{"title": "Salient Contour Extraction by Temporal Binding in a Cortically-based Network", "book": "Advances in Neural Information Processing Systems", "page_first": 915, "page_last": 924, "abstract": null, "full_text": "Salient Contour Extraction by Temporal Binding \n\nin a Cortically-Based Network \n\nShih.Cheng  Yen  and  Leif  H.  Finkel \n\nDepartment of Bioengineering and \nInstitute of Neurological Sciences \n\nUniversity of Pennsylvania \n\nPhiladelphia, PA  19104, U.  S.  A. \n\nsyen @jupiter.seas.upenn.edu \nleif@jupiter.seas.upenn.edu \n\nAbstract \n\nIt has been suggested that long-range intrinsic  connections  in  striate cortex  may \nplay  a  role  in  contour  extraction  (Gilbert  et  aI.,  1996).  A  number  of  recent \nphysiological  and  psychophysical  studies  have  examined  the  possible  role  of \nlong range connections in the modulation  of contrast detection  thresholds  (Polat \nand Sagi,  1993,1994; Kapadia et aI.,  1995; Kovacs and Julesz,  1994) and various \npre-attentive  detection  tasks  (Kovacs  and  Julesz,  1993;  Field  et aI.,  1993).  We \nhave  developed  a  network  architecture based  on  the  anatomical  connectivity  of \nstriate cortex,  as  well  as  the  temporal  dynamics  of neuronal  processing,  that  is \nable to reproduce the observed experimental results. The  network  has  been  tested \non  real  images  and  has  applications  in  terms  of identifying  salient  contours  in \nautomatic image processing systems. \n\n1 \n\nINTRODUCTION \n\nVision is an active process, and one of the earliest, preattentive actions in  visual \nprocessing is the identification of the salient contours in a scene. We propose that this \nprocess depends upon two properties of striate cortex: the pattern of horizontal \nconnections between orientation columns, and temporal synchronization of cell responses. \nIn particular, we propose that perceptual salience is directly related to the degree of cell \nsynchronization. \n\nWe  present  results  of  network  simulations  that  account  for  recent  physiological  and \npsychophysical  \"pop-out\" experiments,  and  which  successfully  extract  salient  contours \nfrom real images. \n\n\f916 \n\n2 \n\nMODEL  ARCHITECTURE \n\nS.  Yen and L.  H.  Finkel \n\nLinear quadrature steerable filter pyramids (Freeman and Adelson, 1991) are  used  to  model \nthe  response  characteristics  of  cells  in  primary  visual  cortex.  Steerable  filters  are \ncomputationally efficient as they allow the energy at any orientation and  spatial  frequency \nto  be  calculated from  the  responses  of a  set  of basis  filters .  The fourth  derivative  of  a \nGaussian and its Hilbert transform were used as the filter kernels to approximate the shape \nof the receptive fields of simple cells. \n\nThe  model  cells  are  interconnected  by  long-range  horizontal  connections  in  a  pattern \nsimilar to the co-circular connectivity pattern of Parent and  Zucker  (1989),  as  well  as  the \n\"association  field\"  proposed  by  Field  et  at.  (1993). \nFor  each  cell  with  preferred \norientation,  e,  the orientations, \u00a2,  of the pre-synaptic cell at  position  (i,j)  relative  to  the \npost-synaptic cell, are specified by: \n\n\u00a2(e,i,j) = 2tan- l(f)-e \n\n(see Figure 1a).  These excitatory connections are confined to two regions, one flaring  out \nalong the axis of orientation of the cell  (co-axial),  and  another confined  to  a  narrow  zone \nextending orthogonally to the axis of orientation (trans-axial).  The fan-out of the  co-axial \nconnections  is  limited  to  low  curvature  deviations  from  the  orientation  axis  while  the \ntrans-axial connections are limited to a narrow  region  orthogonal  to  the  cell's orientation \naxis.  