g . (3.6.b)). This, error i s p a r t i c u l a r l y present with c h i l d r e n , as the appearance of the head of the femur i n early childhood, far from being hemispherical, i s rather f l a t . In F i g . (3.6.b), points c and d represent the in t e r s e c t i o n s of the i n c l i n e d tangents with the r u l e r . The length of cd = 0.57 cm and and ce = 0.46 cm. The range of the p o t e n t i a l e r r o r at the femoral head i s therefore cd + ce = 1.03 cm. (3.1) The maximum reasonable e r r o r , therefore, taking d i s t a l and proximal ends in t o account i s equal to the maximum er r o r at the knee j o i n t plus the maximum error at the femur head; that i s : e = 0.685 + 1.03 = 1.715 cms. (3.2) 50 given the r u l e r i s coincident with the bone axis. I f the r u l e r i s trans-l a t e d away from the femur head, the measurement err o r i s expected to increase. This was simulated by constructing a l i n e p a r a l l e l to the axis and l a t e r a l l y removed by 1 cm. The p o t e n t i a l e r r o r between the -9° tangents increased from 1.03 cm to 1.22 cm, hence inc r e a s i n g the maximum possible error to 1.935 cm. Moving the r u l e r l a t e r a l l y by 1 cm closer to the femoral head decreases the maximum possible error to 1.46 cm. Of course, the erro r at the d i s t a l end when moving the axis p a r a l l e l to i t s e l f was considered constant. F i g . (3.6) A x i a l Relationships at the Bone Extremities The above measurements were repeated on axes making angles of 107° and 111° with the tangent to the condyles. The r e s u l t s are summar-i z e d i n table (3.4). Table 3.4 E f f e c t of Lufkin Ruler Orientation and Human V a r i a b i l i t y * Axis I n c l i n a t i o n to tangent to Condyles •107° 109° 111° Length between medial condyle and femoral head 47.25 47.8 47.7 Probable error (a-b) at knee j o i n t 0.525 0.685 0.875 Probable error (c-d) at femoral head 0.59 0.57 0.47 Probable er r o r (c-e) at femoral head 0.59 0.46 0.71 Tota l probable error at femoral head 1.18 1.03 1.18 Maximum reasonable error i n length measurement 1.705 1.715 2.055 Maximum reasonable error when axis i s d i s -placed 1 cm l a t e r a l l y 1.995 1.935 2.375 Maximum reasonable error when axis i s d i s -placed 1 cm medially 1.40 1.45 1.725 A l l e ntries i n cms. 52 3.7 - Conclusion The r e s u l t s of the orthoroentgenographic length measurements as reported i n t h i s chapter i n d i c a t e that the patient's p o s i t i o n i n g when radiographing his legs for the purpose of measuring t h e i r length a f f e c t s by a varying degree the accuracy of these measurements. The magnitude of the error 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 height was found to be n e g l i g i b l y small. A greater c o n t r i b -utor to measurement e r r o r , though not a serious one, i s the x-ray beam center l o c a t i o n when exposing the femoral head. This error i s less than 1.8% of the anatomical bone length. The most serious error i s caused by the r a d i o l o g i s t ' s subjective estimate of the bone end l o c a t i o n with respect to the Lufkin r u l e r grades. Because of the f a c t that these technical errors are n e g l i g i b l e as compared to the e f f e c t of the radioluscency of unossified c a r t i l a g e on the> ^ measured length of i n f a n t s ' l e g bones, we attempted to solve the l a t t e r problem. This i s the subject of the next chapter. 53 CHAPTER 4 On the Problem of Radioluscency of Unossified  Cartilage i n Children As mentioned i n chapter I I , a key- problem i n the accurate measurement of long l e g bones i n ch i l d r e n i s the radiolusceney of the un o s s i f i e d c a r t i l a g e at the bone extremities. This problem not treated previously, has been dealt with by using a non-routine radiographic imaging technique and by computer processing the r e s u l t i n g image for enhancement and contour e x t r a c t i o n . 4.1 - The Radiographic Imaging Technique The bone,used 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 new born c h i l d . This femur was removed and radiographed using very s o f t X-rays generated by a molybdenum anode at 25KVp. The filament current was maintained at 150 mA and the exposure time va r i e d . The best r e l a t i v e image q u a l i t y i n terms of contrast r a t i o s was obtained using a 0.7 second exposure time. The low energy photons i n the r a d i a t i o n spectrum of the molybdenum target 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 retained. This monochromatic r a d i a t i o n , with i t s low energy, i s mainly absorbed i n the body tissues by photoelectric absorption (see chapter 2). As mentioned before, subject contrast i s maximized when the attenuation 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 t h i s p h o t o e l e c t r i c e f f e c t i s most pronounced when using low -KVp X-rays. 54 4.2 - Image Processing X - rays are characterized by very low-contrast features superimposed on a changing, l o c a l l y uniform background [23]. To be able to r e g i s t e r maximum information during the scanning process, the amp l i f i e r gain, the a m p l i f i e r o f f s e t voltage and the lens aperture opening of the image dissector were so adjusted as to t o t a l l y saturate the photocathode i n the region corresponding to the o s s i f i e d portion of the bone. Saturation, of course, i s not usually desired mainly because of the r e s u l t i n g edge b l u r r i n g and also the masking of f i n e d e t a i l s within the saturation region. This, however, was no serious handicap for our p a r t i c u l a r problem since the saturation region i s contoured by a very d i s t i n c t edge that could l a t e r , i f desired, be p e r f e c t l y o utlined. Also the f i n e r d e t a i l s within the o s s i f i e d shaft are of no importance as f a r as o v e r a l l length estimation i s concerned, and hence can be disregarded. On the other hand, because of the low s i g n a l - to - noise r a t i o of the radiogram, p a r t i c u l a r l y due to quantum mottle, strong i l l u m i n a t i o n and large a m p l i f i e r gain were the only answer to the problem of recording the d i f f u s e d , just-noticeable trace of c a r t i l a g e at the femoral head. 4.2.1 - P r e f i l t e r i n g Contrast Enhancement The 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) and i t s grey-level histogram i s shown i n F i g . (4.1). I t i s apparent that the g r e y - l e v e l d i s t r i b u t i o n i s biased toward high d e n s i t i e s ; b r i g h t e r p i x e l s are sparse, and the histogram peaks at an i n t e n s i t y l e v e l of 63, corresponding to the saturation region at the femoral shaft. The re-s u l t of having a large percentage of the 65536 p i x e l s concentrated 55 around the darkest and the b r i g h t e s t portions of the histogram i s an image with l i t t l e v i s i b l e d e t a i l [33]. Although i t i s generally agreed that 64 quantization 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 l e v e l s are uniformly apportioned over the dynamic range of the system makes the encoding scheme i n e f f i c i e n t . In addition to obscuring genuine contrast r a t i o s , t h i s method of recording information i s wasteful i n an information theoretic sense. This w i l l be apparent when examining the r e s u l t s of contrast enhancement. One possible way to improve the q u a l i t y of the quantized p i c t u r e i s to r e f i n e the grey scale (increase the number of grey l e v e l s ) . This was not possible i n our case due to hardware l i m i t a t i o n s . Another approach was therefore followed, namely the d i r e c t manipulation of the grey l e v e l histogram by p o s i t i o n - i n v a r i a n t non - l i n e a r point operations, as follows: 1. Logarithmic conversion: Software can be used to convert picture brightness function to a density function based upon the fact that the eye 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 [35]. The e f f e c t of the log operation i s to expand the range of the grey scale that i s heavily populated and compress the range where the p i x e l s are sparse, which r e s u l t s i n expanding the contrast r a t i o s that define edges. The r e s u l t i n g histogram i s shown i n F i g . (4.2). 2. - Histogram Equalization: I f the ordinates of the histogram of F i g . (4.1) are normalized with respect to the t o t a l number of pixels (65536), then the r e s u l t i n g curve could be considered as a f i r s t order discrete p.d.f. Summing this curve from l e f t to r i g h t gives a f a i r l y monotone, non-decreasing Cummulative D i s t r i b u t i o n Function F i g . (A.3) Ideal and Actual Cum-mulative D i s t r i b u t i o n Functions F i g . (4.4) Histogram Equalization 57 (CDF) as shown by curve 2 of Fi g . (4.3). Had the number of p i x e l s per in t e n s i t y l e v e l been the same throughout the histogram ( i d e a l rec-tangular d i s t r i b u t i o n ) , the CDF would be represented by curve 1 of Fi g . (4.3). An approximation to t h i s rectangular d i s t r i b u t i o n could be obtained using techniques s i m i l a r to those based upon d i s t r i b u t i o n quantiles i n s t a t i s t i c s [36] (Appendix A). This i s done as follows: The v e r t i c a l axis i n Fi g . (4.3) i s divided into 64 equal i n t e r v a l s . The ordinates of the CDF at the v e r t i c a l axis increments are then ^ > matched to t h e i r corresponding abscissa values to define new quanti-zation l e v e l s for the p i x e l s . The pic t u r e elements are then reassigned to those newly defined values. The r e s u l t i n g histogram i s shown i n Fig . (4.4) 3 - Gamma Correction: Although gamma cor r e c t i o n o r i g i n a l l y referred to grey scale and contrast adjustments intended to compensate for uneven or non-linear responses of the image sensor, the term can be generalized to include any continuous transformation of the grey scale [37]. The transformation consists of p a r t i t i o n i n g the h o r i z o n t a l axis of the CDF int o 256 equal i n t e r v a l s , then using the corresponding ordinates to determine new quantization l e v e l s . There w i l l s t i l l be only 64 quantization l e v e l s , but they w i l l be unequally spaced. The signals w i l l be compressed i n slow-slope portions of the curve (CDF) and expanded i n high slope portions ( F i g . (4.5)). 4 - Smoothing and Re d i s t r i b u t i o n of the pi x e l s over the grey s c a l e : Histogram equali z a t i o n (method 2) has the somewhat undesirable e f f e c t of reducing the number of non-zero quantization l e v e l s . Because of the li m i t e d number of o r i g i n a l quantization l e v e l s (N=64), the p i x e l 58 •lKTEIISirr LEVELS 200 2,0 ca TO ••WHItl LE¥EL5* Fig. (4.5) Gamma Correction Fig. (4.6) Smoothing & Redistribution Fig. (4.7) Original Digitized Radiogram 59 histogram and CDF i s composed of step functions. The more pronounced these steps, the fewer the number of useful (occupied) newly defined quantization l e v e l s . I f one i s t r y i n g to equalize the number of p i x e l s per l e v e l , the effectiveness of the equalization technique w i l l depend upon the number of quantization l e v e l s N and the sizes of the step increases i n the CDF. Fortunately, one can a r t i f i c i a l l y increase N and reduce the X-ray noise at the same time. This i s done by convoluting the p i c t u r e function with a c i r c u l a r l y symmetric low-pass f i l t e r function, whose di s c r e t e impulse response i s : h ( i , j ) = 2 6 ( i , j ) + c S ( i - l , j ) + 6 ( i + l , j ) + 6 ( i , j - l ) + 6 ( i , j + l ) (4.1) The r e s u l t i n g picture's histogram w i l l contain entries from 0 to 378. Histogram equali z a t i o n i s then used to f i n a l l y obtain the histogram of F i g . (4.6) and the corresponding picture of F i g . (4.11). 