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Feasibility of discriminating between buried metallic spheroids by classification of their electromagnetic… Chesney, Robert Harvey 1982

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Feasibility Spheroids  o f D i s c r i m i n a t i n g Between B u r i e d  by C l a s s i f i c a t i o n  of Their  Metallic  Electromagnetic  Response. by  Robert  Harvey Chesney  B.A.Sc.,The U n i v e r s i t y o f B r i t i s h  C o l u m b i a , 1977  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF APPLIED SCIENCE In t h e F a c u l t y o f G r a d u a t e Department o f E l e c t r i c a l  We a c c e p t  this the  thesis  required  THE UNIVERSITY  Studies  Engineering  as c o n f o r m i n g t o standard  OF BRITISH COLUMBIA  September 1982 © R o b e r t H. C h e s n e y , 1982  In  presenting  requirements  this for  thesis  an  of  British  it  freely available  agree for  that  by  for  understood  that  his  that  reference  for  or  be  her or  shall  The  Of  University  Electrical of  British  1956 Main Mall Vancouver, V6T 1Y3  Date  DE-6  (3/81)  Canada  13 October  1982  at  the  shall  and  study.  I  copying by  publication be  allowed  Engineering Columbia  the  University  the  of  of  make  further this  head  representatives.  not  of  Library  granted  permission.  Department  fulfilment  the  extensive  may  copying  f i n a n c i a l gain  degree  agree  purposes  or  for  I  permission  department  partial  advanced  Columbia,  scholarly  in  It  this  without  thesis  of  my  is  thesis my  written  Abstract  An pattern  recognition  metallic ;  investigation  objects  performed. as  object  The  recognition  Implementation novel  which  in  the  the  a  of  objects,  was the  to  A  success  achieved.  It  is  noted  developed  provides  any  single  than  104  rate that  viable  on  the  vector  vary  in  than  to  i1  of  to  be  of  a  c l a s s i f i e r a  curve  was  tested  signatures object 98  of  and  percent  was  extension  classification  continuously  parameter.  type  815  c l a s s i f i e r  approach  pattern  results.  scheme  included  greater  the  a  such  point.  variations  of  was  development  generalized a  of  factors  and  these  recognition  which  to  that  was  various  examined  based  mean  applying  response  of  involved  nearest  set  corresponding  a  was  of  classification  response  pattern  test  signatures  the  proposed  rather  orientation.  response  the  "centroid"  resultant  feasibility  electromagnetic  proposal  the  space  representative  on  to  orientation  class  feature  The  their  and  extension  in  by  scheme  the  concepts  effect  shape  into  with  respect  of to  on  Table  of  Contents  Page  Abstract.. Table  of  ii Contents  *  iii  List  of  Tables  List  of  Figures  vi  Acknowledgement  vii  Chapter  1:  v  Introduction  1.1  Purpose  1  1.2  Scope  2  Chapter  2:  Sensor  Method  2.1  Sensor  2.2  Initial  2.3  Assumptions  Chapter  3:  and  Assumptions  System...  4  Investigations  Feature  and  8  Restrictions.  12  Extraction  3.1  Feature  Types  16  3.2  Feature  Evaluation  19  Chapter  4:  Classifier  Design  4.1  Classifier  Type  4.2  Classifier  Distance  Chapter  5:  Introduction  5.2  Orientation  5.3  Depth  6:  Measure  34  Experiments  5.1  Chapter  27  36 Sensitivity  Sensitivity  Results  and  Tests  40  Tests  41  Evaluation  6.1  Results  of  Orientation  6.2  Results  of  Depth  Sensitivity  Sensitivity  i i i  Tests  Tests.  43 49  Page  6.3  Effects  6.4  Evaluation  Chapter  7:  of  a Modified of  Conclusions  Design  Set  Results  and  7.1  Conclusions  7.2  Recommendations  7.3  Final  53  Summary —  for  55  Further  Study  Remarks  Appendix  A:  Experimental  Appendix  B:  Wilcoxon  Rank  51  56 57  Apparatus  Sum T e s t  Experiments  58  for  Paired 63  References  66  i v  List  Table  Table  Tables  5.1  Primary  5.2  Additional  Data  6.1  Confusion  Tables  6.2  Distribution  6.3  Distance  6.4  Confusion  Tables  for  6.5  E  Object  Type  c  for  Data  of  to  versus Test  Page  Set  of  39 Set  39  for  Test  Failures  Class  Means  1  47  with for  Test and  Angle  Object  2  47 2  48 48  Depth  2  50  6.6  Confusion  Tables  for  Test  3  50  6.7  Confusion  Tables  for  Test  4  52  6.8  E  Object  Type  c  for  versus Test  4  and  Depth 52  v  List  Figure  Figure  Figure  Page  Figures  2.1  Sensor  2.2  Response  variation  with  object  type....  10  2.3  Response  variation  with  orientation....  11  2.4  Response  variation  with  distance  13  2.5  Object  3.1  Feature  3.2  Estimated  P  m  c  (Equal  area  3.3  Estimated  P  m  c  (Equal  length  4.1  Feature and  geometry  6  set  15  extraction•examples  variation  with  18 segments).... segments)..  object  set  definition  anomalies  4.3  Design  set  for  object  1  other  angles  6.1  C l a s s i f i e r  performance  32  compared  to 33  (Equal  area  segments) 6.2  44  C l a s s i f i e r  performance  (Equal  segments)  Figure  A.l  Data  A.2  Overview  A.3  Detail  length 45  collection  of  26  29  Design  for  25  type  orientation....  4.2  data  Figure  of  of  test  coils  system stand and  vi  59 and  object  coils  60  jig  61  Acknowledgement  I  would  supervisors,  like  Professor  their  invaluable  to  colleague  my  helpful  express  my  Mabo  Ito  R.  suggestions Dr.  and  would  the  technical  the  Defence  would  Dr.  support.  E.  McFee  also  like  to  thank,  staff  of  Research  like  to  thank  the  Mines  for  to  my  co-  Yogadhish I  his  Jack  Toews  the  development  system  in  the  subsequent  and  This Defence,  work  Chief 27B.  management  Department  the of  of  am  Das,  also  comments  and  and  support  their  Range  for  grateful and  Mark  the  sensor/data  the  received  Defence  Research  National  Defence  for  under  for  their  acquisition  of  National  Technical  study  Establishment is  of  measurements.  Department  this  Group  especially,  Turnbull  of  Development,  vi i  Most  and  by  acknowledged.  contributions,  Clearance  Suffield.  collection  supported  Research  The  of  was  for  Establishment  in  the  and  John  assistance  program  gratitude  discussion.  I  I  to  gratefully  from  Sub-  the  Suffield  and  1 Chapter 1.1  1:  Introduction  Purpose  A need e x i s t s identify from  buried by  identifying  this  not  explode  remain the  problem metal  for  of  to  and  they  the  object  failure  on m a n u a l l y itself which  this is  detectors.  information  unknown  the  and  greatest  Several of  [8,10].The  most  to  buried  promising  earth's  of  shells  and  impact  impacting  do  they  prohibiting  the  use  the  solution  by  and the  available the  explosive  size  hand-held time  inadequacies detectors  do  accurately  and t y p e  hazard must  of  this  very  and l o c a t i o n  methods  to  area with  a costly  accurate  objects  these  of  of  any  object  therefore  be  object.  field  location  have  been  and  depth  proposed  include:  analysis  magnetic  ferrous  locating  need  yet  about  provide  and  specific  hazard.  metallic  Measurement  a  removal  known  methods  information  )  Hence the  range  an a r t i l l e r y  present  depth  might  and  cause,  Currently  no  detected.  as  made w o r s e  provide  of  other  is  The  locate  shells.  of  sweeping  determine  based  or  The  to  is  used  (.1-10%)  a user  detected  i  been  purposes.  In  that  artillery  other  operation  allow  has  is  hazard  conventional  on  fuze  pipelines.  however,  unexploded  accurately  These o b j e c t s  explosive  detectors.  not  to  to  term  relies  consuming  objects.  percentage  due  a long  area  work,  an a r e a  a certain  fields  artifacts  buried  Wherever zone,  many  metallic  archeological  addressed  in  of  the  induced  anomaly by  the  in  the  presence  o^  2 ii)  A n a l y s i s of a time  Either object  of  depth  consideration feasibility  determine  i n f o r m a t i o n in the object  identification  research  object  of  the  the  object  possible  restricted  the p o t e n t i a l to  the  of  analysis  addresses analysis  to  of  composition, this  applying pattern of  the  response,  such set  objects. purposes  to a set  of  of  this  steel  This  prolate  object  set  retaining  a r e a d i l y character!"zable  responses  shape with  research  object  in a i r ,  the  analytically  from w i t h i n a known  realistic  respect  r a t h e r than in  the  object  spheroids was chosen geometry.  set  was  of varying to provide .a  to a r t i l l e r y  studied were r e s t r i c t e d  shells  while  Additionally,  to those of  the  object  soil.  Scope The t h e s i s  recognition the  thesis  such as m a t e r i a l  might be c l a s s i f i e d  shapes and volumes.  1.2  under  by s u i t a b l e  response  parameters  techniques  For the  the  This  (<2m)  of  response.  investigates  recognition  an  shown to be capable  range  application.  analysis  the  can be used to l o c a l i z e  have been  to  field.  and volume has not proven promising [ 3 ] . Hence  shape  of  these methods  for t h i s  of  Direct  of a conducting object  v a r y i n g electromagnetic  electromagnetic  that  response  and both approaches  providing  its  the  object  to the  covers  structure, signatures  development  the  development  from determination for meaningful  and t e s t i n g  of  of an of  entire  the  potential  classification  a prototype  through  classifier.  of  3 Chapter documents Included  the  as w e l l  contained  on' t h e  third  also  chapter  to to  are  five  details  evaluating  the  results.  including of  the  an  an o v e r a l l research.  summary  the  the  the  work.  initial signatures  discrimination  in  the  their  object  feature  orientation  the  and  extraction  details  relative  classifier nearest  the  a  effectiveness.  implementation.  mean  vector  orientation  of and  of  the  The  techniques  dependence  tests  performance  The  data  analysis  significance  allow  in  of  whether  changes  into  describes  and  test  results  determine to  made  and  of  the  discussed.  classifier  representative  the  implementation  the  accommodate  Chapter  of  of  conventional  responses  assumptions  describes  for  describes  methodology  examined.  investigation  four  necessary  to  effect  considered  preliminary  extensions  is  and  sensor  information  The  response  the  a summary  undertaken  objects.  techniques  object  is  sufficient  The  Chapter  describes  restrictions  investigation  between  two  is  the  failure  examined  results.  