{"title": "Can VI Mechanisms Account for Figure-Ground and Medial Axis Effects?", "book": "Advances in Neural Information Processing Systems", "page_first": 136, "page_last": 142, "abstract": null, "full_text": "Can VI mechanisms account  for \n\nfigure-ground and  medial axis effects? \n\nZhaoping Li \n\nGatsby Computational Neuroscience Unit \n\nUniversity College London \n\nzhaoping~gatsby.ucl.ac.uk \n\nAbstract \n\nWhen a  visual image consists of a figure against a background, V1 \ncells are physiologically observed to give higher responses to image \nregions  corresponding  to  the figure  relative  to  their  responses  to \nthe  background.  The  medial  axis  of the figure  also  induces  rela(cid:173)\ntively  higher  responses  compared  to responses  to  other  locations \nin the figure  (except for  the boundary between  the figure  and the \nbackground).  Since the receptive fields  of V1  cells  are very smal(cid:173)\nl  compared with  the global  scale  of the figure-ground  and  medial \naxis effects, it has been suggested that these effects  may be caused \nby feedback from  higher visual areas.  I show how these effects can \nbe  accounted  for  by  V1  mechanisms  when  the  size  of the  figure \nis  small  or  is  of a  certain scale.  They are  a  manifestation  of the \nprocesses of pre-attentive segmentation which detect and highlight \nthe boundaries between homogeneous image regions. \n\n1 \n\nIntroduction \n\nSegmenting figure  from  ground is  one of the most important visual tasks.  We  nei(cid:173)\nther know  how  to execute  it  on  a  computer  in  general,  nor  do  we  know  how  the \nbrain executes it.  Further, the medial axis of a figure has been suggested as provid(cid:173)\ning  a  convenient  skeleton  representation of  its  shape  (Blum  1973).  It is  therefore \nexciting to find  that responses of cells in V1,  which is  usually considered a low level \nvisual area, differentiate between figure  and ground  (Lamme 1995, Lamme,  Zipser, \nand  Spekreijse  1997,  Zipser,  Lamme,  Schiller  1996)  and  highlight  the medial  axis \n(Lee,  Mumford,  Romero,  and Lamme 1998).  This happens even though the recep(cid:173)\ntive fields  in  V1  are much  smaller  than the scale of these  global  and perceptually \nsignificant phenomena.  A common  assumption is that feedback  from  higher visual \nareas is  mainly responsible for  these effects.  This is  supported by the finding  that \nthe figure-ground effects in V1  can be strongly reduced or abolished by anaesthesia \nor lesions in higher visual areas  (Lamme et al 1997). \n\nHowever,  in  a  related  experiment  (Gallant,  van  Essen,  and  Nothdurft  1995),  V1 \ncells were found  to give higher responses to global boundaries between two texture \nregions.  Further, this border effect was significant only 10-15 milliseconds after the \ninitial  responses  of the  cells  and  was  present  even  under  anaesthesia.  It is  thus \n\n\fCan  VI Mechanisms Account/or Figure-Ground and Medial Axis Effects? \n\n137 \n\nplausible that VI mechanisms is  mainly responsible for  the border effect. \n\nIn this paper, I propose that the figure-ground and medial axis effects are manifes(cid:173)\ntations of the border effect,  at least for  apropriately sized figures .  The border effect \nis  significant  within  a  limited  and  finite  distance from  the figure  border.  Let  us \ncall the image region within this finite distance from the border the effective border \nregion.  