4.2.2- Results and Evaluation A f i r s t order entropy measure was computed for each of the 64 grey - l e v e l histograms of the radiograms shown i n Figs. (4.7) to (4.11). The computation i s given by \ 63 H(P) = -E p i l o g 2 P i b i t s / p i x e l (4.2) i=o The P i values were computed as the r a t i o of the number of p i x e l s with grey l e v e l i , to the t o t a l number of p i x e l s i n the image. The maximum value of H(P) i s s i x b i t s / p i x e l , which occurs when the Pi's are equal. The t o t a l redundancy i n b i t s / p i c t u r e was then cal c u l a t e d . Redundancy i s defined as the difference between maximum and actual entropy [38], and therefore i s given by: 60 R = (6+Ep ± l o g 2 v±) * 65536 b i t s / p i c t u r e (4.3) i where 65536 i s the t o t a l number of p r i x e l s The r e s u l t s are tabulated i n table 4.1. I t i s obvious from the table that each of the four methods increases the entropy i n b i t s with respect to the number of non-zero quantization l e v e l s . Although method 4 produces the greatest number of occurring quantization l e v e l s 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 at the expense of edge b l u r r i n g as can be e a s i l y seen i n the minuscule o s s i f i c a t i o n center i n the condyles (F i g . (4.11)). One can p a r t i a l l y correct t h i s undesirable e f f e c t by considering the output of the contrast enhancement stage as a weighted average of the output pictures of method 2 and method 4. The reason for t h i s i s that while method 2 t o t a l l y preserves edge sharpness, method 4 has b e t t e r contrast r a t i o s . Each of the four techniques investigated i s equivalent to a non-l i n e a r operation on 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 . P r e - f i l t e r i n g contrast enhancement i s p a r t i c u l a r l y impressive f o r X-rays with histograms h e a v i l y biased toward one end or the other of the grey-s c a l e range. A uniform d i s t r i b u t i o n of grey l e v e l s tends to make equal use of each quantization l e v e l thereby enhancing low d e t a i l information. The technique can be seen as making subtle changes more evident i n the regions for which such changes occur most frequently, while lessening subtle i n t e n s i t y changes i n l e s s frequently occuring grey s c a l e regions [39]. Radiogram O r i g i n a l Processed Logarithmic Conversion Histogram Equalization Gamma Correction Smoothing and Redistribution Actual Entropy (bits) 4.523542 4.379244 4.377023 4.483789 5.338506 Redundancy with respect to 64 l e v e l s ( b i t s / p i c t u r e ) 96 761 106 217 106 363 99 366 43 351 Number of occurring quan-t i z a t i o n l e v e l s i n picture 64 35 26 34 52 Max. Entropy corresponding to the number of non-zero l e v e l s 6.0 5.12928295 4.70043945 5.08746243 5.70043945 Actual Redundancy 96761 49154 21195 39562 23179 Table 4.1 - Redundancy i n Radiograms a f t e r P r e f i l t e r i n g Contrast Enhancement 62 F i g . (4.10) Gamma Correction F i g . (4.11) Smoothing & Redi s t r i b u t i o n 63 To use any of the transformations described i n methods 2, 3 or 4, one must: a) compute the histogram of the image grey l e v e l values, b) compute the empirical d i s t r i b u t i o n function, c) use this d i s t r i b u t i o n curve for the grey l e v e l transformation, and d) rescale and quantize the r e s u l t i n g values. F i n a l l y , although these transformations are very e f f e c t i v e for enhancing low contrast d e t a i l s , they do not discriminate between low contrast information and noise. 4.2.3 - F i l t e r i n g Processed pictures with r e d i s t r i b u t e d grey l e v e l s have better contrast 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 . The edges too appear somewhat stronger (except i n the case of method 4 because of low-pass f i l t e r i n g ) . The v i s u a l acuity of the x-ray image can be further improved by proper manipulation of the image frequency spectrum, however. This i s i n t u i t i v e l y done by accentuating the f r e -quencies that contain edge or d e t a i l information, and attenuating those frequencies that are p r i m a r i l y related to noise. Two approaches can be used to design a required d i g i t a l f i l t e r , namely the Z-trans form and the discrete Fourier transform. The l a t t e r was chosen because design techniques i n the frequency domain are more v e r s a t i l e and no f i l t e r s t a b i l i t y problems have to be considered. The d i s c r e t e , two-dimensional Fourier transform (DFT) of a sampled and quan-tized p i c t ure f(m,n), m,n=0,l, >N-1, whose samples are equispaced 64 i n the x- and y- d i r e c t i o n i s given by N-1 N-1 „ 2. IT F(u,v) = 1 £ f(m,n) exp[-j — (rau + nv)] (4.4) m=0 n=0 u,v = 0,1, ,N-1 Where N i s the number of points per raster i n the square p i c t u r e . The inverse trasform of F(u,v) i s given by: N-1 N-1 2 i t f(m,n) = r^z E E F(u,v) exp [j ^ (urn + vn) ] ( 4 > 5 ) u=0 v=0 Our concern i s to determine high-emphasis f i l t e r which w i l l produce pictures which are s a t i s f a c t o r y i n terms of subjective evaluation while at the time taking into consideration complexity and computation time. However, f o r the moment we w i l l r e s t r i c t ourselves to the design of a low-pass f i l t e r since band-pass, band-rejection, high-pass and high-emphasis f i l t e r s can be derived from the low-pass prototype. Figs (4.12) and (4.13) are plots of the magnitude of the transform c o e f f i c i e n t s of the radiogram i n the u and v d i r e c t i o n s respectively. I t i s apparent that the magnitude transform space i s not obtrusively non-isotropic that we can use- c i r c u l a r l y symmetric f i l t e r s [42]. This being the case,we can confine ourselves to the design of a one-dimensional f i l t e r . The f i r s t problem i s the proper choice of the f i l t e r r o l l - o f f function so as to eliminate as much as possible the o s c i l l a t i o n s i n the f i l t e r out-put caused by the Gibbs phenomenon [40]. Several r o l l - o f f functions have been considered to evaluate t h e i r e f f i c i e n c y i n terms of complexity, computation time and f i l t e r i n g performance. The low-pass prototypes of ABSOLUTE VPLUES OF FOURIER CDEFFS. : PIU.01X100 ABSOLUTE VRLUES OF FOURIER CDEFFS.! PI0.VIX100 r t >J 1 fi1 c 9 66 these f i l t e r s are shown in Fig. (4.14). and H2 are Ormsby and Martin-Graham f i l t e r s , respectively; H3 and are Taylo's f i l t e r s [41], and H5 is related to the Ormsby f i l t e r by the equation H 5(f) - [ H i ( f ) ] 2 (4.6) is our proposed r o l l - o f f function. The mathematical expression for 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). The steps of the convolution w i l l not be elaborated here. Rather, we w i l l concern ourselves with the weight functions or spatial responses of the six f i l t e r s . Again, the process of 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 is lengthy and straightforward. The weight func-tions are represented by equations (4.9) to (4.14), with A M = 9uAf = 9 -rrCf - f 'I (4.7) where f = termination frequency , f = cut-off frequency and Af = f_ - f (4.8) T c F i g . (4.15) The two functions G(f) and K(f) used to generate the proposed f i l t e r response H,(f) f -c t 'T H ^ f ) = <f T - f ) / ( f T - f c ) . ( A > 9 ) . H 2 ( f ) = [ l + c o s [ r r ( f - f c ) / ( f T - f c ) ] ] / 2 (4.10)' H 3 ( f ) = (1/2TT) s i n t 2 T r ( f - f c ) / ( f T - f c ) ] + ( f T - f ) / ( f T - f c ) (4.11)' H 4 ( f ) = (9/16) c o s [ 7 r ( f - f c ) / ( f T - f c ) ] - ( l / 1 6 ) cos t 3 i r ( f - f c ) / ( f ^ - i £ ) ] + i (4.12)' H 5 ( f ) = [ H ^ f ) ] 2 (4.13)' H 6 ( f ) = 1 - 2 [ ( f - f c ) / ( f T - f c ) ] 2 , f c<f< ( f c + f T ) / 2 2 [ ( f - f T ) / ( f T - f c ) ] 2 , ( f c + f T ) / 2 < f < f T (4.14)' F i g . (4.14) R o l l - o f f functions of low-pass prototypes 68 (2/TTAIOX2) [s!±n-(-Aaix/2) sin((co -t- toJx/2)] c T (4.9) h 2(x) = [rr/x ( T r 2-Ato 2x 2) ] [cos(Acox/2) sin((a) + u_) c 1 x/2)] (4.10) h 3(x) = [1/1-(AWX/2TT)2] h ^ x ) (4.11) h 4(x) = [1/1-(AO)X/3TT)2] h 2 ( x ) (4.12) h 5 ( x ) = (2/TTACOX2) [COS(CO X) - (2/Acox) sin(Acox/2) c cos((coT+coc) x/2)] (4.13) h 6(x) = [tan(Aux/4)/(Atox/4) ] h ^ x ) (4.14) The. values of these func t i o n s at t h e i r undeterminate p o i n t s are discussed i n Appendix B. F i l t e r Parameter: High-emphasis f i l t e r i n g of a radiogram p a r t i a l l y r e t a i n s the cont r a s t i n f o r m a t i o n i n a radiogram, 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 r e s p o n s i b l e 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 of the low-pass f i l t e r t r a n s f e r f u n c t i o n as: H R E ( f ) = 1 + a U - H ^ C f ) ) -, a>0 (4.15) Where H^Cf) i s the t r a n s f e r f u n c t i o n of the low-pass prototype. A schematic r e p r e s e n t a t i o n of the e f f e c t of H (f) on an edge i s shown i n F i g . (4.16). Given H^p(,f) , the f i l t e r i s ^ s p e c i f i e d by the f o l l o w i n g three parameters: 1 - the c u t - o f f frequency 2 - the te 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' 69 >hHE(x) hoc f * ^E(x) oversnco_ kQ(_x). X -vs. Pixels. corllrast X Convolution H-E Function Ideal Edge Output Pi c t u r e F i g . (4.16) E f f e c t of High-Emphasis F i l t r a t i o n on Ideal Edge | T r T | • i • i -T M - r - r T T 1 "* ' ' 1 r~r-f-i-T-T-r-t—t-i -3.CD ' D.BO 1.63 2 . - » 5.:D 4.CO 4.00 3.60 F i g . (4.17) Comparison of the weight functions of f i l t e r s H^, H 5 and H & 70 A high-emphasis f i l t e r of the type H,. was i n i t i a l l y used for processing. This f i l t e r i s described i n reference [27] as: " y i e l d i n g images with the greatest v i s u a l acuity regardless of u) c and co^ chosen. Examination of the point spread function for this f i l t e r i ndicated that i t possessed a somewhat narrower spread function than any other of the spread functions f o r a given to^ and ui - . . . Also the point spread function y i e l d e d no negative side lobes ... ". Our own f i n d i n g s , however, indicated that at no point did this f i l t e r perform any better than the other f i l t e r s . In f a c t , i t s point spread function i s the widest when compared to the s i x other f i l t e r s . An example of this i s shown i n Fig . (4.17), where h.(x), h (x) and h^(x) are p l o t t e d for f =0.0159 1/mm 4 5 6 c and f^=o,156 1/mm. I t i s obvious from the graph that h^(x) has the nar-rowest point spread function, while h^(x) has an unacceptable r o l l - o f f . At a r a d i a l distance of 5.6 mm, h^(x) i s s t i l l 0.148 of the c e n t r a l weight. I f we increase f and f m to 0.2 and 0.5 1/mm r e s p e c t i v e l y , h r(x) c T 5 traces a long negative side lobe from x = 1.7 mm to x = 3.8 mm. The s i x f i l t e r s were tested over a wide range of frequencies. Independent of f and f , the Martin-Graham f i l t e r always performs b e t t e r than the Ormsby f i l t e r . Also Taylo's f i l t e r s , whose weight functions are very nearly the same, are better than the Martin-Graham. F i l t e r has the narrowest point spread function and the smallest side lobes. In s p i t e of i t s superior performance, the existance of the side lobes causes s l i g h t , but perceptible ringing to propagate from a strong edge as at the femoral sha f t . Ringing can be eliminated by using a Gaussian f i l t e r . The Gaussian transfer function i s the only simple function whose inverse transform (point spread function) has no side lobes. Also, the low-pass 71 prototype i s t o t a l l y determined by only one parameter, namely i t s standard deviation "a", so that the weight function's spread can be simply deter-mined. This o f f e r s the unique advantage of studying a wide v a r i e t y of outputs with the least manipulations of f i l t e r parameters. A disadvantage can e x i s t , however, i n that the evaluation of the Gaussian f i l t e r t r a n s f e r function i n a computational process involves exponentials as compared to l i n e a r functions only i n the cases of or H . o J Results and Discussion: Figures (4.18) and (4.19) are t y p i c a l pictures emerging from a high-emphasis Gaussian f i l t e r , while Figs. (4.20) and (4.21) are for the same input radiogram a f t e r high-emphasis f i l t r a t i o n through H,_. Because out-of-range p i x e l s are generated by f i l t e r i n g , the p i x e l s are rescaled between 0 and 63 before di s p l a y i n g the processed radiograms. As mentioned before, the contrast r a t i o s i n the f i l t e r e d pictures are reduced. Figures (4.22) and (4.23) contain histograms of the grey l e v e l s of two t y p i c a l f i l t e r e d pictures using a Gaussian and an H,. f i l t e r , r e s p e c t i v e l y , and the C.D.F.'s of these histograms are given i n F i g . (4.25). The picture elements are d i s t r i b u t e d over a narrow range of the i n t e n s i t y s c a l e , thereby giving the pictures a general grey appearance. The introduction of a l i m i t