presents  to  standard  performance  set  these  used of in  trends  the  used  and  an  seven  for  the  in  system  chapter  Chapter  suggestions  evaluate on  a  six, evaluation embodies  future  4 C h a p t e r 2:  Sensing  2.1  System  Sensor  M e t h o d and  While several response promise harsh  of  an  The that  exist,  the  localization  known as  pulse  conducting  develop  pulse  one and  environmeht[9 ] i s pursued  conventionally  Assumptions  methods of m e a s u r i n g  object  for object  System  eddy c u r r e n t s  here.  shown t h e  most  determination  in a  This  i s b a s e d on  w i t h i n them w h i c h  these  eddy c u r r e n t s  e s t a b l i s h e s a secondary  which  can  by  The  sensor  illustrated transmit  geometry  in Figure  2.1.  receive  coils  and  target  object  centre  of mass of  a current during each as  of  such  voltage,  train  and  the  pulse.  Relevant  of  for this  above centre  coil  the to  the  is driven  by  i s monitored  after the  the  fall  of  experimental  t h e s i s are  included  A.  theoretical  s o l u t i o n approximating  a system e x i s t s v ( t ) , induced  transmitter  data  details  field  co-planar  coil  coil  period  of  measurements i s  transmit  receive  decay  in  object.  horizontally  from the  t a r g e t . The  used t o c o l l e c t  Appendix A  d,  field  decay  magnetic  I t c o n s i s t s of placed  The  near the  f o r the  transmitter quiescent  current  apparatus  the  parameters.  coil  used  at a d i s t a n c e ,  pulse  the  a simple  principle  subsequently  by  sensed  object  the  to a stepped magnetic  a manner d e t e r m i n e d be  method i s  induction.  subjected the  electromagnetic  t h a t has depth  induction technique objects  the  current  the  for spherical objects i n the  step  receive  i s given  by:  coil  due  step  [7]. to a  response The  5  2  v(t)=  2  )  T  I  2  2 3 / 2  (R +d  2  oo  2 3 / 2  (R +d  n  )  _  A  k'  e x p (  t  )  u  r  a a  (  2  ,  1  )  2  o  where a - i s t h e r a d i u s  "  n  1  H  0  of the o b j e c t  a - i s the c o n d u c t i v i t y of the o b j e c t \IQ-  i s the p e r m e a b i l i t y  u -  i s the r e l a t i v e  r  of free  space  permeability  of the  object d - coil-object t  - time from  C  = » T R T N  N  R  distance  instant  defined  of f a l l  above  of current  pulse  1  2  RT - r a d i u s R - radius  of the t r a n s m i t of the r e c e i v e  I - t h e change N  i n current  - t h e number o f t u r n s  T  coil coil  i n the transmit  coil  i n the t r a n s m i t  coil -  t h e number o f t u r n s  i n the r e c e i v e  coil 6 \  n  k  =  2 D 2  ( (u -l)( u +2)+k ) r  r  and  the s e t of k  transcendental tan  k  = n k  n  (  n  are the s o l u t i o n s t o the  n  equation  V  1  *  V(u -1) r  As one can s e e , t h e r e s p o n s e , v ( t ) , i s weighted  damped  coefficients  exponentials.  are determined  The w e i g h t i n g  by t h e p r i m a r y  a sum o f and t h e  field  change, t h e  Figure 2.1  Sensor geometry.  7 sphere  dimensions,  effect  of  variations  complex;  however,  The modifies from  effect  only  this  the  observed  complex.  the  amplitudes  time  be  the  in  be  the  response terms  terms  a  with  radius  in  amplitude  Hence,  monitoring  quite  order.  variations the correction  object  dimension  are  both  increases  the  and  lengthens  their  the  terms.  increase  terms of  expected  the  to  reduce  terms,  having having  is  object  object equal  a  An  the  while  very  and  the  However is  more  initial extent  by  in  i n i t i a l  again  complex effect  in  increasing  initial  shorter  constants  also  in  this  case,  initial  a  response  each  term  the  as  in  higher  constants.  reduce  of  change  the  but  time  time  the  of  by  amplitude,  the  however  function  general,  characterized  progressively  the  For order  amplitudes  of  increase.  Superficially, analysis  relevant  shown  C.  multiplicative  described.  objects  increases;  material  term  be  field  applying  signature  non-permeable  permeable  all  primary  by  exponential  of  simply  a  allow  are  eliminated  constant  response  for  the  constant  response  permeability  order  the  can  The  constants.  The  cannot  parameters  observations  in  associated  would of  properties.  response.  the  conductivity  the  and  material  these  change  be  increase  of  increasing  time  can  of  general  overall  effects  An  amplitude  a  sphere  any  some  current  The  the  the  the  in  of  source  transmitter to  and  of  the  this  would  sensor  parameters  properties.  that  it  appear  signatures  detailing  Unfortunately  approach  that  bears  the  to  model  directly  object  other  l i t t l e  this  size  research  promise,  might derive  and [3]  primarily  has due  8  to  the  these 2.2  noise  sensitivity  parameters  Initial  above  induction  model  response  equivalent geometry.  model  of  undertaken  to  with  i)  This  respect  (objects whose and  object the  the  parameterized Changes  in  normalized  to  of  prolate  shape  material  or  defined  in  object  all by  the  allows 0 to  one  speroids  minor  radius  A  of  of  an o b j e c t  the  2.1). an o b j e c t  (d,figure  system, for  one  constrain  the the  2.1).  can  see  of  the  rotations  Additionally to  in  symmetry  of  vertical  90°. were solely  assessed  an c o n s t a n t  prolate  their  sensor  plane.  properties,  E)  depth  of  response  form were  was  behavior  changes  dependence e x i s t s  of  study  in  with  no  complex  examined  (6,Figure  investigations the  trends  orientation  the  horizontal  a range  These  the  symmetry  studied  pulse  However,  a more  objects  ratio  plane  the  to  study  aspect  From  the  for  the  experimental  c o n s i d e r e d were  Changes in  orientation  of  general  object  Changes in  objects  angle  extract  to:  iii)  in  the  predict  object.  objects  s h a p e was  vertical  no  used to  signature.  to  a preliminary  Change of  ii)  for  signatures  shape.  one  a spherical  delineate  induction  spheroidal  that  algorithms  response  allows  exists  Therefore  response  the  the  Investigations  The  pulse  from  of  largely by  after  RMS v a l u e .  its the  qualitative magnitude signatures  and and were  form.  9 The as  results  of  these  preliminary  investigations  were  follows:  i)  The  change  of  material), changed to  its  would of  the  the  same  response  overall  type  depth  signature  amplitude  from  (i.e.  the  and  increased with  target  (material  parameters  significantly  for  aluminum the  similar  signatures  of  three  at the  Changes in  the  variations  in  aluminum to  waveform  with  this  for  to  response the in  shape.  amplitude by  comparing (made  different  objects  of  2.2  to  produced  as  well.  largely of  orientations  in  however,  Figure  responses  steel),at  the  changes  variations  form. the  than  steel,  object  insignificant  and  and  (2  amplitude  response  the  orientation  signatures  Steel  of  changes.  an  the  amplitude  Figure  changes were  relatively  object  three  plane  the  and  of  one  objects  shape.  these  orientation  significant  effect  single  of  variations  waveform  respect  extent  As  constant)  objects  same d e p t h  objects  confined  exhibited  the  respect  size  steel  of  demonstrate  the  for  objects  aluminum)  For  higher  with  the  the  held  or  orientation,  form.  model,  signature  was  and  its  sphere  shape  both  the  1  iii)  object  given  expect  shows  ii)  an  2.3 of  constant in  both  the  in  shows a depth,  vertical  (6=0,45,90°).  Changes in  the  interesting observation.  and  depth  of  the  potentially  Namely,  that  objects  produced  an  beneficial  while  a change  in  depth  o o oo  co o  0 0  STEEL A-33MM E-3.6 9 0 0 EG 40 CU  o o CM  STEEL A-59MM E- 2 . 0 90 DEG 40 CM  ALUMINUM A-33MM E-3.6 90 DEG 40 CM  Q_ CO UJ  cc:  o  J  200  400  600  800  TIME MICRO SECS Figure 2.2: Response variation with object. Depth and orientation held constant.  1000  o  _j 200  ,  1  400  1  1  600  TIME MICRO SECS  1  1  800  1  1  1000  Figure 2.3: Response variation with orientation. Normalized response with distance held constant.  12  affected  the  had m i n i m a l shows,  overall effect  the  object  sensor-object  the  to  being  shown  observed  These significant objects  at  conclusive objects could  was  be  provide  the  that  possible  held  for  object  of  object,  is  at  objects  between  any  to  the  larger  pulse  that  there  and  Restrictions  in The  results  are  of  was  disparate not  reponse  of  That  from  is,  set  promise  would  by  response  a known  two  some  developed which  induction  membership  is  distance. the  orientations,  its  and  in  inherent  of  this  the  identification.  the  noise  responses  of  be  only  slight  the  2.4  the  differing  very  While  two  in  it  studied.  the  separation at  variation  indicate  a method  type  interpretation unknown  all  a response,  As F i g u r e  characteristic  same o r i e n t a t i o n .  proof  of  form.  responses,  taken  investigations differences  of  m a s k e d by  is  for  the  distance,  measurement  figure  on  magnitude  normalized  close  amplitude  suitable from  an  could  be  determi ned.  2.3  Assumptions  Throughout made These  to  limit  the  assumptions  i)  There the  this  certain  complexity are  is  coil  mass). that,  work as  no  response  the  problem  to  have be  been  considered.  follows:  error  axis This  in  of  assumptions  the will  in  sensor  intersects is  not  sphere occur  positioning  the  object's  unreasonable case, in  the  this  as  (i.e.  centre  one  maximum  position.  can  of show:  amplitude  o  ,  200  1  400  1  1  600  1  1  800  1  1  1000  TIME MICRO SECS Figure 2.4: Response variation with distance. Normalized response with orientation held constant.  14 ii)  No e x t r a n e o u s no  shell  nearby,  fragments and h e n c e  of  the  object  an  operational  including before  iii)  Only  in  most  other  the  is  that  artillery  targets  objects  differ  their  objects  All of  ratio  of  determination reflects a major  the  of  that  dimension  figure  target  are  The  B-major  and  used  objects  not  (A)  radii).  2.5.  only  on  on  orientation.  that  and p e r h a p s the  system can  objects.  That  unknown  derive is,  a requisite  This  merely  orientation  derives  associated  with  as  most  is  only  from  rejection  from  importantly,  signatures  response  assumption  hazard  type  their  targets  judged  iii  not  concern.  assumed  not  its  fact  Additionally,  the  target  is  removed  statement  radii  in  in  possible,  steel.  (E=B/A,  Classification validity recognition  the  minor  be  in  of  mild  a r e shown  used  problem set  that  indeterminate.  limited  the  made  are  are  the  are  spheroids  The  are  clutter,  would  of  objects.  aspect  i.e.  assumed t h a t  attempted.  