When  the size  of the figure  is  small enough,  all  parts of the figure  belong \nto the effective border region  and can induce higher responses.  This suggests that \nthe figure-ground  effect  will  be reduced  or diminished  as  the size  of the figure  be(cid:173)\ncomes larger, and the VI responses to regions of the figure far away from the border \nwill  not  be significantly higher  than responses  to background.  This suggestion  is \nsupported by experimental findings  (Lamme et al  1997).  Furthermore,  the border \neffect  can create secondary ripples as the effect  decays with distance from  the bor(cid:173)\nder.  Let  us  call  the distance from  the border to the ripple the  ripple  wavelength. \nWhen the size  of a  figure  is  roughly twice  the ripple wavelength,  the ripples from \nthe two opposite borders of the figure  can reinforce each other at the center of the \nfigure to create the medial  axis effect, which,  indeed,  is  observed to occur only for \nfigures  of appropriate sizes  (Lee et al  1998). \nI  validate this  proposal  using  a  biologically based model  of VI  with  intra-cortical \ninteractions  between  cells  with  nearby  but  not  necessarily  overlapping  receptive \nIntra-cortical  interactions  cause  the  responses  of  a  cell  be  modulated  by \nfields. \nnearby stimuli outside its classical receptive fields  -\nthe contextual influences that \nare  observed  physiologically  (Knierim  and  van  Essen  1992,  Kapadia  et  al  1995). \nContextual influences make VI cells sensitive to global image features, despite their \nlocal receptive fields,  as  manifested in the border and other effects. \n\n2  The VI  model \n\nWe  have  previously  constructed  a  VI  model  and shown  it  to  be able to  highlight \nsmooth  contours  against  a  noisy  background  (Li  1998,  1999,  1999b)  and  also  the \nboundaries  between  texture  regions  in  images  -\nthe  border  effect.  Its  behavior \nagrees  with  physiological  observations  (Knierim  and  van  Essen  1992,  Kapadia  et \nal  1995)  that  the  neural  response  to  a  bar  is  suppressed  strongly  by  contextual \nbars of similar orientatons -\niso-orientation suppression;  that the response is  less \nsuppressed  by  orthogonally  or  randomly  oriented  contextual  bars;  and  that  it  is \nenhanced  by  contextual bars  that  are aligned  to form  a  smooth  contour in  which \nthe  bar  is  within  the  receptive  field  -\ncontour  enhancement.  Without  loss  of \ngenerality, the model ignores color,  motion, and stereo dimensions,  includes mainly \nlayer 2-3 orientation selective cells, and ignores the intra-hypercolumnar mechanism \nby which  their  receptive fields  are formed.  Inputs to the model are images filtered \nby the edge- or bar-like local receptive fields  (RFs) of VI cells. l  Cells influence each \nother  contextually  via  horizontal  intra-cortical  connections  (Rockland  and  Lund \n1983,  Gilbert,  1992),  transforming patterns of inputs to patterns of cell  responses. \nFig.  1 shows  the elements  of the  model  and  their interactions.  At  each  location \ni  there is  a  model  VI  hypercolumn  composed  of K  neuron  pairs.  Each  pair  (i, fJ) \nhas  RF  center  i  and  preferred  orientation  fJ  =  k1r / K  for  k  = 1, 2, ... K ,  and  is \ncalled  (the neural representation of)  an edge segment.  Based on experimental data \n(White, 1989), each edge segment consists of an excitatory and an inhibitory neuron \nthat are interconnected, and each model cell represents a  collection of local cells of \nsimilar types.  