i n g operation can be used to eliminate out-of-range p i x e l values while enhancing contrast i n the processed p i c t u r e . We note that negative p i x e l s and p i x e l s of large p o s i t i v e value occur due to overshoot i n regions of abrupt change i n i n t e n s i t y . These are the regions of f i n e d e t a i l s or edges that f i l t e r i n g i s working to emphasize. Instead of re-s c a l i n g the f i l t e r e d image between 0 and 63, we can set to zero a l l the 72 73 •WTUSITT LEVELS ' F i g . (4.22) Gaussian F i l t e r F i g . (4.23) H 5 F i l t e r ' imcnin L E T E L I ' in « « i n I E V E U F i g . (4.24) Non-Linear F i l t e r F i g . (4;25) CDF of Gaussian, Non-Linear and H,. F i l t e r e d Images 74 negative 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 of range, then l i n e a r l y map the r e s t of the p i x e l s contrast enhanced values between 0 and 63. The r e s u l t s of applying the l i m i t i n g operation to the radio-grams shown i n Figs. (4.18) to (4.21) are shown i n Figs. (4.26) to (4.29). Observe that 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 of range have been dramatically overemphasized i n F i g . (4.26). The reason for the brig h t " r i n g " c l o s i n g at the bottom of the radiogram i s the assumed p e r i o d i c i t y of the picture function, whereby the bottom of the shaft i s interpreted as an edge by the DFT. F i g . (4.27) i s a tremendous improve-ment attained by increasing a from 1 to 2. Figures (4.28) and (4.29) demonstrate the unpredictable patterns that one gets using f i l t e r H,. because of excessive ringing around t r a n s i t i o n regions. The correct choices i n f i l t e r design lead to s i g n i f i c a n t l y improved pictures a f t e r contrast enhancement, as can be seen by inspect-ing Figs. (4.30) to (4.33). The radiograms on the r i g h t of the page are the r e s u l t of applying non-linear contrast enhancement to the cor-responding radiograms on the l e f t of the page. Observe that even with the best choice of f i l t e r parameters, the radiograms f i l t e r e d through H,. always contain a r t i f a c t and f a l s e contours. Tables (4.2) and (4.3) l i s t the f i l t e r i n g parameters used to obtain the pictures i n Figs. (4.30.b), (4.31.b), (4.32.b), and (4.33..b). 75 Fig. (4.28) Contrast Enhancement of Fig. (4.20) Fig. (4.29) Contrast Enhancement of Fig. (4.21) 76 a) F i l t e r e d b) Contrast Enhanced Fig. (4.31) Gaussian 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 b) Contrast Enhanced F i g . (4.32) Hq F i l t e r : f = 0.3213 , f T = 0.0714 , a = 2.0 5 c T a) F i l t e r e d b) Contrast Enhanced F i g . (4.33) H 5 F i l t e r : 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' Number of -ve P i x e l s % Number of -ve P i x e l s 4.30.b 5 .60 2.5 .11324 17.28% 4.31.b 6.16 2.0 10809 16.49% Table 4.3 - High-Emphasis F i l t e r of type H Figure # f c f T a //of -ve Pix e l s % # o f•-ve P i x e l s 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(m,n) F(u,v) = | F ( u , v ) | e j < ! ) ( f ) F(u,v) = | F(u,v) | V * ( f ) f(m,n) DFT Non-Linear F i l t e r Inverse Trans-Form F i g . (4.34) Block Diagram of Non-Linear F i l t e r i n g Process 79 Non-Linear F i l t e r i n g : A property of the Fourier spectrum of the radiogram i s i t s large dynamic range [42]. Only a few points are highly energetic and these are concentrated i n the low-frequency portion of the spectrum. Because the HVS i s more responsive to the higher frequencies [31], we can consider using a non-linear f i l t e r i n the transformation domain that tends to suppress large-valued terms and non-linearly enhance small valued terms. A block diagram of such a f i l t e r i s shown i n Figure (4.34). The r e s u l t of applying such a f i l t e r i n g process to our radio-gram i s shown i n Figu'. (4.35. a); the grey l e v e l histogram and the CDF of a t y p i c a l output picture are pl o t t e d i n Figs. (4.24) and (4.25), res-p e c t i v e l y . Figure (4.35.b) i s the contrast enhanced version of F i g . (4.35.a). I t i s apparent that noise i n the d i g i t i z e d radiogram generates a very 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 , using d i f f e r e n t parameter values i n the processing, are shown i n Figs. (4.36.a) and (4.36.b), the radiogram i n (4.36.b) being obtained from (4.36.a) a f t e r contrast enhancement. 4.3 Conclusion The radiogram presented here was processed with the primary goal of increasing contrast r a t i o s of image edges and increasing the v i s i b i l i t y of the condyles. The properties of the human v i s u a l system were used as motivation and j u s t i f i c a t i o n for various enhancement tech-niques. Of the designs tested, the Gaussian high-emphasis f i l t e r y i e l d e d images with the greatest v i s u a l acuity. The point spread function of this f i l t e r can be made as narrow as desired to create a more narrow and steep over-response at an image edge thereby increasing a c t i v i t y . Also t h i s 80 a ) F i l t e r e d b) Contrast Enhanced Fig. (4.35) Non-Linear F i l t e r i n g : y = 0.5 a) F i l t e r e d b) Contrast Enhanced Fig. (4.36) Non-Linear F i l t e r i n g : y = 0.83 81 f i l t e r y i e l d e d no negative side lobes which produce an under-damped , response at edges, and as such would best reinforce the HVS created Mach bands. For high-emphasis design,a was kept between 2.0 and 4.0, and a between 5.0 and 7.0. Non-linear f i l t e r i n g also produced radiograms with good v i s u a l acuity for y between 0.8 and 0.9, with the salt-and-pepper e f f e c t decreasing and edge d e f i n i t i o n weakening as y increased. 82 Chapter 5 Edge P e t e c t i o n and Contour Traci n g 5.1 - Introduction In recent years, there 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 detection and contour t r a c i n g algorithms for use i n the automatic p i c t o r i a l pattern recognition of medical images. The general p i c t o r i a l pattern recognition scheme i s depicted i n F i g . (5.1) [ADAPTIVE" 1 [SUPERVISOR , picturel DIGITIZER ! control i I _ J PREPROCESSOR] FEATURE EXTRACTOR T — ' 1 I I rpTeorocessina 1 TpTcTuTe class 1 I techniques ;appli-i i features; picture • ^cation dependent^ dependent J CLASSIFICATION FEATURE ~^ DISPLAY \ I •-\MEASUREMENT\-F i g . (5.1) Block Diagram of P i c t o r i a l Pattern Recognition The feature extraction element i s simply a scheme whereby v a l -ues are calculated from a d i g i t i z e d and preprocessed p i c t u r e for a pre-s p e c i f i e d set of features (measures). This i s done to reduce the data used for decision making, while attempting to s e l e c t the set of features to be c h a r a c t e r i s t i c s of the classes of images under consideration. I t i s also a p p l i c a t i o n dependent, i n the sense that the features to be ex-tracted, for example, from a chest radiogram for detecting congenital heart diseases would be d i f f e r e n t from the ones needed for pulmonary diseases. Edge detection and contour t r a c i n g i s an important feature ex-t r a c t o r for p i c t o r i a l pattern recognition of radiograms. Several schemes 83 have been proposed i n this context. Campbell [24] used two one-dimen-s i o n a l edge detectors of the form shown i n F i g . (5.2) to enhance the edges of a d i g i t i z e d radiogram. He approximated the r o t a t i o n a l l y i n -variant detector by adding the absolute values of the outputs of two one-dimensional detectors to obtain the output. The output p i c t u r e was kD(x) -oc CC -7 F i g . (5.2) Edge Detector then thresholded to r e t a i n points that q u a l i f i e d as edge candidates. A global contour t r a c i n g al pori trim fhe.n searched the m'r.t.ure f o r a Start — of-Contour (SOC) point, followed by a systematic search f o r subsequent edge points u n t i l the e n t i r e p i c t u r e i s canvassed. Chow and Kaneko [45] suggested a threshold method f o r boundary detection i n a p i c t u r e . Other s i m i l a r approaches have been taken by Harlow et a l . [46, 47]. Roellinger et a l . [48] adopted a scheme whereby a midline i n a chest radiogram i s determined f o r subsequent use i n determining the heart shadow. In t h i s scheme a maximum gradient technique was applied to h o r i z o n t a l scan l i n e s to locate edge points of the right-hand edge by making use of the con-s t r a i n t that an edge point must not vary appreciably i n p o s i t i o n from the p o s i t i o n of the edge point located i n the previous l i n e . This con-s t r a i n t was added to prevent the algorithm from t r a c i n g such l i g h t areas as r i b s and excessive v a s c u l a r i t y . I t i s doubtful whether any of the above-mentioned edge detec-84 t i o n and contour tracing techniques would function properly on low S/N radiograms. They usually r e s u l t i n disconnected structures and f a l s e contour de s c r i p t i o n s , unless the " f i e l d of v i s i o n " , or the area of 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 texture. Some schemes do not function as hoped because they are inappropriately applied to s o f t t i s -sue regions where edges are exceptionally b l u r r e d , while other proposed schemes f a i l because of t h e i r ad hoc, i n t u i t i v e d e f i n i t i o n s of what con-s t i t u t e s an edge. 5.2 - Edge Point: D e f i n i t i o n and Location An edge may be conceived i n a d i g i t i z e d picture as a ridge constituted by a number of points ( d i g i t a l picture elements) running along a c e r t a i n pathway that i s often monotone. A d e s c r i p t i o n of an edge would then be i n terms of the edge points that form i t . I t should be emphasized, however, that using the word ridge does not imply that an edge should n e c e s s a r i l y be a regional [ or global pathway through intens-i t y peaks i n a given p i c t u r e . In f a c t such an implication i s the cause of the i n e f f i c i e n c y of c e r t a i n edge detection algorithms as i n [24]. What i t does mean, however, i s that i f a f t e r edge detection and t r a c i n g , while edge points are i n t e n s i f i e d and a l l other picture elements are assigned to zero i n t e n s i t y (for convenience), t h e i r appearance i n a three-dimensional representation would be as ridges. In the context of x-ray images, an edge usually separates, or contours a region of high information content i n a background of i r r e l -evant d e t a i l s . Figure (5.3) i s composed of t y p i c a l segments of scan l i n e s from a radiogram of a c h i l d ' s femur, each segment containing an edge point marked by a v e r t i c a l arrow. Scan segments l i k e those of Figs. 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 of s i m i l a r grey l e v e l value. Figures (5.3.c) and (5.3.d) represent the edge configurations i n regions of s o f t tissues surrounding strong bony structures. The scan segment i n F i g . (5.3.e) has been subjected to high-emphasis f i l t e r i n g . (e) F i g . (5.3) T y p i c a l Edge Configurations 5.3 - The Edge Detection Algorithm B a s i c a l l y , any edge detection algorithm i s a canvassing scheme by which each point of a p i c t u r e function and i t s neighbors are examined to see i f there i s a s u f f i c i e n t rate of change of the p i c t u r e function to q u a l i f y the point as an edge point. A p l a u s i b l e approach i s to use e i t h e r the gradient or the Laplacian of the p i c t u r e function at the point under consideration to determine whether or not i t i s an edge.point. This i s the basis of our edge detection algorithm. 