prolate  their  is  is  with  shells  in  objects  surface  orientations  four  and  It  fragments,  Specifically,  comprises  present;  response measured i s  number  consistent  is  metal  isolation.  shell  their  This  clutter  environment,  a limited  variety.  v)  or  identification  although  iv)  metallic  of  for the  the  known  object.  set  This risk  explosive  is  test  targets  system.  prohibitive  m i s c i a s s i f y i n g an  a non-hazardous  used to  unknown  the  it  of is  A \J  STEEL A-60MM E-4.3  e  STEEL A-33MM E-3.6  STEEL A-37MM E-7.1  Figure 2 . 5 : Object  set.  0  STEEL A-59MU E - 2.0  16 Chapter 3: Feature 3.1 Feature As  Types  i n a l l pattern  prerequisites the  data  f o r feature  r e c o g n i t i o n problems, the s e l e c t i o n comprise compression of  to the fewest p o s s i b l e f e a t u r e s while  important possible feature  Extraction  discrimatory to c o n s i d e r  vector  information.  in i t s e l f ,  the computational  as a  and memory  size  are p r o h i b i t i v e . Hence, some  to compress the response i s r e q u i r e d .  The thesis  While i t would be  the sampled response s i g n a t u r e  requirements of that approach algorithm  retaining  methodology chosen f o r f e a t u r e  is a straightforward  e x t r a c t i o n in t h i s  one, extending  the approach  used  by Das et al [ 4 ] . The technique c o n s i s t s of n o r m a l i z i n g the response s i g n a t u r e  to a constant  RMS value,  response i n t o k time segments and developing  segmenting the a single  feature  element f o r each segment. The time sequence of these elements then comprise  the feature  Normalization this  vector.  of the o v e r a l l  a p p l i c a t i o n as the amplitude  response i s r e q u i r e d i n  of the s i g n a l i s much more  a f u n c t i o n of the depth of the o b j e c t offsets  than i t s type.  in depth, which one cannot expect accurate  knowledge of, would otherwise swamp the r e l a t i v e l y response v a r i a t i o n s a s s o c i a t e d with  Small  a priori small  d i f f e r e n c e s i n the object  type. The  original  work with  this  concept used equal  segments and e s t a b l i s h e d as the f e a t u r e constant  of a s i n g l e exponential  element the time  term f i t t e d i  length  to the data  17 within  the  segment.  simulated  data  differing  radii  scheme  were  The  This  (using and  hence  the  individual  sphere  material  scheme  segment.  tested  arid  the  Four  encouraging model)  for  properties.  implemented  variations  segmentation  produced  for  feature  feature  cases  on  of  Extensions  this  included  results  of  this  thesis.  changes  developed  types  were  in  both  for  the  the  considered,  these  were:  Fl  -  The  time  constant  exponential  term  of  a single  fitted  to  decaying  the  data  within  the  segment.  F2  -  The  slope  of  a line  segment  fitted  to  the  segment  data.  F3  -  The  mean  value  F4  -  The  difference  successive being  The one  would  the  form  ability & b,  of  where on  feature  poor in  expect  to  overlaid two  first the  two  the  data  used  extraction in  the  to  techniques.  is  these  develop  This  is  element  are  chosen  since  characterize  of  this  type.  Their  shown  in  Figures  3.1  two  features  them.  suffer  cases  of  itself.  accurately  signatures  noise  values  feature  (F1.F2)  techniques  high  last  types  signal  to  mean  segment  features for  the  that  associated with  the  fitting  of  feature  these  segment.  between  mean  characterize fits  the  segments,  response  performance  the  the  of  due  to  are  However,  from  the  the  especially  these  prospect limitations  true  a  when  the  of  o o o  o o o  rO  KJ  I  -  Feature  •  -  Data points  too c °  Wg  § s  aT  Q. CO CD  co  0)  a: 250  Time  500  750  1000  250  Time  (microseconds) (a) exponential tit (F1)  o o o_ to  500  750  1000  (microseconds) (b) linear fit (F2)  O  o  R -•  a) too  CD  rO  Q. co CD  OL CO CD  1  1  1  250  500  750  1000  0  ,  1  1  250  500  750  Time (microseconds) . (microseconds) (d) mean difference (F4) (c) segment mean (F3) Figure 3-1: Feature extraction examples. Data is from object 1 at d-60 cm.,0=45. Three equal length segments are used.  Time  00 1000  19 number would  of be  points the  feature  used  to  if  many  segments  feature  types  case  last  two  as'essentially  reduced  (Figures  & d).  3.1  emphasizes rather  c  the  than  inherently  but  cannot  the  case  of  these  segments  in  the  features  and  used  the  equal  hence  averaged  to  small,  as  develop  the  segmentation for  the  the  design  3.2  Feature  that  combination  types  be  considered  the  response  difference,  two  very  to  segment  feature  easy  the  F4)  to  types  implement,  response  well  for  to  fifteen  based  the  This  signal  to  under plan  segment  second noise  for  numbers  two used  length  equal on  segmentation of  the  mean-based  constant  The  segment  limits  required  to  on  observed  response  dependent data  This of  set  the  plan in  all  assumed  components  a  and  plan  used  to  is  achieve  response  calculating  segmentation  segments  in  plan  roughly  entire  number  considered  segmentation  segmentation  required.  was  be  are  test  two  areas.  the  would  the  and  While  second  second  chosen  and  can  segment  characterize  first  segments  over  These  The  space.  the  (mean  itself.  of  segment  (F3,F4)  area  of  from  feature  the  such  feature  type  insensitive to  (F3,F4)  response  range  plans.  segments;  designed  equal  are  is  segments.  of  achieving  in  expected  Each  length  of  feature  versions  last  response  few  segmentation  The  noise  be  sample  changes  the  are  is  the  vector.  The  of  estimate  the then  process  fixed both  set.  Evaluation  it of  would these  be  conceivable  feature  to  extraction  take  every  techniques  and  submit  20  them  to  the  c l a s s i f i e r  effectiveness,  that  To  a  avoid  this,  undertaken.  For  extraction typical class the  means)  design  various  performance in  respect  this  and  set  their  be  time  a  and  evaluation  A  design  estimate  of  developed  feature  measure  each  sets  consuming of  the  was  the  of  applied  feature  set  variance  at  were  then  evaluated  performance  could  feature  to  a  each  combination.  to  was  (comprising  each  later)  exercise.  features  for  (discussed  changes  relative  combination  segmentation  set.  an  was  very  evaluation  c l a s s i f i e r  to  determine  preliminary  data  design  trends  would  technique  design  to  point  in  These  using  a  establish  what  expected  with  be  the  in:  i)  the  number  of  segments  used.  ii)  the  type  of  feature  i i i )  the  type  of  segmentation  /  The averaging object  design all  and  data  data  set  considered  noise-free  each  object  each  then  replicated  noise  (AWGN)  process  20  such  yields  a  was  that  simulated  the  noisy  data  set  being  comparable  case  for  which  classification  j),  and  the  variance  class  would  consideration means  vectors  in  ratio  worst  and  record  mi j  jh*,j  5  in  is  (class the  were  this  white  with to  is  75.  of  attempted.  then  applied  feature  set  constant that  is  This level the The  to  orientation space  for  Gaussian  be  i,  of  responses  noise  level  set  object  to  signal  noise  data  records  of  the  under  of  of  separately  combination  addition  with  extractor  by  each  set  Each  noise  feature  for  prototypes  with  the  developed  resulting  orientation.  times  used.  available  The  then  and  used  records  orientation.  extracted.  are  this  21  estimated.  The  class  the  set  for  design  data  set  allows  analysis.  i  )  ii)  the  with  to  from  AWGN).  is  probability  of  The set is  under then  point  the  of  set  in  belonging  than  probability (and to  k;  points  this  for  of  artificial  the  following  covariance  will  b  S/N).  ('P  is  m c  )  used  the It  j  is  of  the  class  to  not  context  class  defined  an  (Pmc)  should  a  feature  probability  (mc) at  as  i  at  i  at  j  the  P(mc/i)*P(i)  i where P(mc/i)  = I j  P(mc/i,j)*P(j)  j  an  design  segmentation)  ,P(mc/i,j),  fol1ows:  Pmc = I  when  error.  misciassifying  orientation  for  orientation  an  and  that  occurs  as c l a s s  type of  simple  noted  m i s c i a s s i f i c a t i o n for the  estimate  associated  of  be i  (follows  roughly  e  consistent  classification  hence  from  belonging  no  a m i s c i a s s i f i c a t i o n event  other  derived  from  classifier.  as c l a s s  test  use  misciassification  space p o i n t  orientation  form  assumptions  exhibit  measure  design  application,  classified  The  vectors ^i,j  (follows  performance  feature  will  variance  nearest-mean-vector a  make t w o  features  a particular  this  computed  are:  equal  of  thus  evaluation.  The  The  The  the  one  These  means  (3.1)  any as  22  Lacking assumed  that  Equation  3,1  a basis  all  class  then  Pmc = n  where  1  z  s  i  j  c  Determining for  classifier possible  * n  assumption, are  it  P(mc/i,j)  (3.2)  number  of  classes  -  number  of  orientations/class  probability  point  (i,j)  more  determine  of  is  than  an  is  equiprobable.  -  involving  to  0  the  each  other  and o r i e n t a t i o n s to:  ne  P(mc/i,j)  any  reduces  *  c  n  j  for  misciassification  not  two  upper  v  straightforward  classes.  limit  from  for  However,  the  it  a is  following  r e l a t i on:  P(mc/i,j)<  I  P(dec'n=k/i,j)  the  probability  where  P(dec'n=k/i,j)  is  class  centred  point  to  another  at  the  class  k  misciassification value  for  without Hence  this  as  a two class  to  assumption  is  made a b o u t  It  is  approximated  by  P(dec'n=k,1/i,j)  should is  be  only  Hence  point  noted  one  the  of  assumed t h a t  the  class  that  i.e.  only  k  to  the  ))  of  value  the  point  P(dec n = k / i , j ) , m c  (Eqn  error.  not  P(dec'n=k/i,j)  1  P  is  magnitude the  3.7)  of can  point (i,j) the  method. this be  only  an  is  any  general the  A  available  (k,l) for  albeit is  the  where  computational  where  of  belonging  possible  P ( d e c ' n = k , 1 / i , j ) , in  component  resultant  case;  the  a member  c l a s s i f i e d as  extensive  probability. nearest  that  (P(dec'n=k/i,j  a very is  is  class k  probability  resorting  an  in  (i,j)  (3.3)  the  1.  case, largest.  It  23  approximation  to  the  probability  of  misciassification.  Thus,  A  P  m  c  should  be  measure,  from  estimate  of  considered  only  one  to  the  calculation  of  method  two  class  is  deriving  from  construction  variance  v e c t o r s ) [ 1 5 ].  