These constraints are expressed as: \n\n1,  if tan-I (f) -e < 1(, \n1  zif tan -I (1) _ e = 7! \u00b1 E \n\ni  2 '  \n\nr(e i  J.  III)  -\n\n, ,  ,..\"  - ,  \n\n0,  otherwise. \n\nwhere K  represents the maximum angular deviation from the  orientation  axis  of the  post(cid:173)\nsynaptic cell and \u00a3  represents the maximum angular deviation from  the orthogonal axis  of \nthe post-synaptic cell.  Connection weights decrease for positions with  increasing  angular \ndeviation  from  the  orientation  axis  of  the  cell,  as  well  as  positions  with  increasing \ndistance,  in  agreement  with  the  physiological  and  psychophysical  findings.  Figure  1 b \nillustrates \nis  physiological,  anatomical  and \npsychophysical evidence consistent with the existence of both sets of connections (Nelson \nand  Frost,  1985;  Kapadia  et  at.,  1995;  Rockland  and  Lund,  1983;  Lund  et  at.,  1985; \nFitzpatrick,  1996; Polat and  Sagi,  1993,  1994). \n\nthe  connectivity  pattern. \n\nThere \n\nCells that are facilitated by  the  connections  inhibit  neighboring  cells  that  lie  outside  the \nfacilitatory  zones.  The  magnitude  of  the  inhibition  is  such  that  only  cells  receiving \nstrong  support  are  able  to  remain  active.  This  is  consistent  with  the  physiological \nfindings of Nelson and Frost (1985) and Kapadia et al.  (1995) as  well  as  the  intra-cellular \nrecordings of Weliky et al.  (1995) which show EPSPs followed by  IPSPs when  the  long(cid:173)\ndistance  connections  were  stimulated.  This  inhibition  is  thought  to  occur  through  di(cid:173)\nsynaptic pathways. \n\nIn  the  model,  cells  are  assumed  to  enter a  \"bursting  mode\"  in  which  they  synchronize \nwith  other  bursting  cells. \nIn  cortex,  bursting  has  been  associated  with  supragranular \n\"chattering cells\" (Gray and McCormick (1996). In the model, cells that enter the bursting \n\n\f8 j (/)= \n\nJ \n\n, \n\nW ii  =1 \n\nL w .. 8 .(1 -1) \n\nIJ \n\nLWij \n\nSalient Contour Extraction by Temporal Binding in a Cortically-based Network \n\n917 \n\nmode are modeled as homogeneous coupled neural oscillators with a common fundamental \nfrequency but different phases (Kopell and Ermentrout,  1986; Baldi and Meir,  1990).  The \np~ase of  each  oscillator  is  modulated  by  the  phase  of  the  oscillators  to  which  it  is \ncoupled.  Oscillators  are coupled only  to  other oscillators  with  which  they  have  strong, \nreciprocal, connections.  The oscillators synchronize using a simple phase averaging rule: \n\nwhere  e represents  the  phase  of  the  oscillator  and  W U  represents  the  weight  of  the \nconnection  between  oscillator  i  and  j.  The  oscillators  synchronize  iteratively  with \nsynchronization defined as the following condition: \n\n18;Ct)-8/t)1 < 8,  i.j E  C, \n\nt <  t max \n\nwhere  C  represents  all  the  coupled  oscillators  on  the  same  contour,  8  represents  the \nmaximum phase difference between oscillators,  and  Imax  represents  the  maximum  number \nof time steps the oscillators are allowed to synchronize.  The salience of the  chain  is  then \nrepresented by the sum of the activities of all the synchronized elements  in  the  group,  C. \nThe chain with the highest salience is chosen as the output  of the  network.  This  allows \nus to compare the output of the model to psychophysical results on contour extraction. \n\nIt  has  been  postulated  that  the  40  Hz  oscillations  observed  in  the  cortex  may  be \nresponsible  for  perceptual  binding  across  different  cortical  regions  (Singer  and  Gray, \n1995).  Recent studies have questioned  the  functional  significance  and  even  the  existence \nof  these  oscillations  (Ghose  and  Freeman,  1992;  Bair  el  ai.,  1994).  