86 In developing the algorithm, care has been taken to make i t as modular as possible. I t i s hoped that t h i s main feature w i l l maximize i t s e f f i c i e n c y over a broad class of picture functions. To achieve t h i s , two t o t a l l y decoupled algorithms have been developed, a global algorithm and a l o c a l one. The function of each w i l l be apparant l a t e r and for the moment i t i s s u f f i c i e n t to know that the global algorithm commands the main search strategy, contains stopping c r i t e r i a to prevent the de-tecto r from following f a l s e contours, supplies the parameters used by the l o c a l algorithm for edge detection, displays the contour, e t c . . . The l o c a l algorithm i s c a l l e d by the main routine and performs the actual detection. The edge detection algorithm i n i t s e n t i r e t y may be found i n Appendix E. The algorithm's function and features can probably be best understood i n the context of i t s operation on the radiogram which was used i n the development and t e s t i n g of the algorithm. This radiogram i s the enhanced version of the c h i l d ' s femur considered i n the previous chapter. A further reason f or using t h i s approach to explain the algo-rithm i s that the present implementation requires c e r t a i n parameter v a l -ues be supplied by the user a f t e r v i s u a l examination of the radiogram to be processed. I t i s possible, however, that t h i s dependency on user assistance can be removed by extensions to the software. In beginning the development of the algorithm, h o r i z o n t a l and v e r t i c a l scan segments across edges were v i s u a l l y examined i n order to gain an appreciation f o r the required software complexity to recognize edge points. As an example of the data, Figure (5.4) i s a presentation of scan segments taken from every eighth row i n the lower h a l f of the -1 "5* F i g . (5.4) Intensity P r o f i l e s I - j — , — : — , — i — | — i — i — i — i | i i — i — • | i — i — i i j i i i i — | — i — i — i — i — | — i — i ' ' i o: the Radiogram in F i g . (4.7) 88 picture and associated with the edges of the femur. Only 50 points about each of the ri g h t and l e f t hand edges are displayed i n order to s i m p l i f y v i s u a l examination. It was apparent from examination of the data that i t would not be s u f f i c i e n t to base the edge detection upon a simple one-dimensional difference c a l c u l a t i o n as was done i n [48]. Neither did a two-dimensional gradient or Laplacian seem appropriate, since the edge point l o c a t i o n tends to vary slowly from one row to the next or from column to column. Instead i t was recognized to be computationally f a s t e r and to allow fewer errors to make use of knowledge of the lo c a t i o n of the edge point i n the previous l i n e , and to follow the contour from row to row or c o l -umn to column, using e i t h e r h o r i z o n t a l or v e r t i c a l edge detection. The global algorithm o f f e r s the option of conducting e i t h e r a ho r i z o n t a l or a v e r t i c a l search for edge points. The l o c a l algorithm uses a l o c a l operation at each point that minimizes the e f f e c t s of noise before t e s t i n g the point for edge candidacy. The l o c a l operation con-s i s t s of least-mean-square-error f i t t i n g of a f i r s t and a second degree polynomial to sets of points surrounding and incl u d i n g each of points i n the scan segment under consideration. The f i r s t d e r i v a t i v e i s then c a l -culated for each of the f i t t e d f i r s t - o r d e r and second-order curves at the p o s i t i o n of the edge point candidate. The maximum rate of change of the derivatives of the f i r s t - o r d e r curves i s then compared to the maxi-mum rate of change of the derivatives of the second-order curves. I f i t i s greater, the edge point i s chosen as the point whose f i t t e d f i r s t -order curve has the largest magnitude f i r s t d e r i v a t i v e ; i f i t i s l e s s , then the edge point i s chosen to correspond to the f i t t e d second-order 89 curve with the second derivative of l a r g e s t magnitude. As mentioned before, the general structure of the edge detec-t i o n algorithm was determined on an ad hoc basis a f t e r v i s u a l examin-ation of scan segments taken from the enhanced radiogram i n F i g . (4.7). For example, since edges i n the radiogram of F i g . (4.31.b) could be sim-i l a r to e i t h e r F i g . (5.3.e) or Figs. (5.3.a) and (5.3.b), the p o s s i b i l i t y of t e s t i n g an edge point candidate 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 second-derivative i s included. Figures (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), while F i g . (5.3.e) corresponds to an edge of the femur shaft i n F i g . (4.31.b). I f the radiogram to be. processed i s very noisy, which was the case i n F i g . (4.31.b), i t i s advantageous to also smooth the data before applying the edge detection algorithm. This was done using the f i l t e r function of equation (4.14) with a cut-off frequency of 1.071 1/mm and a termination frequency of 1.428 1/mm. As an example of the e f f e c t of t h i s smoothing, Fig. (5.5) i s a presentation of the scan segments i n Fig . (5.4) a f t e r f i l t e r i n g . To begin to trace a contour the algorithm must have a s t a r t i n g l i n e to scan. Currently the user s p e c i f i e s t h i s l i n e and also a subset of points i n the l i n e to consider as edge candidates. This i s done since the i n i t i a l decision on an edge point i s c r u c i a l to the lo c a t i o n of edge points of subsequent scan l i n e s which are constrained by the p o s i t i o n of the edge point i n the previous l i n e . In the case of F i g . (4.31.b) the contour trace was started h o r i z o n t a l l y at the bottom row of the image since the bone edges there are strong enough to insure an i n i t i a l correct i i i i 1—^ ' I 1 1 1 1 I ^ ^ ^ ^ ^ ^ F i g . (5.5) Smoothed Intensity P r o f i l e s 91 decision. A set of f i f t y points i n the bottom row and associated with the left-hand edge was s p e c i f i e d f o r consideration i n l o c a t i n g the f i r s t edge point. As the contour i s traced the edge may change from being r e l -a t i v e l y v e r t i c a l i n or i e n t a t i o n to being r e l a t i v e l y h o r i z o n t a l , or vice versa. The software i s able to detect t h i s change i n or i e n t a t i o n and, when detected, begins processing v e r t i c a l scan segments instead of hor-i z o n t a l scan segments, or vice versa. For example, when operating along the l e f t edge of the femur shaft and the l e f t condyle edge the algorithm continues from row to row u n t i l the edge point begins to s h i f t i n l o c a -tion to the r i g h t i n d i c a t i n g that the region of the upper edge of the condyles has been reached. Detection there s t a r t s to operate i n the v e r t i c a l d i r e c t i o n . I t continues u n t i l the edge point drops s i g n i f i -cantly downward i n d i c a t i n g the s t a r t of the r i g h t edge of the condyles, where h o r i z o n t a l detection s t a r t s again to trace down the re s t of the bone contour. An option of weighting the derivatives calculated from the f i t -ted polynomials i s included i n the software, which weights edge point candidates to favor points close i n p o s i t i o n to the p o s i t i o n of the edge point located i n the previous l i n e . The weighting c o e f f i c i e n t s are c a l -culated as points on a Gaussian curve. The standard deviation of the curve i s s p e c i f i e d by the user and the mean i s normally taken to coincide with the p o s i t i o n of the previously determined edge point. This option was included to lessen the l i k e l i h o o d of the algorithm wandering away from the true edge i n regions of strong noise and poor d e f i n i t i o n such as the condyles. 92 5.4 - Experimental Results and Discussion It was decided to te s t the algorithm by attempting to scan the e n t i r e contour of the radiogram i n F i g . (4.31.b). Before proceeding several parameters had to be supplied to the software. The s t a r t of contour point was s p e c i f i e d i n the bottom row and the algorithm directed to search 50 points beginning i n Column 80. The second-order polynom-i a l s were s p e c i f i e d to f i t 11 points and the f i r s t - o r d e r polynomials seven points. The numbers of points spanned by the polynomials were chosen to correspond to t y p i c a l widths of edge t r a n s i t i o n s associated with uses of the f i r s t and second derivatives i n edge detection. The program was structured to begin v e r t i c a l search when the p o s i t i o n of • the edge point s h i f t 20 points to the r i g h t of the maximum excursion to the l e f t 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 set to resume when the trace dropped 20 points beneath the edge point of maximum height. In moving from row to row or column to column the search was r e s t r i c t e d to only 11 points centering on the p o s i t i o n of the previous edge point. This r e s t r i c t i o n was included to reduce errors and minimize computation. In beginning along the l e f t edge of the bone i t was recognized that human intervention was necessary to prevent the algorithm from t r a c i n g the edge of the epiphyseal p l a t e . Because of the concavity of the l e f t edge of the bone i n the region of the epiphyseal p l a t e , t h i s was e a s i l y accomplished by r e s t r i c t i n g the algorithm to locate edge points which moved progressively to the l e f t f o r several rows. I n i t i a l l y the algorithm was used without weighting the d e r i -vatives i n favor of edge candidates close to the edge point i n the pre-93 vious l i n e . This produced the contour i n F i g . (5.6.a). The contour i n F i g . (5.6.b) resulted when the Gaussian weighting function was used with a standard deviation of two sample points. Note the difference between the two contours at the s t a r t of the condyles indicated by the arrow. There are errors i n the contour of F i g . (5.6.a) due to the i n d i s t i n c t edge of the condyles i n the region of the arrow and the low s i g n a l - t o -noise r a t i o of the radiogram. The r i g h t edge of the condyles i n F i g . (4.31.b) i s very poorly defined and i n some places the edge appears to be non-existant. When the algorithm began to trace down the r i g h t edge of the bone i t d i d not s e l e c t edge points which maintained the continuity .of the contour. The algorithm was restarted by searching the next few rows to f i n d a reason-able s t a r t of contour point f a l l i n g along the anticipated path of the contour at t h i s point. The algorithm then proceeded to trace downward u n t i l the edge of the condyles became indis 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 shaft. The algorithm was then directed to s t a r t anew from the bottom row and trace the r i g h t edge of the shaft. This i t s u c c e s s f u l l y d i d , but upon encountering the beginning of the condyles the algorithm wan-dered off on an erroneous contour. See F i g . (5.6.c) where the arrow marks the s t a r t of the condyles. F i g . (5.6.d) i s the completed closed contour obtained by i n -t e r p o l a t i n g between edge points where breaks i n continuity occured due to the lack of d i s c e r n i b l e edge points., Obviously there are many problems to be solved 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 for t r a c i n g the edges of 94 F i g . (5.6) Results of Testing the Contour-Tracing Algorithm 95 the condyles i n radiograms of femurs i n infants and chi l d r e n . However, from the preceeding experimental r e s u l t s i t appears such a development i s a p o s s i b i l i t y . 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 of work preceded the scanning of the radiogram i n chapter IV. An image dissector scanner making use of a computer c o n t r o l l e d mechanical stage was constructed for the following reasons: 1 - To allow image scanning with a greater Signal-to-Noise r a t i o than previously available using alternate equipment av a i l a b l e at U.B.C, i . e . the f l y i n g spot scanner (FSS) [50]. 