The  excitatory  cell  receives  the  visual  input;  its  output  is  used  as \na  measure of the response  or  salience of the edge  segment  and  projects to higher \nvisual areas.  The inhibitory cells are treated as interneurons.  Based on observations \n\nIThe terms 'edge'  and 'bar' will  be used interchangeably. \n\n\f138 \n\nZ.  Li \n\nA  Visual space, edge detectors, \n\nand their interactions \n\nB  Neural connection pattern. \n\nSolid:  J, Dashed:  W \n\n~ 0'\u00b7': . \n\n,-, .\u2022 : \n\n,-, .\u2022 ::  ~ \n\n~ ~ 0' \u00b7': \n\n0' \u00b7':  ~ ~ \n\n~~~-~~~ \n\n~ ~ ><  ,-, .\u2022 :;  ~ ~ \n~ ,-, .. ::  :, .. ::  :, .. ::  ~ \n\nModel  Neural  Elements \nEdge outputs to higher visual areas \n\n~~-r--+-~~--r--+~--~ \n\nInputs Ie to \ninhibitory cells \n\nAn interconnected \n--~ neuron pair for \n:  edge segment i e \n\n-\n\nInhibitory \ninterneurons \n\nExcitatory \nneurons \n\n'-0-(cid:173)\nI \n\nVisual inputs, filtered through the \nreceptive fields, to the excitatory cells. \n\nFigure  1:  A:  Visual  inputs  are  sampled  in  a  discrete  grid  of edge/bar  detectors. \nEach  grid  point  i  has  K  neuron  pairs  (see  C),  one  per  bar  segment,  tuned  to \ndifferent  orientations  ()  spanning  1800 \u2022  Two  segments  at different  grid  points  can \ninteract  with  each other via monosynaptic excitation  J  (the  solid  arrow from  one \nthick  bar  to  anothe  r)  or  disynaptic  inhibition  W  (the  dashed  arrow  to  a  thick \ndashed bar).  See also C. B: A schematic of the neural connection pattern from  the \ncenter  (thick  solid)  bar to neighboring  bars within  a  few  sampling unit distances. \nJ's  contacts are shown by thin solid bars.  W's are shown by thin dashed bars.  The \nconnection pattern is  translation and rotation invariant.  C: An input  bar segment \nis  directly  processed  by  an  interconnected  pair of excitatory  and  inhibitory  cells, \neach cell  models  abstractly a  local group  of cells  of the same type.  The excitatory \ncell receives visual input and sends output 9x (Xii})  to higher centers.  The inhibitory \ncell is an interneuron.  Visual space is taken as having periodic boundary conditions. \n\nby  Gilbert,  Lund  and  their  colleagues  (Rockland  and  Lund,  1983,  Gilbert  1992) \nhorizontal  connections  JiO,jO'  (respectively  WiO,jO')  mediate  contextual  influences \nvia monosynaptic excitation (respectively disynaptic inhibition) from j(}' to i(} which \nhave  nearby  but  different  RF  centers,  i  -::j:.  j, and  similar  orientation  preferences, \n()  '\" ()'.  The membrane potentials follow  the equations: \n\nXiO \n\nYiO \n\n-axXiO  - 2: 'l/J(f),,(})9y(Yi,9+flO)  + J 0 9x(XiO) +  2:  JiO ,jO' 9x (XjOl ) + fio  + fo \n-ayYiO+9x(XiO)+  2:  W iO ,jOl9x(Xjol)+fc \n\nj#.i,O' \n\nflO \n\nj#i,O' \n\n\fCan  VI Mechanisms Account/or Figure-Ground and Medial Axis Effects? \n\n139 \n\nwhere  O:zXie  and  O:yYie  model  the  decay  to  resting  potential,  9z(X)  and  9y(Y)  are \nsigmoid-like functions modeling cells' firing rates in response to membrane potentials \nx  and  y,  respectively,  1/J(6.8)  is  the  spread  of  inhibition  within  a  hypercolumn, \nJ09z(Xie)  is  self excitation,  Ie  and  10  are  background  inputs,  including  noise  and \ninputs modeling the general and local normalization of activities  (see Li  (1998)  for \nmore details).  Visual input lie  persists after onset, and initializes the activity levels \n9z(Xie).  The activities are then modified by the contextual influences.  