of  the  weighted  question another  (mi,j) class  straightforward  It  distance and  this  the  (  absolute  of the  assumptions  data  set  (AWGN,  merely  the  i , j , k ^ between  the  nearest  an  under  the  involves d  than  assumption,  probability  of  performance  rather  Given  misciassification the  a relative  another,  performance. this  as  design  set  equal  determination point  point  in  of  (m|c i). }  m. , - m. -k,1 - i , J s. . '  mi n 1  i, j ,k  (3.4)  Then P(dec'n=k/i,j)  « P(Z  > d.  .  ./2)  (3.5)  1 , J ,K  where  Z  is  governed  mean=0,  For  this  case  by  a  normal  distribution,  variance-!  then  P(mc/i,j)  -  I k*i  P(Z  > d. 1  , ,  J  ./2) '  (3.6)  K  and  *  P.  ITIC  n  x c  n  Q  I  i  j  I  I  kvi  P(Z  >  d.  . ./2)  (3.7)  24  The Figures  results  3.2  and  expectations. perform they the at  as  represent mean  large  3.3.  The  better  of  this The  evaluation  performance  mean-based  feature  the  of  the  number  signal  feature  numbers  segments  reduction  of  associated with  The  F4  feature  the  increase  in  type  is  error  (F4,  since  sensitive  are  these mean  to  associated with  generally  increased breaks  and  down  for  3.2(d),3.3(d)) cases is  this  the  intuitive  (F3,F4)  trend  the  in  confirm  Figures  for  computing  more  types  This  type  presented  trends  segments  better.  difference  are  the  noise  decreased.  effect  due  to  difference  operation.  The exhibited  feature  a degradation  decreased.  This  estimating  the  segment  is  due  in to  features  definitive  fitting  performance the  as  increase  the  number  conclusions  results  of  these  performance  of  the  based  b a s e d on  the  data  as  the  segment  in  uncertainty  of  points  in  (F1.F2) length in  the  decreases.  No the  types  on  somewhat  equal  two  area  superior  tests  with  the  to  be made  repect  segmentation  appears  for  can  plans,  provide  majority  to  of  at  the  this  relative  although  results cases.  point  that  the are  one  on  o  IO  <0J  o J  3  6  9  12  3  15  Number of segments (a) segment exponential time constant (F1)  6  9  Number of segments  12  —i  15  (b) segment linear slope (F2)  8 i No J  —tM O ( 0  I  3  *  '  t—'—•—1—*—•—r-  6  9  12  Number of segments (c) segment mean (F3)  -oj  —I  3  15  Figure 3.2: Estimated probability of misclass'rfication ( P  •  • — l — • — ' — i  6  9  Number of segments  r-  12  (d) mean difference (F4) m c  ) for equal area segmentation.  15  o to  o to  *?0  <0J  o J  O J  —i  3  6  9  12  3  15  6  9  12  15  Number of segments  Number of segments  (b) segment linear slope (F2)  (a) segment exponential time constant (F1)  S i  8 l  <0J  <0J  o J  O J  -?—•—•—I—•—'—1—'—'—I— 3  6  9  12  i 15  3  »  '  I 6  '  i  '  9  i 12  Number of segments  Number of segments  (d) mean difference (F4)  (c) segment mean (F3) A.  Figure 3.3: Estimated probability of misclassification ( P  mc  ) for equal length segmentation.  15  27 Chapter  4.1  Classifier  4:  Classifier  The  Type  goal  of  extract  meaningful  require  in  order  to  this  allow  manner.  The  interest,  design  any  pattern  information.  application one  to  deal  orientation  is  not  recognition  an  The  is  the  with  of  important  information type  the  the  system  of  the  object  object,  parameter  is  to  that  we  object,  in  in  an  appropriate  while  of  peripheral  for  this  application.  As with  noted  respect  previously,  to  orientation.  changes  This  representation  might  require  this in a  could  be  a b s e n c e of  continuum  of  infinite  hence  form  response plane number  of  points  approximating  it  various  angles,  techniques  in  with  the  signatures  the  feature  in  the  at  for  orientations  cannot  this  One  collection  to  points  use as  any  the  of  space  one  so  that,  class  even comprise  that  object  an must  a  would  infinite consider  of  by  points  the  vertical  solution  design  to  object.  potential  object  for  representing in  a  response  conventional the  not  this  corresponding  acquire  track,  is  a given  all  representing  these  set  feature  some m e t h o d .  then  space  the  by  and  of  one  information,  orientation  design  through  infinite  the  feature  where  problem  faced  define  points  of  some c o n t e x t s orientation  to  sequence  the  with  is  S i n c e one  this  into  change  and  One  object  approximate  over  type  this  feature  (6=0.,90°).  and  object  However,  variability  that  In  signatures  benificial.  points  a locus  of  type  noise,  A complete  the  carries  as w e l l .  the  application.  the  the  both  response  both  behavior  space  variation  in  the  is  small at  classification set.  to  28  Severe one  limitations exist  can see i n t h e example  Figure  4.1,  the d i s t a n c e  within  a class  inter-class that  distance.  a design  representing vertical on  any  angle  such [2]  great  for  nearest  (nearest  mean  design  with  some  which  any  o f an  functions choosing  based  representing  is clearly  any  t o mean  measure  to  unworkable  to define  any  classifier,  distance  clearly  closer  a t 45° than  a distance  on  point  unless  the design  set  The  latter  This  would  mean  vector  the f u n c t i o n  defined  classifier test  point  f o r which  approach  is in itself  this  raises  of a d e f i n i n g a  complex  task  (NMV)  set points  classifier  be  broadened  f o r that  then  on  certain function in that  the  each  classes  distance  class.  determine  determining point  this  t h e use o f a  would  would by  design  allow  mean  to the nearest  fitting  of approximating  to f i t the c l a s s  f o r the i n d i v i d u a l  the c l a s s  however.  method  of the c l a s s  of this  defined  This  be  of a nearest  arbitrary  the t e s t  a better  function.  point  implementation  points  used  (A)  Hence,  computing  would  general  extension  include  from  1.  be  classifier  4  vector),  the d e f i n i t i o n  class  figure  points  object  [ 1 ] o r minimum  were  this  the  class.  s e t track  simple  (0=35°)  neighbor  of points  points  exceed  space  point  representing  would  between  from  f o r any  The  s e t of o b j e c t  Alternatively, design  seen  As  a t 15° i n c r e m e n t s i n  angle  set points  number  the  measure.  set point  space  of feature  inadequate  intermediate  i n the design as a  be  distance  1 a t an  discrete a  would  be  however.  projection in  can g r e a t l y  I t can a l s o  response  approach  vector  i n the f e a t u r e 15° a p a r t  the o b j e c t  the design  point  coordinate  set consisting  simple  object to  measured  for this  and  was  a  in to An  the  distances  of the then minimum.  difficulties to the design we  have  no  se"  2250_  +  45*  30* 35*  CM I—  60' •  LU  Eli  ui oc  215080*  + 45*  75* A  0 0  + 60*  STEEL  A-33MM  E«3.6  90*  40 CU  75'  +  STEEL A-S9UU E«2. 0 50 CU A ro  20501 2500  ±  2600  2700  t  J  2800  FEATURE ELEMENT 1 Figure 4.1: Feature variation with object and orientation. Feature type is segment mean.  30  theoretical function of  fit  basis  fitted  for  for  class  in  a test forming  from  the  test  point  fitting  difficulty  defining  functions  with  classified  be  computed. to  have  direct  to  initial  be  Thus by  and  an  with  of  the  distance  is  to  the  not  iterative  its  problems  to  function  computation  implemented and  minimum  fitted  solution  guesses  be  according  the  the  This  would  classifier  be  defined  goodness  neighbor  should  curve  the  is,  point  track.  the.  approach  a nearest  nearest  for  this  of  amenable  on  Hence,  a model  design  must  dependence  establish  points.  possible  the  would  to  the  n-space  generally solution  the  The m a i n  that  it,  to  various  difficult. however,  on w h i c h  inherent ensuring  convergence.  Hence using for a  a general  a class  series  points  for  of  in  has  the of  computional  The points  in  segments  been  in  the  for  of  set.  this  this  feature  restricted  segments  design  the  purposes  curve  line  approximation solution  the  to  each  approach  distance  as  the  concept  the  design  approximating  application  minimum  space  connecting This  thesis,  and  two  is  a  it  track  good for  with  direct  minimal  complexity.  design the  set  for  feature  defined,  li,j  in  =  c  space,  class,  then  parametric  iy_i,j  where  each  +  JEi.J  V J J = mi,j  form,  as  of  by  ne-1  ne line  follows:  >0<q<l • +i  l<i<n ,l<j<ne-l c  determined  consists  -  mi,j  set  successive  allows  calculation  the  of  (4.1)  by  31  From t h i s t o any the  line  the  segment d e f i n e d  normal to  given  definition  the  line  by .1 i , j  passing  d.  This the  . =c.  c .  . •v . .  v.  . «v.  .-  to that  is within  Wherever t h i s line  magnitude  e  the  line,  the  but  as  segment.  the  This the  of  p o i n t _t. T h i s  is  Examples o f e a c h o f  f o r a 2-dimensional i s d rather  The  c l a s s determined  f o r which d i j f  This  approximation design  set  developed  orientation representing  angle. object  of  the  the  case  not  as  the  track  defined distance  1 at  of  to that  point also  for  (Figure  4.2,  Figure  t o the  class  cases. i s then  that  ( f o r any j ) . an  a p p l i c a t i o n . Figure  This  a  shown i n  classifier  to provide  for object  distance  endpoint  case of  (i.e.,  distance  4.2,pt.B) and  f o r both the  the  nearest  where the  by  segment  the minimum  these cases are  i s a minimum  for this  line  (Figure  t h a n d"  approach appears  . = t-m ,j  of  f o r both  case,  set  c. -i,3  intersection point  t o the  segment  endpoint  with  i f the  defined,  provides  pt.A).  class  the  distance  beyond  design  limits  i s not  a point  v. . . -1,3  valid  segment must be  n e a r a "convex" t r a c k  4.2  n  t  point  11 j  s o l u t i o n i s only  normal  0<q<l).  line  t  through  i /j  the  i s  from a t e s t  by:  where  of  distance  1 based  i s o v e r l a i d with intermediate  on  excellent 4.3  shows  15°  increments  feature  angles.  The  the  space  in  points  deviations  STEEL A-33UM E - 3. 6 40 C U X  2100  2200  -1  L  2300 FEATURE ELEMENT 2  Figure 4.2: Distance calculation anomalies.  2400,  20001 i i . i I . i i i__J___< i 1 i . i . L_ 2500 2600 2700 2800 2900 3000 FEATURE ELEMENT 1 Figure 4.3: Design set for object 1 compared to data for angles other than those used to form the design set.  3100  34 seen in these points within  the  noise  from the  design  bounds for t h i s  set  line  segments are  data. Hence,  the  approximation would appear to be s u f f i c i e n t l y classifier 4.2  implementation using t h i s  Classifier  accurate that a  approach is  Distance Measure  Having developed a concept d e f i n i n g the must s t i l l  approach other d e c i s i o n s  the p r e c i s e descisions  to choose  • = ( (t-m.  ,)  - 1  where the matrix C may take one of i)  .)  ]  these  as  follows; (4.3)  H  three common forms:  an i d e n t i t y m a t r i x . In t h i s measured is  one  The form of  work is  C (t-m.  T  set  One of  a measure of d i s t a n c e .  d i s t a n c e measure considered w i t h i n t h i s d.  design  on the methods used for  implementation of the c l a s s i f i e r . is  valid.  the E u c l i d e a n  instance  distance  the  distance  between  the  poi nts _t and m ' j . n  ii)  }  a matrix with the components Terms off  of the  diagonal  terms equal  the variance vector diagonal  are z e r o .  measure then computes a weighted which the E u c l i d e a n the feature  space  is  distance divided  to  the  estimated. The d i s t a n c e distance  in  in each dimension of by the  estimated  standard d e v i a t i o n in that dimension. iii)  an estimate  of the c o v a r i a n c e m a t r i x . The  d i s t a n c e measure would then be computing the Mahalanobis  [16]  distance  between  the points ^t  and m-j j . t  In t h i s variance  of  work, the  signal  to noise  r a t i o and hence  the data can change with a change in depth or  the  35 orientation.  Therefore,  variance  covariance)  is  (or  intended  The  only  test  to  be  generate  record an  use  simpler  weighted  No  to  be  of  the  to  the  errors  in  of  the  the  design  points  are  line  can  must  be  computation and  the  line  More information were  the  complex  In  of  set,  this  knowledge  of  establish  a  warranted.  line  implies  the  exact  however,  distance  less  at  at  class  track  these the  will  where  locus.  the  This  as  the  to  allow  between  the  the  as  i t  is  that  than  valid  However,  from  the  measure  responses  feature  the  work.  segments,  the  weighting  general,  to  they  require  at  at that  orientation  of  averaging  by  each felt  weighting  the  test  based  on  point  the  a  were  considered  knowledge  point  relative  in  of  the  require  the  object.  One  the  misclassification  included  complexity  in  the  entailed  but  the  design  would  orientation that  [17]  feature,  implementation  weight  i t was  feature  systems  misciassification  the  probabilities however,  this  is  five  single and  this  This  available.  throughout  content,  probability in  the of  avoided  minimum  set.  a  to  segments.  rejected.  and  simply  in  along  deviates  be  used  i t  the  possible  from  for  as  of  precluded  assumption  average  ratio  is  a  depth.  that  not  significantly  defining  points  uniform of  This  the  noise  other  not  set  from  approximation  effect used  at  point.  then  used  weighting  are  in  down  the  was  object  matrix  distance  measure  in  is  establish  structure,  i t is  covariance  set  points  break  the  As  design  test  to  variance  design  the  signal  of  to  set  changes  the  in  taken  design  in  errors  highest  of  error  possible  classified.  distance  possible  the  Mahalanobis  component  due  not  under  estimate  estimate  record,  for  invariant  available  data  i t is  a  priori  could  design was  not  set:  36 Chapter  5.1  5:  Experiments  Introduction  Three developed  goals  for  i)  were  this  To  established for  work.  validate  the  particular correctly  These  design  ii)  To  the  an  estimate  value  for  extraction possible the  to  other  that  any  design  than  also the  P  be  set  distribution  used  to  the  the  examined  of  taken  at  used  in  the  various  proposed, the  and  most  to  forming  the  the  feature to  determine  promise  This  the and test  in  for  derived  forming  at  of  assumption  this  the  In  was  of  the depths  design  of  set.  the In a  segmentation valued  from  point.  which  assumption  data.  extending  performance  single  the  for  data  developed  combination  points  for  with  its ability  a s s o c i a t e d with  classify  was  m c  techniques. due  those  potential  defining  given  only  than  holds  the  classifier  of  testing data  techniques  determine  must  classifier,  work.  criteria  classifier  the  test  trends  technique  further  The  to  performance  extraction  To  other  of  set.  predicted  iii)  design  classify  validate  which  experiments  were:  reference  orientations  the  chapter  single and  feature  characterization  absolute  knowledge  of  theoretical  practice  a  3,  this  would  is of  imply  37 that  the  number  classifier  was  More for  of  records  Pj^  generally,  determined  c  classifier  and  classes.  The  determined  mean-vectors  the  the  the  a random  by  the  statistical of  number  of  of  reflection  uncertainty  a finite  lim/it  value  number  of  any  finite the  to  The  classification on  set, The  relies  on  m  use  of  test  set  will  the  class  be  a good  run  conventional the  of  reflect the  the  of  of  P^  the  The  c  of  members P  as  is  c  class  of (P  m c  be  )  the of  the  of  class the  class  each  class  tend  means  as  the to  associated  classifier, drawn  noted  trials) with P  m  c  a  and  This  sets.  implies  statistical is  observation  then of  E  c  finite  . P  and  a  the  characterizing test  using  from  that  of  value,  means  class.  the  the  classifier, this  the  is  m c  means went  the  in  the  errors/no.  classifier  Pj£ .  central  form  would  then  design  closely  resulting  pr.timate  the  of  method  large  population. and  and  should c  to  estimating  a sample  (E =no.  of  misciassification  an e s t i m a t e  definition  set  It  single  only  of  only  .  error  accurate  test  c  used  thought  in  form  a  associated with  implementation is  P  any  is  test  the  variable  distribution  used to  set,  distribution  test  the  particular  be  records  probability  design  observed  of  which  can  m c  with  of  random  distribution  number  records  infinity. with  the  variable  records  This; distribution  from  and  misciassification  distribution  the  the  P  of  structure  and  of  design  probability  is  variance  by  both  infinite.  a NMV c l a s s i f i e r  value  used to  m c  allows  that  the  distribution run is  against presumed  of the to  38  While records allow  at  first  available  this  in  six  22  to  points for  set.  Given  this  very  single  test  of  any  characterize  to  run  each  its  classifier  resulting  value  implementation classifier data  set  error  of of  is  a  results.  computationally involve  over  given is  then  of  of  observations  spread  of  which  set.  This  that, six  if  samples  be  were  different entirely  of  E  used  of  assume the  noted  choices  of  independent  design of  each  which  set  the  for  as  each  work and  P  values  it  would The  six,  the  given  the  data  basis  probability  of  [14].  of  cannot  is  m c  the  the  the  test.  is  on  97%  as  of  approach  this  other  the  method  average  was; c h o s e n  the  the  the  the this  be  a  of  this  independence,  that  in  characterize  mean w o u l d  is  observing  partitions  structure  observations  to  be  to  on  choosing  application in  design  accurately  For  classifier c  the  reduced  [18,6]  as  this  classifier  spanning  should  in  the  and  of  in  the  limitation  data  size.  estimated  considered  the  number  It for  for  one  set  average  case.  time  a  the  test  to  each is  an  observed  c  this  possible  implementation  runs is  the  method  design  prohibitive  250  times,  all  E  of  single  to  general  counter  approach  for  and  unlikely  a more  to  holdout  number  adequately,  This  c  A complete  is  a  allows  the  would  design  segment  set,  from w i t h i n  the  probability  set  data  herein  evaluated  with  design  518  5.1)  define  a line  in  The  This  classifier  E .  case. to  the  (Table  four.  about  several  set  the  all  performance  the  set  segments  limited  used  seem t h a t  data  the  region  method design  line  the  would  not  define  The different  is  define  to  classifier  it  primary  this  requires  twenty-four  of'only  the  approach,  classifier class,  glance  be  they  E  c  observed  considered  to  all  from  derive  39  Table  5.1:  Primary  Data  Number o f Records  Set  Object Identifier  Depth (cm.)  Description  1  40  130  10 e a c h 5 each  at at  9=0 , 1 5 , . . 9 0 ° 9=5,10,20,..85'  2  50  128  10 each 5 each  at at  8=0,15,..90° 9=5,10,20,..85'  a  D  3  60  130  10 e a c h 5 each  at at  9=0,15,..90° 9=5,10,20,..85o  4  50  130  10 e a c h 5 each  at at  9=0,15,..90° 6=5,10,20,..85'  a) b)  9 only 4 only  at at  6=30° 8=40°  Table Object Identi fier  Depth (cm. )  5.2:  Additional  Number o f Records  Data  Set  Description  1  50  70  10  each  at  8=0,15,. .90°  2  60  70  10  each  at  9=0,15,. .90°  3  70  69  10 each  at  9=0,15,. .90°  4  60  68  10 each  at  6=0,15,. .90°  a) b)  9 only 9 only  at at  8=30° 9=75,90°  a  D  40  the  same  data  s e t . Hence  must,  in general,  gross  trends  exists in  a  restricted  are e v i d e n t .  f o r cases  series  be  conclusions  of  An  to  the  same  group  trials.  For  this  instance,  results  of  runs  reduce  the e f f e c t s  of  dependence  performance  conventional sum  test  which  5.2  from  is  i n each  The  f o r each  seven  vertical  five  at each and  used  contributing  Test (one the  These  1  this  relatively  limitation  design  sets  i s used  i t is possible  same  design  analyzing  allows  techniques  such  as  whether  to  s e t and  the  This  differ  runs  segments, were  of  differences  one  t o use  the Wilcoxon the  in performance,  rank  classifier and  i f so,-  (Table  then  one  ten  object  a t each  of  measurements  in angle.  Of  five  set with  f o r each  the ten were  randomly  the  remainder  the  classifier  the t e s t s e t .  consisted  repeated and  three, be  used  of  choice  extraction  schemes  namely  from  the design s e t  set angles,  the design  data  general,  f o r each  additional  design  to form  In  used  to develop  increment  different  were  used  five  the  5.1).  available  angles  degree of  Test  the c l a s s i f i e r  were  with  then  feature  segmentation  trial  to  f o r each four  test  records  intervening  chosen  by  determine  trial  object  ( 0 , 1 5 , 30 ,.. , 9 0 )  records  to  the  results  where  to t r i a l .  Sensitivity  first  independent the  8)  using  of  these  superior.  Orientation  depth  trial  statistical  (Appendix  structures  to  where  the  on  instances  exception  "pair"  in  based  s i x runs of  design  techniques  f o r each f o r three s i x and to  the  of  of  previously  t h e two  choices  twelve.  determine  s e t ) f o r each detailed.  