2 - To eliminate a necessary a d d i t i o n a l photographic processing step i n photo reducing an X-ray i n preparation for scanning by the FSS. 3 - To allow f l e x i b i l i t y i n s e l e c t i n g subsections of large X-ray images for examination by computer a n a l y s i s ; t h i s to be accomplished while p r e c i s e l y s p e c i f y i n g subsection l o c a t i o n to allow accurate measurements of large image structures while not r a d i c a l l y increasing scanning resolution requirements. A d e s c r i p t i o n of the structure of the image scanning and display system and i t s operation i s the subject of this chapter. A photograph of the data a c q u i s i t i o n system i s shown i n Figure (6.1) 6.2 - The Image Dissector Camera An image dissector camera purchased from International Telephone and Telegraph I n d u s t r i a l Laboratories i s used as the input l i g h t sensing device for the system. The camera has a s p e c i f i e d maximum res o l u t i o n of 1000 l i n e s over the useful diameter of i t s s e n s i t i v e front surface (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 safe i l l u m i n a t i o n at the photocathode, and f o r best r e s u l t s the most transparent parts of the f i l m being scanned should allow close to this amount of l i g h t to reach the cathode. This insures that the maximum number of electrons reach the photomultiplier f o r a given f i l m density and thus minimizes the undesirable quantum e f f e c t s . This camera accepts input X and Y control voltages which are proportional to the coordinates of a point to be scanned. Its output i s an analog s i g n a l with an average value proportional to the i n t e n s i t y of l i g h t at the point being scanned. The dissector camera does not integrate the l i g h t incident on i t s photocathode as do vidicons and s i m i l a r t e l e -v i s i o n camera tubes. As i n other tubes the incident l i g h t knocks loose electrons from the photocathode. These are immediately acceler-ated toward the rear. A magnetic f i e l d whose strength i s proportional to the input X and Y voltages moves the whole f i e l d of electrons i n a d i r e c t i o n perpendicular to the front to back axis of the tube. Only those electrons coming from one small region on the face of the tube get through a 5 mil round aperture i n a plate at the rear. Behind t h i s plate i s a conventional 10 dynode photomultiplier which converts incoming electrons into a measurable current proportional to the l i g h t at the point being scanned. The bandwidth of t h i s system i s f a i r l y high and because only a very small region of the s e n s i t i v e surface i s being measured at any instant the quantum e f f e c t i s apparent. That i s , the a r r i v a l of i n d i v i d u a l electrons i s evident and shows up as rather large voltage spikes at the output of the camera video a m p l i f i e r . Consequently, the s i g n a l from the camera i s extremely noisy and must be smoothed i f i t i s to be us e f u l . The desired s i g n a l i s the average 99 value of the camera output. 6.3- Noise Removal Sys tem As a f i r s t step, a 250 KHz pass-band, low-pass f i l t e r i s used to smooth the video s i g n a l . The s i g n a l from t h i s analog device i s fed to the i n t e n s i t y input of a Tektronix 602 display unit during various adjustments of the scanner system. However, t h i s f i l t e r e d video i s s t i l l quite noisy, and further smoothing i s performed with the switched a m p l i f i e r - i n t e g r a t o r combination shown i n F i g . 6-2. The 256x256 g r i d points that form the radiographic image are sampled sequentially, l i n e by l i n e , and the following steps i n d i c a t e what i s involved i n scanning a s i n g l e point: 1 - The D i g i t a l Equipment Corporation (DEC) PDP-9 computer sends out the appropriate X and Y voltages to the dissector camera. These are proportional to the coordinates of the point to be sampled. 2 - A -10 v o l t s i g n a l i s sent out on the control l i n e going to the switched units. C a l l t his time t=0. This causes both the a m p l i f i e r and integrator to turn on. The i n t e g r a t o r now begins to average the video s i g n a l . 3 - At t=l m i l l i s e c o n d the voltage on the c o n t r o l l i n e i s changed to -5 v o l t s causing the amplifier to switch o f f but leaving the i n t e g r a t o r on. Although the integrator continues to operate, i t s output holds constant since i t s input i s zero. 4 - The condition i n step 3 continues for 50 microseconds or long enough for the A/D converter to sample the integrator output. 5 - At t=1.05 mi l l i s e c o n d , a zero v o l t s i g n a l i s sent out on the control l i n e which turns o f f the integrator and resets i t s output adjustable \heght ~H I D C film d-c light source fmSile 'stage i r camera control 'swftched' amplifier offset switched integrator low-pass filter gam 0> o o offset 0 H > a tektronix display, unit video output -i-<x stooe position sW matron control y control for switched yyiiiuaun co trol units •vcontrol pDp.g DIGITAL COMPUTER v 0) -1 Q O ~1 a/d digital output v OD TTY CRT DEC TAPES '-{scope o o F i g . (6.2) Data Acquisition System Organization 101 to zero v o l t s . The cycle i s complete and a new point can now be scanned. This analog s i g n a l i s then fed to an A/D converter, quantized to 6 b i t s , and stored on a DEC magnetic tape. 6.4 - Light source and movable stage The radiogram to be scanned i s illuminated from behind by a l i g h t box which provides a f a i r l y homogeneous i l l u m i n a t i o n within 4 or 5% over an area of 11x11 inches. The l i g h t box i s mounted on a stage that i s free to move on two perpendicular racks i n the X & Y dir e c t i o n s under computer c o n t r o l , or using a manual j o y s t i c k . The maximum-excursion along any d i r e c t i o n i s 6 inches. This provides the freedom to expose any p a r t i c u l a r area i n the radiogram to the d i s s e c t o r . The s i z e of the area that i s being scanned depends on the height of the dissector with respect to the transilluminated radiogram. This height could be varied between. The programmable motion of the stage and the adjustable dissector height provide the f l e x i b i l i t y of deciding 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 large range, yet with-out being r e s t r i c t e d to a p a r t i c u l a r p i cture s i z e . I t should be noted however that the higher the scanning r e s o l u t i o n the smaller the picture s i z e scanned, or the l a r g e r the number of raster points needed to represent 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 possible by using t h i r t e e n supporting columns capped with b a l l bearings. The accuracy of p o s i t i o n i n g the stage a f t e r any complicated excursion i s within one step displacement of the stage, that i s 102 0.0015 inches. The excursion can be i n the X or Y d i r e c t i o n , or diagonally. Diagonal motion i s accomplished by^accades of X and Y a l t e r n a t i v e displacements. The motion of the stage on the racks i s e f f e c t e d by two powerful SLO-SYN stepping motors, activated by computer pulses under software command or a manual j o y s t i c k c o n t r o l . 6.5 - The Computer Interface The computer used i n t h i s system i s a DEC PDP-9 equipped with 16K of memory and three Dectape u n i t s . The i n t e r f a c e for the dissector and the d i g i t a l control used with i t i s w e l l documented [51], [52], although a few hardware modifications have been made. Appendix C summarizes the software i n s t r u c t i o n s used to control the hardware. These descriptions should adequately explain the possible hardware functions from the user's point of view. 6.6 - The Software Implementation Five global routines have been implemented to control the stage p o s i t i o n i n g with respect to the di s s e c t o r , to focus the image, to d i g i t i z e the image, to read the image onto DEC tape, and to t r a n s f e r the data e i t h e r to the DATA GEN 840A computer for display using the FSS, or to the IBM system 370/67 for processing. The following sections are a b r i e f discussion of these routines. 6.6.1 - Axes Alignment I t i s imperative to determine very accurately the d i r e c t i o n of t r a v e l of the stage i n the Y- (or X-) d i r e c t i o n r e l a t i v e to the o r i e n t a t i o n of the dissector axes and to make t h i s d i r e c t i o n exactly coincident with the dissector Y- axis'. (X- a x i s ) . To achieve t h i s , the transparency of a very s t r a i g h t edge (black to bright t r a n s i t i o n ) 103 i s taped on the i l l u m i n a t i o n box, so that the edge i s approximately along the stage Y- axis. The routine EDGTST i s c a l l e d , and through conversational made on the teletypewriter (TTY), the user s p e c i f i e s whether he intends to a l i g n the edge with the Y- d i r e c t i o n of stage t r a v e l or with the dissector Y- axis. The easiest procedure i s to s t a r t with the stage. The following steps describe the program oper-ation. 1 - The routine i n s t r u c t s the dissector to scan the h o r i z o n t a l l i n e whose Y- coordinate i s 512 (midline i n the 1024 possible entries i n the raster) and to t r y to detect an edge point. 2 - If the h o r i z o n t a l l i n e ;3s scanned and no edge point i s detected, control returns to the user who then repositions the trans-parency and r e s t a r t s the program. 3 - Upon detection of an edge point, i t s X entry i s stored i n a buffer and the stage i s instruc t e d to move along the Y- d i r e c t i o n 100 steps (0.15 inches). 4 - The program goes to a 30 second waiting loop to score time u n t i l any possible mechanical j i t t e r fades away, and steps 1 to 4 are repeated u n t i l 32 edge points are located. 5 - The 32 edge points are then displayed on the display unit i n t e r f a c e d to the computer. The f i r s t edge point i s used as a reference to construct a v e r t i c a l l i n e , and subsequent edge points are displayed i n positions r e l a t i v e to this v e r t i c a l l i n e . The display unit has a reso l u t i o n of 1024 points along the X and Y axes, and three b i t s of brightness c o n t r o l . The v e r t i c a l l i n e represents the stage Y- axis. I f any detected edge point appears on the display 104 screen other than on the v e r t i c a l l i n e , then the s t r a i g h t edge trans-parency i s repositioned and steps 1 through 5 are repeated. 6 - Sometimes the difference between a located edge point and the v e r t i c a l l i n e i s only one b i t p o s i t i o n which might not be detect-able on the display screen. To avoid t h i s , the four most s i g n i f i c a n t Accumulator b i t s on the operator console are used to accentuate the deviation from the v e r t i c a l l i n e by as much as 128 times. The three l e a s t s i g n i f i c a n t AC b i t s are used to control the brightness on the screen. 7 - Aft e r p o s i t i o n i n g the test edge along the stage Y- axis, the user requests, through the TTY, an alignment of the dissector Y- axis with the stage Y- axis (which i s coincident with the test edge). The routine followed i s e s s e n t i a l l y the same as used when al i g n i n g the test edge with the stage Y- axis. Minor changes i n the program occur," however, when incrementing the Y- coordinate of the h o r i z o n t a l l i n e to be examined f o r edge detection. 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 at the bottom of the p i c t u r e , and every subsequent l i n e i s 32 entries above the previous l i n e . 8 - I f the dissector axes are not coincident with the stage axes, the user c a l l s DISEDG to e f f e c t the alignment. The strategy of search for edges i s the same as i n EDGTST, except that the tes t edge i s continuously scanned, and the edge locations on the display screen are constantly updated as t h e i r entries are s p e c i f i e d . Each edge point i s displayed f o r 3 seconds before i t s l o c a t i o n i s updated, to allow the operator s u f f i c i e n t time to manually adjust the dissector o r i e n t a t i o n while r e f e r r i n g to the display. 105 6.6.2 - Stage P o s i t i o n i n g Control The routine STAGE, when invoked, requests the user, v i a teletype conversation, to enter the sign and magnitude of the X and Y displacements he wants the stage to undertake. The program then adjusts i t s i n s t r u c t i o n s to execute the required excursion. I f , say, the displacement along the Y- d i r e c t i o n i s longer than along the X- d i r e c t i o n , the stage f i r s t moves a distance Y-X along the Y-direc-ti o n and then moves diagonally to i t s destination. 6.6.3 - Focusing Focusing i s achieved by a program c a l l e d SCANLN which continuously scans a h o r i z o n t a l l i n e whose Y- co-ordinate i s entered v i a the TTY. A scope i s used to display the i n t e n s i t y v a r i a t i o n s along that l i n e and the user attempts to maximize the d e t a i l s as seen on the scope. When the best subjective focusing i s attained the user c a l l s the routine FOCUS. Here again the user i n t e r a c t s with the software and the following message i s prompted on the TTY: ATTN! FLAG FOR FOCUSING SET BY BIT 9 NEED FOCUSING? Y OR N —> If the answer i s N (no), execution terminates; 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 the d i r e c t i o n of the l i n e he wants to be used by FOCUS. 