We  use  neural \noscillators only as a simple functional means of computing synchronization  and  make  no \n\nassumption regarding their possible role in cortex. r-------------------, \n\n(x \"  y,l \n\n=-6  ifLll=O.  4,=0 \n\nFigure  I:  a)  Co-circularity  constraint.  b)  Connectivity  pattern  of a  horizontally  oriented  cell.  Length  of line \nindicates connection strength. \n\nb \n\n3 \n\nRESULTS \n\nThis  model  was  tested  by  simulating  a  number  of  psychophysical  experiments.  A \nnumber  of  model  parameters  remain  to  be  defined  through  further  physiological  and \npsychophysical  experiments,  thus  we  only  attempt  a  qualitative  fit  to  the  data.  All \nsimulations were conducted with the same parameter set. \n\n3.1 \n\nEXTRACTION  OF  SALIENT  CONTOURS \n\nUsing  the  same  methods  as  Field  el al.  (1993),  we  tested  the  model's  ability  to  extract \ncontours embedded in noise (see Figure 2).  Pairs of stimulus arrays were  presented  to  the \n\n\f918 \n\nS.  Yen and L  H.  Finkel \n\nnetwork,  one  array  contains  a  contour,  the  other  contains  only  randomly  oriented \nelements.  The network determines the stimulus  containing  the  contour  with  the  highest \nsalience.  Network  performance  was  measured  by  computing  the  percentage  of correct \ndetection.  The network was tested  on  a range of stimulus  variables  governing the  target \ncontour:  1) the angle,  ~, between  elements on  a  contour,  2)  the  angle  between elements \non  a  contour but  with  the  elements  aligned  orthogonal  to  the  contour  passing  through \nthem, 3) the angle between elements with a random offset angle, \u00b1a,  with  respect  to  the \ncontour  passing  through  them,  and  4)  average  separation  of  the  elements. \n500 \nsimulations were run at each data point.  The results  are  shown  in  Figure  2.  The model \nshows good qualitative agreement  with  the  psychophysical  data.  When  the  elements are \naligned, the performance of the network is mostly modulated by  the  co-axial  connections, \nwhereas  when  the  elements  are  oriented  orthogonal  to  the  contour,  the  trans-axial \nconnections  mediate  performance.  Both  the  model  and  human  subjects  are  adversely \naffected as  the  weights  between  consecutive elements decrease  in  strength.  This  reduces \nthe length of the contour and thus the saliency of the stimulus. \n\na) Elements aligned \n\nparallell to path \n\nb) Elements aligned \n\northogonal to path \n\nc) Elements aligned parallel \n\nto path with a = 30' \n\n~I:~-U:\":-,,~_,:_,,,~ \n~ 70 \n~ 60 \n~ 50 \n\n''0 \n\"'\"0 \n\nI:~~~o,. I:~ \n\n:\"'~ \n\n70 \n60\n50 \n\n\" \n\n.. _._.\" \n\n\u2022 \n\n70 \n60 \n50 \n\n70 \n60\n50 \n\n_  \u2022\u2022 _  \u2022\u2022 _  \u2022\u2022 _. \n\nd) Elements at 0.9'  separation \n\nI:~ ~ ~\\~ .. ,  .........  All \n\n'b \n'  \" ,  \n\n---0--- DW \n..::&  - 0 - - Model \n\n4 0 ~~~~~~ 40 ~~-~1~~~4 0 ~~~~~~40~~~r-~~ \n\n15 \n\n:\\ 0  45  60  75  90 \n\nAngle  (deg) \n\no  15  30  45  60  75 \n\nAngle (deg) \n\no  15  30  45  60  75 \n\nAngle (deg) \n\n15 \n\n:\\0 \n\n45  60 \nAngle (deg) \n\n75 \n\nFigure 2: Simulation results are compared to the data from 2 subjects (AH, DJF)  in  Field  ef  al.  (1993).  Stimuli \nconsisted  of 256  randomly  oriented  Gabor  patches  with  12  elements  aligned  to  form  a  contour.  Each  data \npoint represents results for 500 simulations. \n\n3.2 \n\nEFFECTS  OF  CONTOUR  CLOSURE \n\nIn a series of experiments using similar stimuli to  Field et al.  (1993),  Kovacs  and Julesz \n(1993)  found  that  closed  contours  are  much  more  salient  than  open  contours.  