different  i n the  The  of  number  results  the v a l i d i t y  of  of the  of this  .41 i  predicted  performance  promising  feature  trends,  extraction  classifier  at handling  parameters  due t o c h a n g e s  was  also  test  5.3  assessed  Depth  the  tests  classifier  signatures These judged  to provide  These  tests  which  includes  greater set  made  a n d 6.3.  The classifier However  using  in this  points  represents  both  those  Test data  taken  used  trial,  this  This  structure  t o form  test.  set (Table at a  depth  this  sets  data  in  sections  of the  i n the f i r s t  such  determines data  as  s i x runs  s e t i s expanded  against  cm.  set(0,15,..90°).  are included  the data  5.2) 10  However,  developed  trial  from  to  test.  include  that i t  the  performance  depths  other  the design s e t .  comprises  solely  data  involves  sets  both  i n the f i r s t  the design  the t e s t  technique  a t t h e 15° i n c r e m e n t s  2)  of  of the o b j e c t .  test.  of t r i a l s  (Test  from  depths.  3 again from  with  the design  the c l a s s i f i e r  than  taken  series  trial  derived  of  in  extraction  objects  i n the f i r s t  associated  second  variations  performance  the four  records  6.2  of  from  only  of t h i s  results  the s e n s i t i v i t y  i n depth  u s e o f an a d d i t i o n a l  included  results  minor  use o f the f e a t u r e  used  angle  of the o b j e c t  6.1.  a change  that  The  test  with  the best  data  in feature  angle  The  run to determine  than  vertical  experiment.  to the r e l a t i v e l y  a l l made  changes  of the  Tests  were  observed  tests  this  t h e most  The s u c c e s s  i n the v e r t i c a l  in section  Sensitivity  Three  technique.  the continuous  from  are presented  and t o i s o l a t e  s i x runs  the additional  of the c l a s s i f i e r data  s e t . That  witi  i s , both  42  the  design  depth not  and  greater  not  classifier that  of  the  from  simply  being  determine that  the  data  first  results  one six  from  markedly and  of  1.  in  this  For  rather  may  interest  for  This  the  signal  a this  is  vertical  this  from  the  in  presents to  both  design  the  noise with  test  depths  set set  is  the than  which  rather  the  design  set  than  five,  with  three  trial  by  design  is any  designed depth  in  than  records  to  sensitivity  incorporating set.  as  drawn  test,  reducing  exhibit, in  at  a reference  derived  this  depth.  potential  classifier  set  instance  records each  poorer  at  Although  data set,  taken  2.  represented  depth.  of  provides  Test  a test  depths  of  of  trial,  4 uses  the  depths  Test  design  of  used  the  the  two  due  in  data  associated with  however,  consisted  used  from  lack  Test  from  that  derived  the  the  2;  are  to  the  Test  set  test  with  compare  ,  all  than  a complete  angles  to  test  data  from  43 Chapter  6.1  6:  Results  Results  The 6.2.  These  developed for  the  of  and  Evaluation  Orientation Sensitivity  results  of  figures  overlay  in  Chapter  Test  3  segmentation  1  the  with  and  are  Tests  shown  in  predicted  the  range  feature  Figures values  of  the  6.1  of  and  P  m c  observed  extraction  E  c  techniques  tested.  The  results  confirm  performance  with  and  feature  type  of  extraction  respect  to  changes  (F3.F4)  especially  for  these  results  equal  areas  provides  of  cases.  and  One  observed  were  based  should results  on  a  Additionally, incorporate design  set  note are  show  had  be  an  number  that  of  of  expected  for  based  the  than  the  classifier on  those  artificially  other  segments.  since  based  segments  the  segmentation  results  simple  classifier  feature  outperform  numbers  p r e d i c t i o n s were  which  the  of  d i f f e r e n c e s between  o r i e n t a t i o n s other and  trends  mean-based  better  that to  in  clearly  comparitively  the  The  larger  Additionally, segment  predicted  extracted.  techniques  techniques,  the  majority predicted  predictions  structure.  data  used  on  that  to  did  form  established  not  the  noise  characteri stic.  As to  have  area  one  been  with  This  the  Wilcoxon  the  performance  to  the  see  (Figure  achieved  segments  extracted.  can  others  the  the  segment  observation  rank  in  using  sum  of  test  this  the  6.1(a))  best  combination mean  was  (F3)  (Appendix  B)  results  of  as  confirmed  classifier  trial  the  twelve  the by  which  level  equal  feature  application indicates  implementation  (confidence  appear  is  is  of  that  superior  98%).  Not  o .  o J  o  3  6 9 Number of segments  12  —i  3  15  (a) segment exponential time constants (F1)  o J  o L U  3  6 9 Number of segments  12  (c) segment mean (F3)  15  12  15  (b) segment linear slopes (F2)  o J  o  6 9 Number of segments  I  Observed range  •  Predicted value  0  3  6 9 Number of segments  12  (d) mean difference (F4)  Figure 6.1: Classifier performance with equal area segmentation.  15  o  .  J  •I  •—*. Lift, -J  Left,  3  6 9 Number of segments  12  "I  15  3  (a) segment exponential time constants (F1)  6 9 Number of segments  12  15  (b) segment linear slopes (F2)  I Observed range • Predicted value o  J  o UJiO  I 3  6 9 Number of segments  12  (c) segment mean (F3)  15  —i 3  r  1  6 9 Number of segments  1  12  (d) mean difference (F4)  Figure 6.2: Classifier performance with equal length segmentation.  15  tn  46  only  were  the  the o v e r a l l  other  cases,  smallest, set  this  observed 2 E  case  A  over set  6.2.  are presented  in Table  which  errors  No  data  at other  object  even  than  this  a l l design  from  the result  table  versus were  angles  2 at vertical  5,10°  were  records these each  data was  records  unusual  orientations case  was  individual weighted  observed  that  as  class  mean.  further  to  of the  observed  was  error test  angles  s e t . The  degrees.  A l l of  f o r object  2 at  misciassifying This  the  coincidence  for this  investigated.  mean  i s made i n  misciassifications  o f 5 a n d 10  and t h e d i s t a n c e ,  measure  object at  A class  d-j , f r o m  computed  of  mean f o r  each  using  a  as f o l l o w s .  i n the c l a s s i f i e r While  of  classification  the design  due  the data  m  one c a n s e e i n T a b l e  failing  the values  angle  instance.  and hence  ii " As  of o b j e c t  f o r any o f t h e  into  were  to the c l a s s  distance  associated  classification  the v e r t i c a l  i n each  developed  point  design  errors  technique  of the c l a s s i f i e r  was  in  the average  angles  misciassifications  two  object  extraction  are largely  these  same  6.1. T h e  to  of m i s c i a s s i f i c a t i o n  incorporated  the r e s u l t  was t h e  f o r t h e runs  for this  shows  errors was  than f o r  sensitivity  of the e r r o r s  feature  sets  better  2.2%.  breakdown  This  objects.  minor  tables  less  case  of the o b s e r v a t i o n s  relatively  although  with  for this  The c o n f u s i o n  further  occurring  of  1,  are s t i l l  Table  a  are mainly  as o b j e c t c  the range  indicating  variation.  with  results  one c a n n o t  (6.1)  6.3,  t h e two  are r e l a t i v e l y discard  these  points distant points  identified from  the  on t h e  47  Table  6.1:  Confusion  F e a t u r e : s e g m e n t mean ( F 3 ) Segmentation: 12 e q u a l a r e a C o n d i t i o n s : D e s i g n and t e s t set. \Dec n 2 3 4 Obg\  Tables  segments s e t s drawn  1  1 2 3 4  95 2 0 0  0 91 0 0  a ) D es i gn set 1 2 3 4  94 2 0 0  1:  0 91 0 0  c) D e s i g n s e t 1 2 3 4  0 0 95 1  95 2 0 0  0 91 0 0  e) D e s i g n s e t  Table  5:  6.2:  94 2 0 0  0 0 1 95  95 2 0 0  1 2 3 4  .06%  d)Design  0 0 0 94  E = 0. 7 9 %  f)Design  c  Distribution  of  3  4  1 91 0 0  0 0 95 1  0 0 0 94  E = l . 06% c  0 91 0 0  0 0 95 0  with  0 0 0 95  E = 0 . 53% c  1 91 0 0  s e t 6:  Failures  data  2  set 4: 94 2 0 0  1 2 3 4  1  primary  set 2:  b)Design  c  0 0 95 1  from  1 2 3 4  E = 0. 7 9 %  3:  Test  \Dec:'n 1 0bj\  0 0 0 94  1 0 94 0  for  0 0 95 1  0 0 0 94  E = l . 06% c  Angle  Object 1 2 3 4  2 6  1  6 1 3  0  5  10  15  20  25  30  35  Vertical Note:  R e s u l t s from a l l ( T o t a l number of  1 40  45  E0  Angle design trials  55  60  65  70  75  (e,°) sets included. = 2268)  80  85  90  48 Table  6.3:  Distance  Object number  to  O r i e n t a t i on  Class  Means  for  Record number  Object 2  D i s t a n c e to c l a s s mean  2  5°  1 2 3* 4 5  2.34 2.70 4.83 2.68 2.17  2  10°  1 2 3* 4 5  2.93 2.54 4.91 1.96 2.24  records causing classifier (Test 1). des i gn s e t s  Table  6.4  Confusion  failures  Tables  for  for  all  Test 2  F e a t u r e : segment mean (F3) S e g m e n t a t i o n : 12 equal a r e a segments C o n d i t i o n s : D e s i g n s e t s drawn from p r i m a r y d a t a s e t . T e s t s e t i n c l u d e s r e m a i n d e r of p r i m a r y d a t a s e t and whole of a d d i t i o n a l d a t a s e t . v Dec n  vDec'n  1  Obj\ 1 2 3 4  1  2  3  4  156 5 1 0  9 158 0 0  0 0 157 11  0 0 0 152  a ) D e s i g n set 1 2 3 4  155 6 1 0  10 157 0 0  c ) D e s i g ns e t  1 2 3 4  155 5 1 0  1:  c  0 0 156 11 3:  10 158 0 0  e) D e s i g n s e t  E = 4.89%  E = 5.34% c  0 0 157 11 5:  0 0 7 152  0 0 6 152  E = 5.34% c  1  2  3  4  153 4 2 0  10 159 0 0  2 0 155 11  0 0 7 152  Obj\ 1 2 3 4  b)Design 1 2 3 4  154 4 1 0  d)Design 1 2 3 4  s e t 2:  s e t 4:  156 5 2 0  f)Dosign  9 159 0 0  9 158 0 0  s e t 6:  E = 5.50% c  2 0 158 11  0 0 5 152  E = 4.89% c  0 0 156 12  0 0 6 151  E = 4.89% c  49  basis  of  have  this  been  the  the  data  6.2  Results  of  seen,  the  that  again  this  increments  in  Two f i r s t  in  poorer that  shown  of  results.  signatures  indeed  the  are  obvious  because  This  would  space The of  and  objects  at  to  such  would  an  not  in  results.  signal than  taken  that  at  of  to  the  data  contribute  to  factor  that  of  a  orientation,  extent  be  shown  these  spread  same  indicates  98%  contributing  the  this  types.  poorer  to  of  for  c  the  was  be  a  is but  design  representative  of  depth.  contribution  misciassifications However, which  data  potential  depth  to  markedly  added  E  can  degraded  is  to  that  expected  one  extent  contributing is  a  object  be  on  at  of  would  set  another  value  As  B),  results  greater  second the  these  to  differ  determine.  test  is  (Appendix  lead  may  The  the  analysis  significant  is  the  depths,  from  in  6.4.  c l a s s i f i e r Further  these  data  different  data  may  error  with  Table  different  as of  done  in  test  of  the  seen  added  the  observed  versus  the  only  systematic  runs  data.  breakdown  shows  data  feature  is  A  most  depth.  based  of  Wilcoxon  depth  and  original  the  are  the  factors  ratio  greater  depths  using  which  the  the  degradation  6.5,  noise  for  extra  Table  The  tables  the  level.  