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 response to the following f i n a l message: ENTER COORD. VALUE — > The 'COORD. VALUE" i s the Y- coordinate of a h o r i z o n t a l 106 Figure (6.3) - Radiogram Out-of-Focus Figure (6.4) - Radiogram i n Perfect Focus 107 r a s t e r or the X- coordinate of a v e r t i c a l raster along which focusing i s attempted. A search s t a r t s along t h i s l i n e for an edge point. I f no edge point i s detected, the program r e s t a r t s and requests user inputs. Upon detection of an edge point, the f i v e points previous to the edge point and the next consecutive nine points are displayed on the display u n i t , together with the located edge point. The display i s continuous, and the screen i s refreshed every 2 seconds. The user attempts to maximize the edge slope as seen on the display. F i g . (6.^3) i s a photograph from the display of an out of focus s i t u a t i o n , while F i g . (6..4) i s of an edge i n a picture p e r f e c t l y i n focus. As i n EDGTST and DISEDG, the AC b i t s on the operator console c o n t r o l the scale and brightness on the display. When focusing i s accomplished, the user sets b i t 9 of the AC to one. This w i l l i n t e r r u p t the program, and allow the user to c a l l the routine LINTST which p r i n t s for inspection the i n t e n s i t y values along any p a r t i c u l a r l i n e whose coordinate i s entered v i a the TTY. Note: I t was found that the photomultiplier and the output from the preamplifier on the dissector do not saturate at any of the camera F- stops. The d.c. output voltage from the preamplifier varies with the lens opening as follows: F - stop 22 15 -.11 8-11 8 5.6-8 5.6 4 Pream Output(v) .22 .29 .42 .52 .78 . 1.17 1.55 2.2 Hence F-4 was always used i n scanning ;the maximum RMS dissector noise was found to be 54mV. This would insure a signal-to-Noise r a t i o of 2.2/0.054 = 40.7 before 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 radiogram scanning and quantization i s performed at t h i s stage. Before a c t u a l l y reading the picture on DECtape, the user can get information 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 of the picture by c a l l i n g the routine AVERAG. When c a l l e d , t h i s routine echoes the following message on the TTY: SIDE OF SQUARE TO BE SCANNED > & the user enters a number that s p e c i f i e s the side of the square. The TTY echoes: PLEASE ENTER STARTING COORDINATE > The s t a r t i n g coordinate i s the coordinate of the lower l e f t corner of the square. The program then outputs on the TTY the maximum, minimum & average i n t e n s i t i e s within that square. The routine PICTUR reads the e n t i r e picture onto DECtape, This routine also provides the user with the f a c i l i t y of i n t e r r o -gating each picture point two, four or eight times as desired. This would simulate averaging multiple copies of the same picture and reduce the noise. Interrogating a point 4 times and averaging the reading i s adequate to achieve a reasonable signal-to-noise r a t i o i n a reasonable amount of time. In th i s case, the picture scanning time i s 5 min. 50 sees. 6.6.5 - Data Transfer Data i s transmitted, e i t h e r f o r processing on the IBM 370 or for display on the NOVA 840A, v i a the DATA LINK. A b r i e f descrip-t i o n of important l i n k ' s features follows: The data l i n k system operates on a l i n e - at - a - time basis. At the end of a l i n e , the 109 Transmitting computer reverts to the receive mode and waits for a s p e c i a l message from the receiving computer to i n d i c a t e whether or not the message was received c o r r e c t l y . I f the message was c o r r e c t l y received, then an ACK ( p o s i t i v e acknowledgement 006) character i s transmitted i n duplicate and the o r i g i n a l transmitting computer w i l l proceed to the next l i n e . I f an error i s detected, another s p e c i a l message, a negative acknowledgement (NAK 025) i s sent, and the o r i g i n a l transmitting computer w i l l re-transmit the l a s t l i n e . A SEL character (select character (41 or 61 for binary mode)) i s used to communicate to the receiving computer that the l i n e being transmitted i s e i t h e r a re-transmission of the l a s t l i n e or a new l i n e . To achieve t h i s , the s e l e c t character i s alternated between 41 and 61 f o r each suc-cessive l i n e . I f the receiving computer detects a l i n e with the same sel e c t character as i n the previous l i n e , i t w i l l ignore the current l i n e [53]. Binary mode was f i r s t attempted for data transmission. The basic character s i z e f or the data l i n k i s eight b i t s , s i x of which correspond to a transmitted s i x b i t binary character. The l i n e length was set to 42 words (126 characters). The data rate for the l i n k i s 4800 b i t s / s e c , which i n BIN mode corresponds to approximately 200 eighteen words/sec. Unfortunately, t h i s mode of transmission was not successful, the reasons being the following: 1 - As mentioned above, at the end of each transmitted l i n e , the PDP-9 (transmitting computer) expects the IBM-370 (re c e i v i n g computer) to check for p a r i t y errors and to ask for a retransmission of that l i n e i f any errors are detected. Otherwise a p o s i t i v e acknowledgement 110 i s sent to in d i c a t e to the PDP-9 that the l a s t l i n e was received corr-r e c t l y and the next l i n e i s desired. However, what appeared to be happening was that a f t e r a NAK requested a re-transmission of a l i n e , the l i n e was not received by the 370. In s p i t e of t h i s , an ACK was promptly sent to the PDP-9 to resume transmission, and the l i n e was l o s t . The sequence of l o s t l i n e s was completely random and was de-tected i n one of two ways: a - A counter was set up i n the data l i n k handler (DPH.) to count the number of transmitted l i n e s up to the f i r s t NAK. When a NAK i s received the handler causes a transmission interrupt and out-puts on the TTY the number of transmitted l i n e s so f a r . b - In the process of data a c q u i s i t i o n from the dis s e c t o r , each 42nd data word was replaced by a l i n e number that i s incremented by one for each new l i n e . After the data i s written on a dis c f i l e , the 370 checks the f i r s t number of each l i n e i n the f i l e to detect missing l i n e s and p r i n t s t h e i r numbers s e r i a l l y . The missing l i n e s could then be read from the o r i g i n a l f i l e on DEC tape and written onto another f i l e to be transmitted through the l i n k , with the p o s s i b i l i t y of s t i l l other losses. A les s expensive but extremely tedious way to achieve transmission was to p r i n t out the missing l i n e s from the DECtape f i l e , punch them on cards and read them into a disc f i l e . 2 - The second handicap of the binary mode of transmission i s i t s i n e f f i c i e n c y . Since 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 , then 12 b i t s of a PDP-9 eighteen b i t word contain no information and yet are s t i l l transmitted. This increases the f i l e space requirements I l l s i g n i f i c a n t l y , slows the rate of useful information transfer hence increasing used CPU time of the IBM-370, and f i n a l l y requires a s p e c i a l packing routine ( c a l l e d (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 binary transmission i s that at present communication between the PDP-9 (scanning) and the 840A ( d i s -play) i s only i n SRC MODE. Therefore a scanned image can only be displayed by f i r s t transmitting i t to the IBM-370, then reformating the data and then retransmitting i t to the NOVA-840A. Because of these major disadvantages, a Peripheral - Inter-change - Program for the Link between the Nova 840 and the PDP-9 (PIPLN9) has been w r i t t e n . A flow chart of the program i s shown i n f i g . (6.5), and the complete l i s t i n g i s i n Appendix D. One should be aware of the following provisions concerning this program: 1 - The maximum s i z e of a DEC tape buffer (always even) i s 252 words. Each ASCII l i n e can at most be 126 characters long, terminated by a carriage return. This corresponds to a maximum of 63 data words /ASCII l i n e , or 4 ASCII l i n e s per DT b u f f e r . 2 - When using the DEC macro .INIT, no d i s t i n c t i o n need be made as to whether the DPH. handler w i l l be used for input or output as both transmit and receive function are used i n e i t h e r case. 3 - The Word - Pa i r - Count (WPC) i n the .WRITE macro i s replaced by a l i n e count and i s used as an End - Of - Transmission (EOT) f l a g . A f t e r each bu f f e r i s transmitted, control returns from DPH. to PIPLN9 where another buffer i s b u i l t f o r transmission. A f t e r the l a s t b u f f e r i s transmitted, the l i n e count i s set to zero i n the .WRITE macro and 112 ^START ^ GET ti OF ibWlQDS N Ft fl \SET UP COU\ INTERS FOR )LAST ASCII LINES TO BE XMITTED OPEN l/P FILE USE A.!. REGS TO POINT AT 1st DATA WORD IN DT l/P BUFFER READ A MAX OF 252 DATA WORDS N l/P BUFF. no no 4 COMPLETE ASCII LINES TO BE XMITTED 5/7 ASCII PACKING OF DATA IN 0/P BUFFER no TERMINATE LINE BY A C.R. a TRANSMIT IT no yes yes CLOSE l/P FILE GIVE ERROR MESSAGE SET EOT FLAG F i g . (6.5) Flow Chart of PIPLN9 113 the handler i s re-entered. The handler then sets the EOT f l a g and re-turns to PIPLN9 which closes the active input f i l e and waits f o r subsequent transmission. 4 - After transmission to the IBM-370, the ASCII data can be read into a l i n e a r array using the following program INTEGER*2 ARRAY(65536) , DATA(126) DO 10 I = 1, 1041 READ (1,2) DATA 2 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  Conclusion and Summary The purpose of t h i s thesis was to investigate and correct the human and t e c h n i c a l sources of measurement errors i n determining the length of long l e g bones i n infants and children. I t was shown that the femur and the t i b i a are not e a s i l y modelled and hence v a r i a t i o n s i n t h e i r o r i e n t a t i o n with respect to the x-ray tube when radiographing a patient lead to changes i n length estimates from a radiogram. The e f f e c t s of a x i a l r o t a t i o n and knee i n c l i n a t i o n , as w e l l as x-ray beam centering and height, were experimentally determined for a phantom femur using a spe^ c i a l l y constructed test f i x t u r e and making a series of orthoroentgeno-graphic exposures. I t was found that a reasonable bound on the error due to r o t a t i o n and i n c l i n a t i o n together was 0.9 mm. i n the measured length of a femur 43.00 cms. long. Varying the beam height over a range of eight inches caused a measurement difference of 1.9 mm. A more pro-nounced e r r o r , however, i s caused by varying the beam center over the femur proximal end. Here the maximum reasonable er r o r was 7.75 mm. Changes i n p o s i t i o n i n g of the Lufkin r u l e r were found to cause v a r i a t i o n s i n measured length which could reasonably extend up to 2.375 cms. Com-puter automated schemes to correct for v a r i a t i o n s i n the placement of the Lufkin r u l e r and l o c a t i o n of the beam center might be u s e f u l . Knowledge 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 of the above para-meters can perhaps help c l i n i c i a n s to devise better c l i n i c a l procedures for the production of radiograms. Psychophysical sources of measurement errors were considered and the d i f f i c u l t y of mathematically modelling these contributors to 115 error was discussed. We concluded that degradation of the radiogram by the x-ray imaging system could not be countered by a simple r e s t o r a t i o n scheme. On the other hand, the v i s i b i l i t y 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 therein could be greatly enhanced. This was demonstrated by the a p p l i c a t i o n of image enhancement techniques to a test radiogram of a c h i l d ' s femur. The most serious source of error i n measuring the leg bones of c h i l d r e n i s the radioluscency of the unossified c a r t i l a g e i n i n f a n t s . This problem was studied and a possible s o l u t i o n proposed and b r i e f l y i n vestigated. The proposed s o l u t i o n consists of f i r s t r e g i s t e r i n g the unossified condyles on the radiogram using very-low-energy monochromatic x-rays generated from~.a molybdenum target. The