Depending on \nthe visual input, the system often settles into an oscillatory state (Gray and Singer, \n1989, see the details in Li 1998).  Temporal averages of 9z(Xie) over several oscillation \ncycles are used as the model's output.  The nature of the computation performed by \nthe model is  determined largely by the horizontal connections  J  and W, which  are \nlocal  (spanning  only  a  few  hypercolumns),  and  translation  and rotation invariant \n(Fig.  IB). \n\nA: \n\nInput image  (li8)  to model \n\nB:  Model  output \n\n-------------111111111  II  III \n-------------11111  I  I  I  I  I I  I I  I \n-------------1 I I  I I  I  I  I  I  II  I I  I \n-------------1 I I  I I  I  I  I  I  I I  III \n-------------1 I I  III  I  I  I  I I  I  I  I \n-------------1 I I  1 I  I  I  I I  1 I  III \n-------------1 I I  I I  I I  I II  I  I I  I \n-------------1 I  I  I 1 I I  I I  I I  I I  I \n-------------1 I  II  I  I II  I  I I  I I  I \n-------------1111111  I III  III \n-------------1 1 I  1 I  I  I  I I  I  I  I I  I \n\n-------------1.1 I III  II  I I I I I \n-------------111 I  I  I I  II  I I  I I  I \n-------------111 I  I  I 1 II  I I  II  I \n-------------111 I  1 I  1 II  I I  I  I  I \n-------------111 I  III  II  I I  I  I  I \n-------------111 I  I  I 1 II  II  I  I  I \n-------------111 I  I  I  I  II  II  I  I  I \n-------------111 I I  I  I  II  II  I  I  I \n-------------111 II  I I  II  II  II  I \n-------------1.1 I I II  II  II  I I I \n-------------111 I  I  I I  II  II  I  I  I \n\nFigure  2:  An  example  of  the  performance  of  the  model.  A:  Input  li9  consists  of  two \nregions;  each  visible  bar  has  the same  input  strength.  B:  Model  output  for  A,  showing \nnon-uniform output strengths (temporal averages of 9\" (Xi9))  for  the edges.  The input and \noutput strengths are  proportional  to the bar widths.  Because  of the noise  in  the system, \nthe saliencies of the bars in the same column are not exactly the same,  this is also the case \nin other figures. \n\nThe model was applied to some texture border and figure-ground stimuli, as shown \nin examples in the figures.  The input values  fir}  are the same for  all  visible bars in \neach  example.  The  differences  in  the  outputs  are caused  by  intracortical interac(cid:173)\ntions.  They become significant about one membrane time constant after the initial \nneural response  (Li,  1998).  The widths  of the bars in  the figures  are  proportional \nto input and output strengths.  The plotted region in  each picture is  often a  small \nregion  of an  extended  image.  The  same  model  parameters  (e.9.  the  dependence \nof the synaptic weights on  distances  and  orientations,  the  thresholds  and  gains  in \nthe functions  9z0  and 9yO,  and the level  of input  noise  in 10 )  are used for  all  the \nsimulation examples. \nFig.  2 demonstrates that the model indeed gives higher responses to the boundaries \nbetween texture regions.  This border effect is highly significant within a distance of \nabout 2 texture element spacings from the border.  Thus the effective border region \nis  about  2  in  texture  element  spacings  in  this  example.  Furthermore,  at  about  9 \ntexture element spacings to the right of the texture border there is  a  much smaller \nbut  Significant  (visible  on  the  figure)  secondary  peak  in  the  response  amplitude. \nThus the ripple wavelength  is  about 9  texture element  spacings here.  