and  Tests  of  confidence  anomalous  unobserved  performance  inclusion  result,  an  clearly  Sensitivity  two  the  are  process.  Depth  from  they of  confusion  derived  readily by  product  collection  The set  measure,  the  of  observed Test f i r s t  3  each  of  in  this  is  these trial  designed  factor  to  factors is  to  the  d i f f i c u l t  investigate  contributes.  The  to the  approach  50  Table  6.5:  E  versus  c  Object  Type  E  1 2 3 4  Results  Table  for  6.6:  F e a t u r e : s e g m e n t mean S e g m e n t a t i o n : 12 e q u a l C o n d i t i o n s : D e s i g n and set. \Dec 'n 1 2 3 O b j \ 1 2 3 4  35 0 0 0  0 35 0 0  a ) D e s i g n set 1 2 3 4  35 0 0 0  35 0 0 1  e) D e s i g n  1:  0 35 0 0  c ) D e si gn set 1 2 3 4  0 0 34 3 c  0 0 34 1 3:  0 35 0 0 set  E  E  c  0 0 33 2 5:  E  C  c  and  Depth  13.80 4.05 10.63 15.44  0.88%  10.83%  Initial depth  Second depth  a l l design  Confusion (F3) area test  for Test  2  (%)  0.53 2.15 0.18 0.70  Overall  Note:  Type  sets  Tables  segments s e t s drawn  included.  for Test  from  3  additional  data  \Dec 'n ^ 4 0 0 0 30  = 2 . 19% 0 0 0 32 = 0 . 73% 0 0 1 30 = 2 .92%  Ob.iX 1 2 3 4 b)Design 1 2 3 4 d)Design 1 2 3 4 f)Design  35 0 0 0 set 35 0 0 0 set 35 0 0 0 set  2  3  4  0 35 0 0  0 0 34 2  0 0 0 31  2:  E  c  0 35 0 0 4:  0 0 33 1 E  c  0 35 0 0 6:  = l . 46%  = l . 46% 0 0 34 3  E  c  0 0 1 32  0 0 0 30  = 2. 1 9 %  51  undertaken gre.ater any  for  depth  for  increased  are  the  a  6.3  that  the  for are  enough  Effects  One  depths  of  a  due  than  in  into  the  the  data  set.  to  from,  This  the  removes  depth  variability  design  in  an  of  depths, for  The as  improvement c l a s s i f i e r  if  fourth  is in  depti.  to is  due  to  the  trial in  in  comparison Comparing  6.7 the to  have  This  of  the  is  of  the  set  class  same to  with collected  this  depth data  can  to  be  some for  expected  from  may  both  of  formed  taken it  from  effect  point  means  to  either  improve  depths.  implemented and  6.8.  overall one  tables  they  4)  incorporate  separately,  series  table  gained  problem  While  of  data  the  design  considered  2.  1,  interfere  (Test  two  Test  6.6.  data.  each  c l a s s i f i e r  for  Set  to  Table  indistinguishable  set  for  the  in  Test  to  will  combination  shown  design  independently.  inferior  the  exists  This  between  result  for  set.  point  depth.taken  those  virtually  Design  set  shown  signatures  test  solution  design  as  those  the the  a Modified  potential  are  good  are  when  intermediate  single  the  test  greater  difference  mean  results  set,  normalized  class  results  solely and  trial  as  the  the  of  than  the  depth  of  dependence  each  design  this not  c l a s s i f i c a t i o n  shifting  use  design  better  while  different  depths  the  to  expense  at.different  eye,  proper  results  markedly  indicates  the  the  results  s t i l l  object  in  is  noise.  The While  at  test  both  p o s s i b l e . - , b i as  sensitivity,  at  this  approach  and  a  with  noticeable  performance  using 6.5  A  this  design 6.8,  one  of  set can  the based  on  see  that  a  52  Table  6.7:  Confusion  tables  for  Test  4  F e a t u r e : s e g m e n t mean ( F 3 ) Segmentation: 12 e q u a l a r e a s e g m e n t s C o n d i t i o n s : D e s i g n and t e s t s e t s drawn f r o m c o m b i n a t i o n p r i m a r y and a d d i t i o n a l data s e t s . v De c ' n ic' n 1 2 3 4 2 3 1 Obj\ 0b,]\ 1 2 3 4  164 3 2 0  0 160 0 0  a) D e s i g n s e t 1 2 3 4  164 2 1 0  0 161 0 0  165 3 1 0  e ) D e s i gn  Table  set  6.8:  1 2 3 4  0 0 4 157  1 2 3 4  Ec = 2 . 14%  3:  0 0 153 8  1 2 3 4  E =3 .36%  E  versus  c  object  Type  E  1 2 3 4  Results  C  0.92 2.15 1.07 1.84  Overall  Note:  type  for  and  s e t 6:  depth  Second depth  design  0 0 153 9  sets  0 0 10 154  E = 3 . 36% c  0 0 158 7  0 0 5 156  E = 2 . 29% c  for  0.00 0.00 15.97 13.12  Initial depth  0 0 6 154  c  (%)  7.17%  4  E = 3 . 97%  0 161 0 0  1.63%  all  0 0 156 9  0 161 0 0  set 4:  165 2 1 0  f)Design  C  4 158 0 0  set 2:  165 2 1 0  d)Design  0 0 10 155  5:  161 5 2 0  b)Design  C  1 0 159 6  0 160 0 0  0 0 10 153  E =3 .97%  1:  c ) D es i g n set 1 2 3 4  1 0 152 10  of  included.  Test  4  53  the  classifier  expense than  those  recorded  and  test  Evaluation  The  excellent  applying  of  however.  The  absolutely  against  multiple  information  acceptable depth  i n an  would  techniques define  even  a l l depths.  appear  t o be  still  different  to  use t h e most  appropriate  of  the object.  While  demonstrated shown  [5]  no  to determine  that  from  than  Hence  t o be  depth  based  depth  f o r the sphere  able  to  depth  than  in  performance  would  be precise  , some  the order  of  *5  system  based  on  would  allow  one t o  different  has  a  and  depth  been  accuracy,  such  these  depths  the estimated  system  model,  clearly  set included  while  on  on  to this  are was  necessary  for a  empirical  are  results  a single  f o r several one  of  variation  these  the design  system.  sets  by  classifier  adequately. This  design  depth  degradation  of o b j e c t  of  results  responses  greater  necessary  to f u n c t i o n  single  have  orientation.  data when  The  feature  herein  the continuous  The  This  operational  localization  a  the object  against  the  developed  are raised  d e t e r m i n a t i o n i s not seen  preliminary cm.  from  invariant.  b u t was  that  objects.  to object  depths,  not dramatic,  indicate  metallic  issues  results  from  depth.  to the problem  i s that  depth  better  worse  where t h e  solution  considering  respect  first  above  to data  important  achieve  was  as a  encouraging  Three  t h e same  and t h e c l a s s i f i e r  of buried  with  at the  are s i g n i f i c a n t l y  of the i n s t a n c e s  summarized  the c l a s s i f i e r  in/features  depth  Results  potential  especially  f o r the l a r g e r  results  for either  technique  identification  The  s e t are from  results  extraction  not  i s reduced  of the l e s s e r .  design  6.4  error  i t has  been  determination i s  54 p o s s i b l e using  a pulse  c o i l s of d i f f e r i n g The  i n d u c t i o n system with two  receive  radii.  second issue r a i s e d by these r e s u l t s r e l a t e s to  the adequacy of the f i t t i n g procedure used to approximate  the  locus of c l a s s means i n the f e a t u r e space. In the m a j o r i t y  of  cases,  the l i n e segment approximation r e s u l t e d i n e x c e l l e n t  performance. However, the a r b i t r a r y d e f i n i t i o n of segment endpoints based on f i x e d changes i n o b j e c t o r i e n t a t i o n cannot be expected to be optimal feature  as the r a t e of change of  space r e p r e s e n t a t i o n  f o r a c l a s s does not  the follow a  s t r a i g h t l i n e r e l a t i o n with the o b j e c t angle ( r e f . F i g u r e s 4.1,4.3).  The classifier  l a s t major issue i s that of the s e n s i t i v i t y of to the s e l e c t i o n of the design  the  s e t . The v a r i a t i o n  in r e s u l t over d i f f e r i n g s e t s i n d i c a t e s that a much g r e a t e r amount of data would have to be taken to a c c u r a t e l y e s t a b l i s h the c l a s s means at the design  set p o i n t s . T h i s would be most  e s p e c i a l l y true at g r e a t e r depths where the s i g n a l to  noise  r a t i o of the responses i s lower. Both of these l a t t e r  issues r e f l e c t  l i m i t a t i o n s i n the  a v a i l a b l e data set r a t h e r than l i m i t a t i o n s i n the One  technique.  can e a s i l y envisage an i n t e r a c t i v e system which would  e s t a b l i s h the number of segments and forming the c l a s s design "curvature" feature plane.  space f o r that o b j e c t  of p o i n t s developed i n the as  i t was  As w e l l , the number of records  r a t i o of the data,  rotated  in a v e r t i c a l  d e f i n i n g a design  based on the a c t u a l s i g n a l to  desired  accuracy.  set  noise  such that the c l a s s mean f o r a p o i n t  be e s t a b l i s h e d to any  in  d e f i n i t i o n by examining the d i s c r e t e  of the s u c c e s s i o n  p o i n t could be adjusted  the endpoints to use  could  55 Chapter  7.1  7:  Conclusions  and Recommendations  f o r Further  Study  Conclusions  This  work  identifying  steel  electromagnetic set.  has  demonstrated  spheroids  response,  In t h e p r o c e s s ,  two  by  the f e a s i b i l i t y  interpretation  given  that  they  other  notable  of  of  their  are from  results  a  known  have  emerged.  An form of  effective  of response  the samples  roughly  equal  absolute  methods the  distinct  feature  While  The  of p o i n t s  respect  some  limits).  o f an e x t e n s i o n  The  have  about  to the  the  other  Additionally,  i t has  implementation  established herein t o t h e NMV  space  whose  implementation  to the l o c u s .  value  possible  to implementation  type  the c l a s s  defining  of s i g n a t u r e s  to a parameter  which  a l l other  relative  generalizes  in feature  t h e mean  in  either  has  been  hardware.  result  f o r computational  approximation  against  amenable  extension  being  for this  c a n be made  of e x c e p t i o n a l  notable  classification  with  statement  is excellent.  purpose  developed  of the response  i t s performance  advantage  other  no  feature  herein  or s p e c i a l  classifier.  approach,  segments  of t h i s  development  allows  this  and o f b e i n g  The  locus  signature;  certainly  simplicity  the  has been  area.  proposed  software  type  within  merit  features,  feature  whose  range  mean  the c l a s s . features  to the This  vary  i s continuous  described  simplicity,  of  herein  (within  limits  t o a pi.ecewise  this linear  56  It extend  should  the  be  noted  classifier  continuous  parameter  locus  most  that  example,  in  determine  the  intersection line e  l> 2 e  line  based  to  on  of  From  the  this  c o r r e s p o n d i n g to  the  one  q,  of  the  test  could  estimate the  herein  determine  to  the and  and  interpolate  line  an  the  For  one  must  i f the is within  knowing  end  of  to  design  point.  to  parameter, start  straightforward  an  point  detailed  normal  the  be  extract  approaches  parameter,  point  segment,  i t would  implementation  line  segment.  concept  closely  the  that  the  points  the  angles  of  the  estimate of  9  as  follows:  9=(62-8i)*q  7.2  Recommendations  Several further  study  adequately  aspects to  the  the  Development  Study  work  possible  of  These  a  method  d e t e r m i n i n g the performance  number  segments.  