r e s u l t i n g radiogram i s then d i g i t i z e d and processed on the IBM 370/67 computer. Various dig-i t a l processing techniques are then applied to the radiogram, some with success. P r e f i l t e r i n g contrast enhancement using any of four d i f f e r e n t methods (histogram e q u a l i z a t i o n , logarithmic conversion, gamma correc-t i o n or smoothing and r e d i s t r i b u t i o n of the p i x e l s ) was applied to the radiogram of a c h i l d ' s femur and y i e l d e d increases i n entropy and im-provements i n o v e r - a l l v i s u a l q u a l i t y . F i l t e r i n g s u c c e s s f u l l y enhanced the edge v i s i b i l i t y using a high-emphasis Gaussian f i l t e r or a non-l i n e a r f i l t e r . Several f i l t e r s were studied and tested and a new f i l t e r i s proposed for picture enhancement. This f i l t e r has improved perform-ance over previously considered f i l t e r s i n terms of narrower point spread function and smaller side lobes. The f i l t e r e d radiograms were further processed using a non-linear mapping technique which greatly enhanced edges sharpness. The processed radiogram was seen to be s u f f i c i e n t to 116 be e a s i l y used f o r length measurement, which i s t o t a l l y impossible i n any routinely radiographed c h i l d ' s femur. An edge-detectiori-contour-tracing algorithm was developed to trace the edge of the condyles. The algorithm can possibly be used i n other radiographic applications and i s e f f i c i e n t both i n computation time and i n o v e r a l l performance. The f e a s i b i l i t y of human assisted contour trac i n g of the condyles by computer has been demonstrated. At present certain i n i t i a l i z a t i o n parameters must be defined by the user based on examination of the x-ray to be processed. Future experiments should be done with a larger data base. Also, e f f o r t s might be made to further automate the procedure. Comprehensive i n t e r a c t i v e software was established to operate a scanning and d i g i t i z i n g system with great f l e x i b i l i t y . The system o f f e r s the f a c i l i t y of d i g i t i z i n g radiograms of var i a b l e s i z e and reso-l u t i o n . I t also provides the option of inexpensively transmitting the d i g i t i z e d radiogram to the IBM 370/67 for processing or to the DATA GEN 840A for picture display using a f l y i n g spot scanner. In summary, this, study has accomplished many objectives-; much work remains to improve the techniques and also to develop an on-line computer system which i s usable and economical i n the c l i n i c a l environ-ment of the h o s p i t a l . 117 Appendix (A)  The Transformation of a Grey-Level Histogram  to an Approximately Rectangular D i s t r i b u t i o n I f the grey l e v e l s were close enough so as to approximate the x^'s by a continuous v a r i a b l e X, defined on (a,b) : a < x < b , with the p.d.f. f (x) , then the summation Z f(x n-) would be replaced by the in t e g r a t i o n F x(x) = Pr { X * x } = a ' X f x ( x ) dx (A.l) where F (x) i s the CDF. A. Now l e t Z = F(X) (A. 2) and F(X) = 0 X < a = a ; f v ( x ) dx a < X < b (A.3) = 1 b < X The transformation Z = F(X) maps the set x: a < x ^ b onto the set z: 0 ^ z < 1 ; the Jacobian of the transformation being dz dx Z dx. Since dz _ f ( x ) , a < x < b, then the p.d.f. of z, p„(z) w i l l be equal to P z(z) = f(x) = f(x) = 1 That i s the p.d.f. of Z = F(X) i s P z(z) = 1 0 <. z < 1 = 0 elsewhere dx' dz = f(x) dx dz 1 f(x) 1 dz/d X f(x) a < 118 Appendix B  Undeterminate Points  of the Six Linear F i l t e r s of Chapter IV The undeterminate points are those points at which the weight functions ( s p a t i a l response) of the f i l t e r s assume an undeterm-? : value l i k e °°/°° , 0 x 0 0 or 0/0. L'Hospital's rule i s applied at of the undeterminate points and the re s u l t s are as follows: 1 - h 1(0) = h 3(0) = f T + f c (B. 1) 2 - h 2(0) = h 4(0) = fT + fc (B. 2) 3 - h (Tr/Aoo) = (Af/2) cos(irf c/Af) (B. 3) 4 - h (2-ir/Ato) = -(Af/2rr) sin(2Trf /Af) (B. 4) 5 - h4(3Tr/Aco) = (Af/16) cos(3iTf J M ) (B. 5) 6 - h 5(0) = 2 ( f T + 2 f c ) / 3 (B. 6) 7 - h 6(0) « f T + f c (B. 7) 8 - h^(2Tr/Aco) = (2Af/rr3) sintirCf^  + f )/Af] o 1 c (B. 8) I 119 Appendix C The IOT in s t r u c t i o n s f o r the s p e c i a l hardware of the data ac-q u i s i t i o n system are l i s t e d below. Mnemonic Code Description SSNS 702201 Skip i f stage needs service RSSC 702202 Read scanning stage code SLAS 702221 Skip i f l i m i t alarm set STCL 707042 Start remote scan of dissector SPCL 707021 Stop remote scan of dissector LDX 707002 Load X-coordinate of dissector from AC (10 b i t s ) LDY 707022 Load Y-coordinate of dissector from AC (10 b i t s ) ADCV 707041 Start A/D conversion on dissector s i g n a l ADSF 707061 Skip i f dissector A/D conversion i s done ADRB 707076 Read r e s u l t of the dissector A/D conversion i n t o the AC (6 b i t s ) SSXP 707242 Step the stage i n the X-positive d i r e c t i o n SSXM 707204 Step the stage i n the X-negative d i r e c t i o n SSYP 707241 Step the stage i n the Y-positive d i r e c t i o n SSYM 707202 Step the stage i n the Y-negative d i r e c t i o n SSKP 707201 Skip i f scanning stage step i s done APPENDIX' (D) 120 c T I T L E P I P L N 9 / n /DT2 ;S PROGRAM PACKS B I N A R Y DATA I S THEN TRANS"! /IBM SYSTEM. .370/67 FOR D I S /ROUT I [IF. C A L L S / / I N I T DATA .T.NTO 5/7 A S C I I FROM AM l / P F I L E ON I T I E D E I T H E R TO THE NOVA 8-A0A OR TO THE PLA 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 THE DATA PHONE HANDLER DPH. . ' • / START A /GET D; / / NOEROR / /START / / .IODEV „ 1 9 9 5 .GLOBL G E T F I L , DP H. . I N I T 2 , 0 , 1 M I T / R E S E T A LL SOFTWARE F L A G S IM DPH. . I N I T 5 , 0 , I N I T / I N I T I A L I Z E D T 2 FOR l / P & L I N K FOR 0/P LAC I N I T / OPEN l/P F I L E J M S * n G E T F I L HLT L A C ( B U F 1 0 + 1 / A . I , REG. 10 USED FOR R E A D I N G DAC* CUTO / DT2 B I N D A T A . I N T O B U F 1 0 .READ 2, 1 , BUF 1.0 ,25A .WAIT 9 L A C BUF 10 / SAVE V A L I D I T Y B I T S OF AND / 1ST HEADER WORD SZ A / DATA CORRECT ? J M P ERROR 1 / M O ; r G I V E ERROR MESSAGE DZ M FORI.. IN' / Y E S ? I N I T I A L I Z E PROGRAM P A R A M E T E R S L H C ( B u FC ri T D AC . FORCMT LAC BUF 10 / CHECK W.P.C. AND ( 3 7 7 0 0 0 SAD ( 1 7 7 0 0 0 / B I N . DATA WORDS = 2 5 2 ? SK P ./ JMS BUPTAR / NO t T H I S I S L A S T B U F F E R . LAW - A / Y E S ; SET A -A COUNTER TO T R A N S F E R A D AC F O R L I N / A S C I I L I N E S / DT B U F F E R . LAW -77 / EACH ASCII. L I N E HAS A D I F F E R E N T COUNTER D AC BUFCNT / I N I T I A L I Z E D AT - S 3 . D AC 3UFCNT+1 D.AC BUFCNT+2 -D.AC BUFCMT+3 TA WORDS READY FOR A S C I I P A C K I N G ---> LAC ( B U F ! 1-1 / I N I T I A L I Z E P O I N T E R TO READ INTO BUF 11 DAC* DUTO / F.ROM BUF 10 S3 B I N A R Y DATA WORDS ( OR JMS PREPAC / L E S S I F L A S T B U F F E R ) DZM PNTER / I N I T . PNTER AT ZERO TO PACK C H A R A C T E R 1 L A C ( O P B U F + 2 / IN 5/7 , & BUFPNT TO P O I N T AT 1ST DAC BUFPNT / CHARACTER . A S C I I P A C K I N G ---> ' . -L A C ( B U F 1 1 - 1 / RE IN I T . P O I N T E R AT TOP OF B U F 1 ! . D.AC* DUTO / ELECTRICAL U s B e C « ENGINEERING PIPLMQ SRC 121 LAC* 1 1 JMS PACK ISZ OPCNTR / 0/P ASCII LIME READY ? JMP o-3 / NO : KEEP ON . LAC (15 / YES ? TERMINATE BY A CR JMS PACK / /TRANSFER A S C I I / / CHECK L I N E TO LINK -• LAC ( 3 3 0 3 2 / SET HEADER WORDS 0 & 1 D AC OPPU.F DZM 0P3UF+1 .WRITE 5,2,0PBUF » 1 / A L I N E COUNT P ARAMETE .WAIT 5 / S P E C I F I E D RATHER THEN A WORD COUNT / IN THE .WRITE MACRO LAC CHECK+3 / CHECK+3 IS ZERO AT EOT . SNA / END-OF-TRANSMISSION ? JMP CLOSE / YES: CLOSE I/P F I L E ISZ - FORLIM / NO : DT2 BUFFER EMPTY ? J M P MOEROR / NO : R E F I L L 0/P PUFFER CLC / YES: WAS IT LAST BUFFER SAD EOT / TO BE TRANSMITTED ? JMP START / MO : READ MORE RIN. DATA DZM CHECK+3 / YES: SET EOT FLAG IN .WRITE MACRO TO LAC ( 1005 A D n i | r JMP CHECK / .FORCE DPH. TO END TRANSMISSION / / ERROR 1 / CLOSE .WRITE .WAIT .CLOSE CLC D AC JMP - 12,2,ERMSG1,3 4 - 12 2 / R E I N I T . / RESTART EOT PARAMETER ***** PROGRAM SUBROUTINES ***** EOT IMIT / / / / ; / BUFPAR 0 /THIS•SUBROUTINE CALCULATES THE 9 OF RIM DATA IN THE LAST BUFFER /TO BE PACKED & TRANSMITTED . THE # OF L I N E S (MAX. 4) I N I T I A L I Z E S /THE COUNTER FORL I'M THE 4 LOCATIONS AT BUFCNT ARE USED TO COUNT /THE LAST DATA TO BE TRANSMITTED . LRS 10 / GET WORD COUNT = AND (776 / (W.P.C„*2)-2 TAD (-2 TAD. (-77 / TEST I F # OF WORDS IS LESS THAN 63 DAC TMRARY / STORE WORD COUNT - S3 IN .TMRARY . SPA / LESS THAN 63 ? JMP • ONE / YES : SET COUNTER FOR # OF WORDS TAD (-77 / & TERMINATE TRANSMISSION . D.AC TMRARY / NO : E L E C T R I C A L E N G I N E E R I N G P I PL N 9 SRC -122 U.B.C. . / • • THREE TWO ONE SPA J M P TAD D AC SPA J M P T A D DAC LAW DAC IS?. I S Z LAW DAC I S Z I S Z LAW DAC I S Z I S Z LAC TAD CM A TAD DAC* LAC TWO (-77. TMRARY THREE (-77 TMRARY -77 BUFCNT+ FORCMT F O R L I N -77 RUFCNTi-FORCNT F O R L I N (-77 BUFCNT FORCMT F O R L I N TMRARY ( 7 7 ( 1 • FORCMT F O R L I N / L E S S THAN 126 .? / YES ... / / L E S S THAN IBS '? / YES I F THE L A S T L I N E I S P A R T I A L L Y S E T THE COUNTERS FOR L I N E S 1, AT - 6 3 , & INCREMENT FORCMT T RUFCNT-f 1 , AT THE END OF THE I T WILL P O I N T AT RUFCNT+3 TO CHARACTERS COUNT FOR•THE L A S T A S C I I L I N E F O R L I N W I L L BE S E T AT 3 , 2 , AT SUBR. END D E P E N D I N G ON THE # (WHETHER 4 , 3 , 2 OR 1) THEN I T PLEMEMT WLL BE THE # - O F - L I N E S F U L L THEN 2,3 0 P O I N T AT S U B R O U T I N E READ IN THE I N C O M P L E T E 1 OR 0 A S C I I L I M E ! 3 ONE'S COM• COUNTER / SET CNTR FOR L A S T A S C I I L I N E / / PREP AC DAC L A C DAC DZ M L.AC DAC J M P * 0 ' L A C * C L L RAL D.AC L A C * L R S AND TAD D.AC* L L S AND TAD DAC* I S Z * J M P I S Z JMP* F O R L I N (BUFCNT FORCMT EOT (NOEROR BLIFPAR BUFPAR FORCMT OPCNTR 10 3 (7 ( 2 6 0 I I 3 (7 ( 2 6 0 1 1 FORCMT PRE P A C + 5 . FORCMT PREP A C / L E T FORCMT P O I N T AGAIN TO 1ST A S C I I L I N E / WORDS COUNTER . / S E T EOT F L A G / SET S U B R O U T I N E RETURN ADDRESS . / GET # OF B I N DATA W O R D S / A S C I I L I N E ( I N / TWO'S COMPLEMENT) & M U L T I P L Y BY 2 TO COUNT / # OF C H A R A C T E R S / L I N E / READ B I N DATA FROM DT2 B U F F E R / 3 M.S . 3 . SAVE THEM / A S C I I CODE / A S C I I DATA / SAME FOR 3 BUF1 1 / 63 (OR L E S S ) B I N DATA WRITTEN INTO BUF 11? / NO : C O N T I N U E / Y E S ; P O I N T AT NEXT A S C I I L I N E E L E C T R I C A L E N G I N E E R I N G U . B . C . PIPLN-9 SRC 12 3 / PACK / PACK CHARACTERS INTO 5/7 A S C I I . / SHORTEN TO S E V E N B I T S / F I R S T / TAG / SECOND / THIRD / FOURTH / F I F T H 0 AND ( 1 7 7 DAC TEMP LAC PNTER SAD (5 J M P NEWORD SAD (.A J M P * F I F T H SAD (3 JMP FOURTH SAD ( 2 J M P T HIRD SAD ( ! J M P SECOND DZM* BUFPNT LAC TEMP C L L ALS 13 ND ( 7 7 4 0 0 0 T AD* BUFPNT DAC* BUFPNT I S Z PNTER I M n . U l ' M T i -\ o ; \ LAC TEMP C L L ALS h AND ( 3 7 6 0 J M P TAG L A C TEMP C L L L R S 3 AND ( 17 TAD * BUFPNT DAC* BUFPNT DZM* BUFPNT L A C TEMP C L L . ALS 17 AND ( 7 0 0 0 0 0 J M P TAG L.AC TEMP C L L ALS 10 AND ( 7 7 4 0 0 J M P TAG L A C TEMP RCL AND ( 3 7 S E L E C T R I C A L E N G I N E E R I N G P I P L N S SRC 124 U.B.C. / ME WORD / / / /. / ERi'lSG 1 / CUTO DUTO F O R L I N FOR CUT B U F P N T OPCMTR TEMP P M T E R TMRARY EOT BUF! 0 n u r i ( O P B U F BUFCNT / J M P TAG DZM PNTER / R E S E T P O I N T E R S7 BUFPNT / INCREMENT B U F F E R P O I N T E R DZM* BUFPNT / ZERO OUT NEXT B U F F E R L O C A T I O N J M P F I R S T * * * * PROGRAM CONSTANTS * * * * 0 4 2 0 C 2 0 • . A S C I I ' ERROR IN R E A D I N G B I N A R Y DATA *<15><12> 10 / / A . I . P O I N T E R TO DT2 B U F F E R 11 // ............... P R E P A C A S C I I B U F F E R 0 /./ COUNTER FOR # OF A S C I I L I N E S / DT B U F F E R 0 // P O I N T E R TO L O C A T I O N OF A S C I I L I M E S C H S . COUNTERS 0 // P O I N T E R TO O/P A S C I I L I N E S 0 // COUNTER FOR # OF A S C I I C H S . TO BE P A C K E D 0 // USED IN PACK S U B R O U T I N E 0 / / . . . . . . . . . . . . . . . . . 0 -1 // END-OF-TRANSMISS'IOM F L A G o BLOCK /-'00 .BLOCK 70 ' .BLOCK 4 . E N D ' I N I T 125 APPENDIX (E) MICHIGAN TERMINAL SYSTEM FORTRAN GI41336I OOOl 0002 0003 0004 OOOS 0006 0007 000 8 0009 0010 0011 0014 0015 0016 0017 0018 001 9 002 0 0021 002 2 002 3 0024 002 5 0026 002 7 002 8 002 9 0030 0031 0032 003 3 0034 0035 0036 0037 003 8 003 9 0040 0041 0042 004 3 004 4 004 5 004 6 EDGE OET ECTION ALGORITHM 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 .TRUE. 