They \nreported that when the inter-element spacing between all elements was gradually increased, \nthe maximum  inter-element  separation for  detecting  closed  contours,  ~ c  (defined  at  75% \nperformance),  is  higher  than  that  for  open  contours,  ~ o . \nIn  addition,  they  showed  that \nwhen elements spaced at  ~o  are  added to  a  'Jagged\"  (open)  contour,  the  saliency  of  the \ncontour increases  monotonically  but  when  elements spaced  at  ~ c  are  added  to  a  circular \ncontour,  the  saliency  does  not  change  until  the  last  element  is  added  and  the  contour \nbecomes closed.  In fact, at  ~c,  the contour is not salient until it is closed, at  which  point \nit  suddenly  \"pops-out\"  (see  Figure  3c).  This  finding  places  a  strong  constraint  on  the \ncomputation of saliency in  visual perception. \n\nInterestingly,  it  has  been  shown  that  synchronization  in  a  chain  of  coupled  neural \noscillators  is  enhanced  when  the  chain  is  closed  (Kopell  and  Ermentrout,  1986; \nErmentrout,  1985; Somers and  Kopell,  1993).  This  property  seems  to  be related  to  the \ndifferences  in  boundary  effects on  synchronization  between  open  and  closed  chains  and \nappears  to  hold  across  different  families  of coupled  oscillators.  It has  also  been  shown \nthat synchronization is dependent on  the  coupling  between oscillators  -- the  stronger the \ncoupling,  the  better the  synchronization,  both  in  terms  of speed  and  coherence  (Somers \n\n\fSalient Contour Extraction by Temporal Binding in a Cortically-based Network \n\nand  Kopell,  1993;  Wang,  1995).  We  believe  these  findings  may  apply  to \npsychophysical results. \n\n919 \n\nthe \n\nAs  in  Kovacs  and  Julesz  (1993),  the  network  is  presented  with  two  stimuli,  one \ncontaining  a  contour  and  the  other  made  up  of all  randomly  oriented  elements.  The \nnetwork picks the stimulus containing the synchronized contour with  the  higher  salience. \nIn separate trials, the threshold for maximum separation between elements was  determined \nfor open and closed contours.  The  ratio  of the  separation  of the  background  elements  to \nthe that of elements on  a  closed  curve,  <Pc,  was  found  to  be  0.6  (which  is  similar  to  the \nthreshold  of 0.65  recently  reported  by  Kovacs  et al.,  1996),  whereas  the  ratio  for  open \ncontours,  <Po,  was found  to be 0.9.  (11  is the threshold separation  of contour elements,  <P, \nat a particular background separation).  We then examined the changes in salience for open \nand closed contours.  The performance of the network was measured as additional elements \nwere added to an initial  short  contour of elements.  The results  are  shown  in  Figure  3b. \nAt  <Po,  both  open  and  closed  contours  are  synchronized  but  at  <Pc,  elements  are \nsynchronized only  when  the  chains  are  closed. \nIf salience  can  only  be  computed  for \nsynchronized contours,  then  as  additional  elements  are  added  to  an  open  chain  at  <Po'  the \nsalience would increase since the whole chain is synchronized.  On  the  other hand,  at  <Pc, \nas long as  the last element is missing, the  chain  is  really  an  open  chain,  and  since  <Pc is \nsmaller  than  <Po'  the  elements  on  the  chain  will  not  be  able  to  synchronize  and  adding \nelements  has  no  effect  on  salience.  Once  the  last  element  is  added,  the  chain  is \nimmediately able to synchronize and the salience of the contour increases  dramatically  and \ncauses the contour to \"pop-out\". \na) Performance as a function of \n\nc) Performance as a function of closure. \nb) Performance as a function of closure.  