of  tests  classifier cm.) set.  test  to  improvements performance  to  depth  choose  line  require  and in  to  an  the  segments,  design such  i s o p t i m i z e d f o r any  determine  performance set  herein  include:  classifier  Further  presented  classifier  environment.  points  ii)  of  determine  delineate  unconstrained  i)  for Further  of  the  effect  relatively  variations  for a  set  that given  on minor  (±1..5  given  design  57 iii)  Further  tests  effects  of  work.  The  also  relaxing effects shapes  determined.  Also  test  data  Finally, the  to  is  be  minor  background local  more  object  interest  made  for  this  complex  set  i s the  error  the  should  be  effect  of  when  the  induced  a  collected.  further  than  determine  assumptions  i n the  of  to  including  positioning  effect  rather  required  the  of  assymmetric  horizontal  iv)  are  of  tests  are  measuring  in  variations  in  could  to  in  soil  to  reponses  this  due  subtraction  permeability  the  a i r . While  in extent  required  the  in  effect  the  use  data  determine  is  effects  expected  of  collection,  conductivity  induce  earth  and  that  would  bear  investigation.  Many  aspects  of  these  straightforward;  however,  much  set.  7.3  a  larger  data  Final  Remarks  In  overall  feasible  summary,  solution  to  the  recommendations  they  must  a l l await  the  work  detailed  problem  assumptions.  Excellent  results  depth  While  cannot  cases.  further  work  unconstrained promise  one  necessary  to  environment,  for this  are  are  application.  the  the  concept  collection  herein  the  achieved  project  determine the  within  quite of  develops  stated  f o r the  result  of  performance provides  single the in  an  exceptional  a  58  Appendix  A:  An for  overview  this  (coils,  Experimental  research Tx  and  of is  Rx)  A  constructed  entirely  metal  the  data  shown  in  was  laboratory.  Apparatus  collection Figure  located  feature  of  this  without  in  a  A . l . The special  laboratory metal,  system  so  developed  sensor  system  purpose  is  that  that  the  i t is responses  of  objects  can  be  measured  in  isolation.  Outputs  of  sensor  system  are  transmitted  to  a  support  building  (35  distant)  m.  associated serial  computer.  data  link  processing. which data  receive shown  the  a  data  second  digitizer  sensor  These  from  the  platform  designed  to  vertical  plane  A.2  allow  a  are  to  and  transmitted  over  for  and  storage  special of  system  purpose  successive  its  a later  system  frames  of  noise.  A.3.  co-planar  mounted This  the  the  changes  while  is  comprises  and  holding  then  computer  used  coils  coils  is  digitization  averaging  system  Figures  distance  The  the  uncorrelated  coils.  in  to  houses  synchronous  reduce  The  of  The  allows to  which  separate  the  stand  object  object  in  the  maintaining  on  a  test  allows  by  varying  j i g . The  object  transmit stand  as  control the  object  of  position  j i g is  orientation  constant  and  in  the  coil-object  di s t a n c e .  The  i)  experimental  A  measurement  coil and  ii)  procedure  The  of  interaction,  the  used  is  as  background  earth  follows:  response  response,  etc.)  (due is  to  taken  digitized.  object  is  placed  under  the  coils  (along  the  Data Acquisition Facility  Data Analysis Facility VAX  1 Disk/Tape  11/780 CPU  High Speed  I  Storage  /  Graphics \ ^ Display  A/D System  ^  i  Tenriina!  ~. Terminal  / I  \ /  ~J |  |  I  I I  co  Figure A.1: Data Collection System  Figure A . 2 : Photograph of experimental apparatus.  61  Figure A.3: Detail of coils and object jig.  62  coil  axis)  at  the  correct  distance  and  orientation.  iii)  A  sequence  taken  iv)  The  and  of  response  measurements  (5  or  10)  are  digitized.  previously  subtracted  measured  from  the  background  records  and  response  they  is  are  then  stand  and  stored.  v)  The  object  sequence  A  summary  of  system  turns  -  100  turns  Rj-  28  cm.  R  -  25  cm.  I  -  ~2.6  from  rate  Transmitter  duty  -  gain  Digitization  Note:  of  the  follows  (symbols  Amperes  repetition  Number  test  2):  Transmitter  Receiver  the  parameters  in Chapter  27  N  removed  is repeated  the  defined  Nj-  is  -  cycle 60  rate  frames  Transmitter  -  488.28  50%  dB -  250  averaged  kHz. -  repetition  500  rate  measuring  256  response  period  the  transmitter  of  Hz.  i s based  points  in  cycle.  the  on quiescent  as  63  Appendix  B; W i l c o x o n Rank Sum T e s t  Within  t h i s work a t e s t  d e t e r m i n e whether classifier While  i s required  observed performance  t h i s may seem s t r a i g h t f o r w a r d , application.  no knowledge o f t h e d i s t r i b u t i o n c  (Section  differences  t o determine  e t c . ) cannot  between  two c o n s i d e r a t i o n s  The f i r s t  of P  i f differences  6.3) t o  significant.  (or i t s estimate  m c  statistical  are s i g n i f i c a n t  (Student's  be a p p l i e d . The s e c o n d c o n s i d e r a t i o n  the  method u s e d  to gain  set  with d i f f e r i n g  partitions  not  guarantee  t h e samples  that  samples  of E  c  must  of these i s that  c a n be assumed. Hence, many c o n v e n t i o n a l  tests T,  Experiments  implementations are s t a t i s t i c a l l y  be a d d r e s s e d f o r t h i s  E )  f o r Paired  i s that  (re-use o f the data  o f d e s i g n and t e s t  sets)  does  do n o t t r e n d w i t h t h e s e  changes. The the  first  W i l c o x o n Rank Sum t e s t  statistical  test  distributions hypothesis which  from w h i c h  t h e samples  sets  than t h a t  t h e median o f one  t o compensate  f o r a sequence  (second c o n s i d e r a t i o n ) .  Trials  s e t f o r two e x p e r i m e n t s a r e p a i r e d  performance  from  of the other.  i s used  trends of the r e s u l t s  partitionings  the d i s t r i b u t i o n s  a r e drawn a r e i d e n t i c a l . The  a  experiment  a r e made a b o u t t h e  a r e drawn. The n u l l  i s that  hypothesis (H ) i s that i s less  i s a non-parametric  no a s s u m p t i o n s  D  A paired possible  i s a d d r e s s e d by t h e use o f  [ l l ]. T h i s  (H ) f o r the t e s t  distribution  design  i n which  t h e two sample  alternate  in  consideration  f o r a succesion  of p a i r s  f o r the  of data s e t using  t h e same  and t h e d i f f e r e n c e  i s then the d a t a  analyzed. The H  D  to hold,  test  i s predicated  on t h e h y p o t h e s i s t h a t , f o r  t h e number o f p o s i t i v e  between p a i r s  and n e g a t i v e d i f f e r e n c e s  of experimental r e s u l t s  shoud  be e q u a l .  64  Additionally, absolute should (or  value,  the ranks  be r a n d o m .  negative)  rank by  i f the d i f f e r e n c e s  sum e q u a l l i n g  application  calculation giving  which  this  this,  values  calculations test  value  quite  o f rank  theory  be  [12 ].  tedious;  positive of the determined This  however,  sum a r e a v a i l a b l e  involved  i s invoked  of a l l  can then  of  elements  The p r o b a b i l i t y  probability  i s , i n general,  i n order  and n e g a t i v e  the ranks  a r e summed.  a particular  of basic  critical  The  of p o s i t i v e  To a s s e s s  elements  are ranked  tables  [13 ] .  i n t h e two i n s t a n c e s f o r  i n the text  follow  as  examples.  Example 1: For  Test 1 - Determining the  best combination  segmentation and feature  of  extraction  technique. Case A -• 12 equal mean  area  segments, feature  is segment  segments, feature  is mean  (F3).  Case B •• 12 equal  area  di fference (F4). Desi gn  Result  Di f f e r e n c e  Set  under A  under B  1  .79  1.85  1.06  Sh  2  1.06  1.85  .79  2  3  1.06  1.85  .79  2  4 ,.  .53  1.32  .79  2  5  .79  1.59  .80  4  6  1.06  2.12  1.06  Sh  B-A  No negative elements are p r e s e n t , rank  Rank  Result  sum is  0.  From t a b l e s  the  critical  therefore value  of  the  negative  rank sum  65  (98%  confidence  rejected;  i.e.  level, there  6 trials)  is  is  significant  1.  Hence,  H  difference  is  0  between  the  results.  Example  For  2:  Test  2 -  Determining  if  addition  data,  to  Case  A -  Test the  Case  the  set  is  the  Result under  Set  primary  drawn  data  from  non-design  to  data  form  with  under  set  the  with  set  (Table  design  records  (Table  set  Result A  degrades  depths,  set.  as a b o v e ,  set  addi t i onal  set  removed.  5.2)  included. Rank  B-A  .79  4.89  4.10  2  2  1.06  5.50  4.44  5  3  1.06  5.34  4.26  3  4  .53  4.89  4.36  4  5  .79  5 . 34  4 . 55  6  6  1.06  4.89  3.83  1  performance from  does  rank  sum i s  degrade  non-design  set  0.  H  0  is  significantly depths.  with  from the  Difference B  5.1)  1  Negative data  test  records  B -• T e s t  Design  of  performance  rejected with  as  the  above; inclusion  of  66 References [I]  Chen,  C.H.,  Statistical  1973,  pp.  [2.]  ibid,pp.  21-24  [3]  Y.  Das,J.E.  McFee, of  Electromagnetic Canada, [4]  [ 5 ] Y. [6]  R.  private  Bell,  "Detection  Ordnance Suffield  and  by M a g n e t i c Report  Suffield,  No.  Ralston,  and  283,  Defence  Alberta,  25-29  communication "The D e s i g n  Experiments",  1962 , p p .  Kemp,  Metal  Hayden,  29-33  Recognition [7]  Means",  Highleyman,  March  Buried  June 1 9 8 1 , p p .  Das,  W.H.  and M.E.  Establishment  ibid,pp.  Recognition,  109-111  Identification Research  Pattern  and A n a l y s i s  Bell  Syst.  of  Tech.  Pattern  J . , Vol.  41,  723-744  "A T h e o r e t i c a l  Detector",  Report  Plessy  for  Company  Pulsed  Ltd.,  Eddy  Havant,  Current U.K.,  March  1970 [8]  J . E . McFee Objects", December  [9] [10]  ibid,p.  and Y. Can.  J.  of  1980 , p p .  "The D e t e c t i o n  Remote  Sensing,  of  Buried  Vol.  6,  No.  Explosive 2,  104-121  108  J . E . McFee Detection Research Canada,  [II]  Das,  and Y.  Das,  Methods",  Suffield  Establishment September  W. M e n d e n h a l l Statistics  [12]  ibid,  pp.  [13]  ibid,  p.  [14]  A.F.  of  Unexploded  Report  Suffield,  No.  292,  Ralston,  Ordnance Defence  Alberta,  1981  and R.L.  With  "Review  Scheaffer,  Aplications,  Mathemati c a l  Duxbury,  1973.  pp.  532-535  539-542 A43  Mood,  Introduction  McGraw-Hill,  1950,  pp.  to  the Theory  387-189  of  Statistics,  67  [15]  J . T . Tou  and  Pri nci pies, [16]  ibid,  p.  [17]  ibid,  pp.  [18]  G.T.  R.C.  Addison-Wesley,  Pattern 1974,  Recognition  pp.124-127  87 263-269  Toussaint,  "Bibliography  Classification", IT-20,  Gonzalez,  July  1974,  IEEE pp.  Trans, 472-479  on on  Estimation Information  of Theory, V o l .  


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