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 . > 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 • • 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 WR !TE(6 ,101I SO OENO=SD»(SORT 1 2 . » 3 . 1 4 1 5 9 3 1 I S 0 S 0 = 2 . » I S 0 * « 2 I ' 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 R O W ( J l - O A R R A Y ( 2 5 6 , < I N I T « J ) ) CALL EDGE(ROW,INIT,FIRST,1,S0SQ,DEN0,6,NOWEIT,L0C,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 . DO 2 J - 1 , 1 6 R0W(J)=0ARRAYU257-I1,(L0C + J - U I > CALL EDGE I ROW,IN IT,FIRST,1,SDS0,DENO,6,N0WEIT, IOC,6,2,11,6) 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 LL 12 9 aLOC 1 REAMS, 105IINSID1 NOkEIT=.FALSE. WRIIE 16,104) WRIIE<6,1021 1-128 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 IT ,LOC ,6 ,2 ,11 ,11) * Y . I - 1 X*LOC WR1IFIB.IOSIX.Y IF I (LaC-LL129).LT,1NSI01) GO TO 4 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 O I . U U U 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 U 1 . 0 0 0 112.000 113.000 114.000 126 MICHIGAN T E R M I N A L SYSTEM FOR IRAN C ( 4 1 3 3 6 ) MAIN 004 8 0 0 4 9 0050 00' , 1 0052 0 0 5 3 0054 005 5 005 6 005 7 005 8 0 0 5 1 0060 .0061 0062 WRITE 1 6 , 1 0 4 1 WW I ( 6 . 1 0 3 1 IROW.LOC R E A . ' M 5 , 1 0 5 I I N S I 0 2 R l T M A X - O . 10C-1R0W I - K - 1 . 1-1*1 00 8 L " 1 . 1 6 ROW! L l=OARRAY 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 - 2 5 6 - L 0 C X-I N R 1 T E I 8 , 1 0 8 ) X , Y IF I Y . G T . R I T M A X I R I T M A X - Y IF 1 ! R I T M A X - F L O A T ( ) N S I D 2 ) ) . L T . Y ) CO TO 7 T H E D E T E C T O R HAS NOW F A L L E N S U F F I C I E N T L Y OVER THE R . H . S . C O N O Y I E . D E T E C T O R NOJ O P T I M I Z E S THE S L O P E TO A 1ST O E G R E E POLYNOMIAL . 0 0 6 3 WRIT E C 6 , 1041 0 0 6 4 W R I T E 1 6 , 1 0 6 ) 1 , LOC 0 0 6 5 F I R S T - . T R U E . 0 0 6 6 L L 1 2 9 - L 0 C 0 0 5 7 1 9 0 0 2 0 J - 1 , 5 0 0 0 6 3 2 0 R O W ! J l - 0 A R R A Y I L L 1 2 9 , ( 2 5 7 - J ) 1 0 0 6 9 C A L L 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 0 0 7 0 I F 1 L O C . G E . I 1 GO TO 21 0 0 7 1 L L 1 2 9 - L L 1 2 9 » 1 0 0 7 2 G O T O 19 0 0 7 3 2 1 Y = 2 5 6 - L L 1 2 9 0 0 7 4 X - L O C 0 0 7 5 W R I T E O . 1 0 8 I X , Y 0 0 7 6 F l R S T - . F A L S E . 0 0 7 7 L L 1 2 9 » L L 1 2 9 » 1 0 0 7 8 C O 1 3 K = L L 1 2 9 , 1 4 9 0 0 7 9 0 0 1 2 J - 1 , 1 3 ooeo 1 2 R O W ! J I - 0 A R R A Y 1 K , I L 0 C + 7 - J I ) ooal C A L L E O G E I R O W , 2 5 7 , F I R S T , - 1 , S D S O , D E N O , 4 , N O U E I T , L O C , 4 , 1 , 7 , 7 1 0 0 3 2 Y - 2 5 6 - K 0 0 3 3 X - L O C 0 0 3 4 W R I T E ( 8 , 1 0 3 ) X T Y 0 0 3 5 13 C O N T I N U E 0 0 3 6 F I R S T - . T R U E . 0 0 3 7 D O 1 4 . J - 1 , 5 0 0 0 3 e 1 4 RO WI J I = n ; R R A Y I 2 5 6 , U 4 0 * J I I 0 G 3 9 C A L L E O G E I R O a . 1 4 0 , F I R S T , 1 , S O S O , O E N O , 6 , N O U E ! T , L O C , 6 , 2 , 1 1 , 6 ) 0 0 5 0 S C R A T C 11 , 2 1 = 0 . 0 0 7 1 S C R A T C 1 1 , 1 ) - L O C 0 0 = 2 F I R S T " . F A L S E . ' 0 0 9 3 0 0 1 6 I =2 . 1 0 1 0 0 9 4 DO 1 5 J - 1 , 1 6 0 0 9 5 1 5 ROW( J ) = OA R R A Y ( ( 2 5 7 — 1 ) , U O C * J - 6 ) ) . 0 0 9 6 C A L L E O G E I R O U , 1 4 0 , F I R S T , 1 , S D S O , D E N O , 2 , N O W E I T , L O C , 1 , 2 , 1 1 , 6 ) 0 0 9 7 S C R A T C I I , 1 ) - L 0 C 0 0 9 3 S C R A T C ( I , 2 1 = 1 - 1 0 0 9 9 16 C O N T I N U E • 0 1 0 0 D O 1 7 L - l , 1 0 1 0 1 0 1 1 7 WR I T E i 8 , 1 0 8 I S C R A T C 1 ( 1 0 2 - L 1 , 1 1 , S C R A T C 1 ( 1 0 2 - 1 1 , 2 ) 0 1 0 2 1 0 0 F 0 R 1 A T ( F 1 0 . 0 , 1 3 ) 0 1 0 3 1 0 1 F O R M A T ! ' 1 * , / / / / / / , 2 0 X » * E O G E D E T E C T I O N U S I N G A G A U S S I A N W E I G H I N G FU C N C T I O N WI-TH S T A N O A R O D E V I A T I O N - - > ' , F 8 . 4 / I 0 1 0 4 1 0 2 F O R M A T ( / / / / , 4 0 X , • E D G E D E T E C T I O N S T A R T S NOW I N U P P E R L E F T H A L F OF T C H E R A D I O G R A M ' / , 4 0 X , 6 1 1 ' - ' ) , / / > 0 1 0 5 1 0 3 F O R M A T ! / / / / , 4 0 X , ' E D G E D E T E C T I O N I N V E R T I C A L D I R E C T I O N : S T A R T I N G P C 0 1 N T A T ! ' , 1 4 , ' , ' • 1 4 , ' )* , / , 4 0 X , 6 7 ( . ' - • ) , / / ) 0 1 0 6 1 0 4 F O R M A T ! M M 0 1 0 7 1 0 5 F O R*1 A T 1 1 3 ) 0 1 0 8 1 0 6 F O R M A T ! / / / / , 4 0 X , ' S L O P E O P T I M I Z A T I O N I N H O R I Z O N T A L D I R E C T I O N : S T A R C T I N G P O I N T A T 1 • , 1 4 , ' , • , 1 4 , ' ) ' , / , 4 0 X , 7 3 ( ' - ' ) , / / ) 0 1 0 9 1 0 8 F O R M A T ( 2 F 1 0 . 0 1 0 1 1 0 1 0 9 F O RMA T 1 ' S E N D ' 1 0 1 1 1 9 9 S T O P 0 1 1 2 E N D 1 1 5 . 0 0 0 1 1 6 . 0 0 0 1 1 7 . 0 0 0 lie.ooo 1 1 9 . 0 0 0 1 2 0 . 0 0 0 1 2 1 . 0 0 0 1 2 2 . 0 0 0 1 2 3 . 0 0 0 1 2 4 . 0 0 0 1 2 5 . 0 0 0 1 2 6 . 0 0 0 1 2 7 . 0 0 0 1 2 8 . 0 0 0 1 2 9 . 0 0 0 1 3 0 . 0 0 0 1 3 1 . 0 0 0 1 3 2 . 0 0 0 1 3 3 . 0 0 0 1 3 4 . 0 0 0 1 3 5 . 0 0 0 1 3 6 . 0 0 0 1 3 7 . 0 0 0 1 3 8 . 0 0 0 1 3 9 . 0 0 0 1 4 0 . 0 0 0 1 4 1 . 0 0 0 1 4 2 . 0 0 0 1 4 3 . 0 0 0 1 4 4 . 0 0 0 1 4 5 . 0 0 0 1 4 6 . 0 0 0 1 4 7 . 0 0 0 1 4 8 . 0 0 0 1 4 9 . 0 0 0 1 5 0 . 0 0 0 1 5 1 . 0 0 0 1 5 2 . 0 0 0 1 5 3 . 0 0 0 1 5 4 . 0 0 0 1 5 5 . 0 0 0 1 5 6 . 0 0 0 1 5 7 . 0 0 0 1 5 8 . 0 0 0 1 5 9 . 0 0 0 1 6 0 . 0 0 0 1 6 1 . 0 0 0 1 6 2 . 0 0 0 1 6 3 . 0 0 0 1 6 4 . 0 0 0 1 6 5 . 0 0 0 1 6 6 . 0 0 0 1 6 7 . 0 0 0 1 6 S . 0 O O 1 6 9 . 0 0 0 1 7 0 . 0 0 0 1 7 1 . 0 0 0 1 7 2 . 0 0 0 1 7 3 . 0 0 0 1 7 4 . 0 0 0 1 7 5 . 0 0 0 1 7 6 . 0 0 0 1 7 7 . 0 0 0 1 7 8 . 0 0 0 1 7 9 . 0 0 0 1 8 0 . 0 0 0 • 1 8 1 . 0 0 0 1 8 2 . 0 0 0 1 8 3 . 0 0 0 1 8 4 . 0 0 0 1 8 5 . 0 0 0 1 8 6 . 0 0 0 1 8 7 . 0 0 0 • O P T I O N S IN E F F E C T * I D , E B C D I C , S O U R C E , N O L I S T , N O O E C K , L O A O , N O M A P • OPTIONS IN E F F E C T * NAME - MAIN , L INET NT a 57 • S T A T I S T I C S * SOURCE S T A T E M E N T S - 1 1 2 , PROGRAM S I Z E • 2 6 7 5 9 4 • S T A T I S T I C S * NO D I A G N O S T I C S G E N E R A T E D NO ERRORS IN MAIN M I C H I G A N T E R M I N A L SYSTEM FORTRAN G I 4 D 3 6 ) 000 2 0 0 0 3 0 0 0 4 0 0 0 6 0 0 0 7 0 0 0 B 0 0 0 9 0 0 1 0 0 0 1 1 OD12 0 0 1 3 0 0 1 4 0 0 1 5 0 0 1 6 0 0 1 7 0 0 1 8 ' 0 0 1 9 0 3 2 0 0 7 2 ' 0 0 2 2 0 0 2 3 0 0 2 4 0 0 2 5 002 6 002 7 0 0 2 8 002 9 0 0 3 0 00 31 0 0 3 2 0 0 3 3 0 0 3 4 003 5 0 0 3 6 003 7 0 0 3 8 0 0 3 9 004 0 0 0 4 1 0 0 4 2 0 0 4 3 0 0 4 4 0 0 4 5 0 0 4 6 004 7 0 0 4 S 004 9 005 0 0 0 5 1 0 0 5 2 005 3 0 0 5 4 0 0 5 5 0 0 5 6 S U B R O U T I N E EDGE I ROW, IN I T , F l « ST » N D R P O S , S D S 0 , D E N O , M I O P N T » N O K E IT , L O C , C I U C E D G . I F I T , N P O I N T , L S R C H ) A G I V E N ARRAY DF DATA IS S E A R C H E D . F O R AN EOGF . THE C R I T E R I O N IS O P T I M I Z I N G E I T H E R THE SLOPE OR THE SECOND O E « ! V A T I V E TO A P O L Y -» • NDMIAL 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 PNTS D IMENSION XI11 I , Y ( 1 1 ) , P ( 3 1 ,ROW(501 , P P I 401 01 MrNSI 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 • UTI 111 L O G I C A L F 1 R S I . L K . N O W E I T W E I G H T I K I • ( E X P I - ( H I O P N T - K I * * 2 / S O S O I I / D E N O • » RCW IS A L I N E A R ARRAY C O N T A I N I N G A L L THE P O I N T S USED IN EOGE D E T E C T I O N . * » I N I T I S TH? ENTRY AFTER WHICH S E A R C H FOR AN ECGE SHCULO S T A R T , • • F I R S T WHEN SET TO . T R U E , I N O I C A T E S THAT THE 1ST L O C A L EDGE WILL B E O E T E C T E O . • • NORPOS T A K E S THE VALUE ,1 OR - 1 , OE PE NO ING ON WHETHER O E T E C T I O N I S ALONG 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 ( - 11 M A T R I X I I10EX . • * SDSO C DENO ARE P A R A M E T E R S OF THE G A U S S I A N WEIGHING 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 THE G A U S S I A N WEIGHING F U N C T I O N IS MAX . FOR E.G. , IF S E A R C H IS OVER 6 P O I N T S ANO THE F I R S T IS TO BE E M P H A S I Z E O T H E N MJDPNT • 1 • • NOWEIT A S S U M E S A WEIGHT O F 1 FOR E A C H EDGE C A N D I D A T E WHEN S E T 7 0 . T R U E . » • tOC I S THE 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 THE L O C A T I O N OF THE P R E V I O U S EOGE 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 » MIOPNT . * . I F 1 T I S THE DEGREE OF THE P C L Y N O M I A L . * • N P O I N T 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 . • » I N I T I A L I Z E L . S . F I T P A R A M E T E R S LK «, T R U E . S E C D E R-O. NWT'O L P L S l » L S R C H » l t P L S l « L S R C H » L S R C H 1 1 * I F I T , 1 K . | . ( N P 0 I N T « I > / 2 K F - 5 1 - K I . . • K M I N l » [ N P 0 I N T - l l / 2 . . ' • • - ' DO 1 0 L " l , N P O I N T 10 XI L l — K 1 » L « * F I R S T EDGE TO BE D E T E C T E D ? IF I . N O T . F I R S T ) GO TO 16 0 0 1 2 J'< l . K F 0 0 1 1 I " l . N P O I N T 11 Y ( I ) - R O W I J . l - K I I CALL 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 ) PP I J - N M I N 1 | . P ( I D IF I PI I I ) . L E . S E C O E R ) CO TO 12 S E C O E R - P l I 1 1 L O C - I N I T + J . N O R P O S 12 C O N T I N U E I E N T R Y M N I T . K I . N O R P O S WRIT E ( 6 , 1 10 I L O C I E N T R Y W R I T E ( 6 , 1 1 1 I PP GO TO 2 0 16 L O C l ' L O C W R I T E I 6 . U 4 I L O C 00 17 H * 1 , I S R C H DO 18 l - l , N P O I N T 18 V I L l « R 0 W ( I ' C A L L 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,P I P P ( N I « P ( 1 1 I IF I N O W E I T l GO TO 1 9 PI I I l = P ( I 1 1 . W E I G H T I H I P P I M . L S R C H l - P I 1 1 I 19 IF I PI U l . L T . S E C D E R ) GO TO 1 7 S E C D E R ' P l l l ) L O C " L O C I . ( M - L O C E O G I . N O R P O S 17 C O N T I N U E W R ! T E I 6 , U S I L O C E D G WRIT 5 ( 6 , 1 12 I (PP ( I ) , I - l , L S R C H ) IF ( N O W E I T ) GO TO 2 0 WRIT E ( 6 , 1 1 3 K P P I 1 ] , I - L P I S I . L P L SI) 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 V A L U E S OF 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 , • F O L L O W . . . « / ) 1 1 0 CORRESPONDS TO TH F O R M A T ( ' 0 • . 1 0 F 1 0 . 6 I F O R M A T ! / / / / , ! ? * , ' IN THE F O L L O W I N G . E N T R Y ' , 1 5 . C E P ' E V I O U S E O G E ' / 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 - - > ' , / , C 1 1 F I 1 . 6 / 1 FORI 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 P C I N T S - - > • C / . 1 1 F 1 1 . 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 : ' , 1 4 / 1 R E T J R N ENO . O P T I O N S I N 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 IN E FF EC I* NAME • t O C E , L I N E C N T • 57 • S T A T I S T I C S * SOURCE S T A T E M E N T S • 5 6 , P R O G R A M S I Z E " 2 7 3 4 • S T A T I S T I C S * NO D I A G N O S T I C S G E N E R A T E O NO ERRORS IN EDGE 111 115 1 1 2 113 114 20 1 8 8 . 0 0 0 1 6 9 . 0 0 0 1 9 0 . 0 0 0 1 9 1 . 0 0 0 1 9 2 . 0 0 0 1 9 3 . 0 0 0 1 9 4 . 0 0 0 1 9 5 . 0 0 0 1 9 6 . 0 0 0 1 9 7 . 0 0 0 1 9 8 . 0 0 0 1 9 9 . 0 0 0 2 0 0 . 0 0 0 2 0 1 . 0 0 0 2 C 2 . 0 0 0 2 0 3 . 0 0 0 2 C 4 . 0 0 0 2 C 5 . 0 0 0 2 0 6 . 0 0 0 2 0 7 . 0 0 0 2 C 8 . 0 0 0 2 0 9 . 0 0 0 2 1 C . 0 0 0 2 1 1 . 0 0 0 2 1 2 . 0 0 0 2 1 3 . 0 0 0 2 1 4 . 0 0 0 2 1 5 . 0 0 0 2 1 6 . 0 0 0 2 1 7 . 0 0 0 2 1 8 . 0 0 0 2 1 9 . 0 0 0 2 2 0 . 0 0 0 2 2 1 . 0 0 0 2 2 2 . 0 0 0 2 2 3 . 0 0 0 2 2 4 . 0 0 0 2 2 5 . 0 0 0 2 2 6 . 0 0 0 2 2 7 . 0 0 0 2 2 8 . 0 0 0 2 2 9 . 0 0 0 2 3 0 . 0 0 0 2 3 1 . 0 0 0 2 3 2 . 0 0 0 2 3 3 . 0 0 0 2 3 4 . 0 0 0 ' 2 3 5 . 0 0 0 2 3 6 . 0 0 0 2 3 7 . 0 0 0 2 3 8 . 0 0 0 2 3 9 . 0 0 0 2 4 0 . 0 0 0 2 4 1 . 0 0 0 2 4 2 . 0 0 0 2 4 3 . 3 0 0 2 4 4 . 0 0 0 2 4 5 . 0 0 0 2 4 6 . 0 0 0 2 4 7 . 0 0 0 " 2 4 8 . 0 0 0 2 4 9 . 0 0 0 2 5 C . C 0 0 2 5 1 . 0 0 0 2 5 2 . 0 0 0 2 5 3 . 0 0 0 2 5 4 . 0 0 0 2 5 5 . 0 0 0 2 5 6 . 0 0 0 2 5 7 . 0 0 0 2 5 8 . 0 0 0 2 5 9 . 0 0 0 2 6 0 . 0 0 0 2 6 1 . 0 0 0 2 6 2 . 0 0 0 2 6 3 . 0 0 0 2 6 4 . 0 0 0 2 6 5 . 0 0 0 2 6 6 . 0 0 0 2 6 7 . 0 0 0 2 6 8 . 0 0 0 2 6 9 . 0 0 0 2 7 C . 0 0 0 2 7 1 . 0 0 0 2 7 2 . 0 0 0 2 7 3 . C O O 2 7 4 . 0 0 0 2 7 5 . 0 0 0 2 7 6 . 0 0 0 2 7 7 . 0 0 0 2 7 8 . 0 0 0 2 7 9 . 0 0 0 2 8 0 . 0 0 0 2 3 1 . 0 0 0 NO S T A T E M E N T S F LAGGED I N THE ABOVE C O M P I L A T I O N S . »SIG 128 REFERENCES 1. Anderson, M. et a l , " D i s t r i b u t i o n of Lengths of the Normal Femur and T i b i a i n Children from 1 to 18 Years of Age", J . Bone and  Joi n t Surgery, 46-A: 1197, 1964 2. Maresh, M. M., "Linear Growth of the Long Bones of the Extremities from Infancy through the Adolescence", Am. J . Dis. C h i l d . , 89: 725, 1955 3. Maresh, M. M., "Growth of the Major Long Bones i n Healthy Children", Am. J. Dis. C h i l d . , 66: 227, 1943 4. 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