Data from  Kovacs and Julesz (1993) \n85 \"T \" \" - - - - - - - - ,  \n80_ \n\n85 \n80 \u2022 \n\nbackground to contour separation. \n100 \n\n_  90 \n\ng 80 \n\nu \nC  70 \n~ \n~ 60 \n\n\\ \n\n.. _\" \n\n00cP, \n. \n-.. ~  0 \n--------~---- ~---\n~o \u00bb.,b , \n\n50,..-r----r-\"T\"\" ___ rA-.... \n0 .4 \n\n0.6 \n\n0.8 \n\n1.4 \n\n1.2 \n\nI \n\nIp \n\n,t\"'-~\\ \n~ 75  --------1------8-\n\\ \nI \n,0' \n, \n(S,d \n\nJ. \n~' \no.~'.o. \n/l' \n\n~ 70. \nc  65 \n~ 60 \n\n'0' \n\n55' \n\n50 \n\n\u2022 \u2022  \n\n~  75  ------------'4:i-\n8  70-\n~  65 \nd!  60 . \"  \n\n.... .,..,.~ \n\n/ \n~ \n\n,If:  --o()--\n\n55  9.,,-.0-_--0- 0 ' \n50 \n\n\u2022 \n\nClosed \n\nOpen \n\n01 2345678 9  \n\n0 123 456 7 89 \n\nAdditional  ElemenLS \n\nAdditional  Elements \n\nFigure  3:  Simulation  of the  experiments  of Kovacs  and  lulesz  (1993).  Stimuli  consisted  of  2025  randomly \noriented Gabor patches, with 24 elements aligned to  form a  contour.  Each  data  point  represents  results  from \n500  trials.  a)  Plot  of  the  performance  of  the  model  with  respect  to  the  ratio  of  the  separation  of  the \nbackground elements to the contour elements. Results show closed contours are salient  to  a  more  salient  than \nopen contours.  b) Changes in  salience as additional elements are  added  to  open  and  closed  contours.  Results \nshow that  the  salience  of open  contours  increase  monotonically  while  the  salience  of closed  contours  only \nchange with the addition of the last element. Open contours were initially made up of 7 elements  while  closed \ncontours  were  made  up  of  17  elements.  c)  The  data  from  Kovacs  and  lulesz  (\\993)  are  re-plotted  for \ncomparison. \n\n3.3 \n\nREAL  IMAGES \n\nA stringent test of the model's capabilities is  the  ability  to  extract perceptually  salient \ncontours in real images.  Figure 4  and  5  show  results  for  a  typical  image.  The original \ngrayscale image, the output of the steerable filters, and the output of the model  are  shown \nin Figure 4a,b,c and Figure  5a,b,c  respectively.  The  network  is  able  to  extract  some  of \nthe  more  salient contours  and  ignore other high  contrast edges  detected  by  the  steerable \nfilters.  Both simulations  used  filters  at  only  one  spatial  scale  and  could  be  improved \nthrough interactions  across  multiple  spatial  frequencies.  Nevertheless,  the  model  shows \npromise for automated image processing applications \n\n\f920 \n\nS.  Yen and L. H.  Finkel \n\nFigure 4:  a) Plane image. b) Steerable filter response. c) Result of model showing the most salient contours. \n\nFigure 5:  a)  Satellite image of Bangkok.  b)  Steerable  filter  response.  c)  Salient  contours  extracted  from  the \nimage. The model  included filters at  only one spatial frequency. \n\n4 \n\nCONCLUSION \n\nWe  have presented  a cortically-based model  that  is  able  to  identify  perceptually  salient \ncontours  in  images  containing  high  levels  of noise.  The model  is  based  on  the  use  of \nlong  distance  intracortical  connections  that  facilitate  the  responses  of cells  lying  along \nsmooth  contours.  Salience  is  defined  as  the  combined  activity  of  the  synchronized \npopulation of cells responding to  a  particular contour.  The model  qualitatively  accounts \nfor  a  range  of  physiological  and  psychophysical  results  and  can  be  used  in  extracting \nsalient contours in  real images. \n\nAcknowledgements \n\nSupported  by \nFoundation, and the McDonnell-Pew Program in Cognitive Neuroscience. \n\nthe  Office  of  Naval  Research  (NOO014-93-1-0681),  The  Whitaker \n\nReferences \nBair,  W.,  Koch,  c.,  Newsome,  W.  &  Britten,  K.  (1994).  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