The border \neffect  is  mainly  caused  by  the fact  that  the texture elements  at  the  border  expe(cid:173)\nrience  less  iso-orientation suppression  (which  reduces  the response  levels  to  other \ntexture  bars  in  the  middle  of a  homogeneous  (texture)  region)  -\nements  at  the border have fewer  neighboring  texture  bars of a  similar  orientation \nthan the texture elements  in the centers  of the regions.  The stronger responses to \nthe effective  border region  cause  extra iso-orientation  suppression to  texture  bars \nnear but right outside the effective border region.  Let us call this region of stronger \n\nthe  texture  el(cid:173)\n\n\f140 \n\nZ.  Li \n\nModel Input \n\nModel Output \n\n--\u2022\u2022 1111111111111111111111111 \u2022\u2022 --\n==1111111  11111111111\"111 11111== \n--\u2022\u2022 1111111111111111  11111  I  111.--\n=::= III III :  11I11 111I11 :  I  I III 1.:== \n- .... 1\"11\"1111111111\"111111 \u2022\u2022 -(cid:173)\n==11  11\"11 \n111111  111== \n-\n\u2022\u2022 1111  11111111111111111 \u2022\u2022 --\nI I  I 1'.-(cid:173)\n_ '1  I \n=:= 11I111111111111111111 1111 =:== \n\nI II I\" II \" \n\nI  II I I  I I \n\n.. ------(cid:173)\n.. ------(cid:173)\n.. ------(cid:173)\n.. ------(cid:173)\n.. ------(cid:173)\n.. ------(cid:173)\n.. ------(cid:173)\n.. ------(cid:173)\n.. ------(cid:173)\n.. ------(cid:173)\n.. -----(cid:173)\n.. -------\n\nI  ------(cid:173)\n\nI111 \n\n- - - - - -\u2022\u2022 I  I  I  I \n-------\u2022\u2022\u2022 I  I  I \n-------. I  I  I  I  I \n------. I' I  I  I \n-------\u2022\u2022\u2022 I  I  I \n-------. '1 1 I  I \n::=:=11.111 \n------1.1 1 I  I \n-------11  I  I  I \n\n------- I \nI  I  I \n- - - - - - .  I I I  I  I \n-------\n\u2022  I  I  I \n\nII \nII \nI  I \nII \nII \nI  I \nII \nII \nI  I \nI  I \nII \nI  I \n\nII  - - - - - - - -\n\nI  I  I  I .  --------(cid:173)\nI  I  I  I  \u2022\u2022 ---------\n\nI  I  I 11.--------(cid:173)\nI  I  I  I  1--------\nI II I \u2022\u2022 ---------\nI  111\u00b7---------\nI  I  I  I  1---------\nI II 1 \u2022\u2022 ---------\nI  I 1 \u2022\u2022 --------(cid:173)\nI  I  I 1 \u2022\u2022 --------(cid:173)\nI  I  I  \u2022\u2022\u2022 --------(cid:173)\nI  II \u2022\u2022\u2022 --------\n\n----------.. , \n---------1\u00b7\u00b7 \n----------\u2022\u2022 1 \n--------- .1 \n----------\u00b711 \n----------. \n----------. \n::::::::::111 \n---------... \n----------1. 1 \n---------- ., \n----------1\u00b71 \n-------------.. -------------\n-------------... -------------\n-------------... -------------\n-------------... -------------\n\n-------------\u00b7\u00b71-------------\n-------------1 \u2022\u2022 ------------\n------------\u2022\u2022 1------------\n-------------\u2022\u2022 1-------------\n-------------1.1------------\n-------------1.1-------------\n-------------1 \u2022\u2022 ------------\n-------------\u2022\u2022 1-------------\n-------------1.1-------------\n\n--111 11111111111111111111111 111--\n==11111111111111111111111111111== \n==111 11111111111111111111111 111== \n--11111111111111111111111111111--\n--111 11111111111111111111111111--\n==11111111111111111111111111111== \n==111 11111111111111111111111111== \n--11111111111111111111111111111--\n--11111111111111111111111111111--\n\n-------1 I  I  I  I  I  I \n-------1 II I  I  II \n-------1 I  I  I  I  I  I \n------- I  I  I  I  I  I  I \n------- I  I  I  I  I  I  I \n-------1111 1 11 \n------- I  I  I  I  I  I  I \n-------1 I  I  I  I  I  I \n-------1 I  I  I  I  I  I \n---- --- I  I  I  I  I  I  I \n:::::= IIII III \n------1 I  I  I  I  I  I \n\nIII \nI II \nI  I \nII  I \nIII \nI I I \nII  I \nII I \nI I  I \nI  I \nII I \nII I \nII I \n\n111-------\n111-------\nI  I  1-------\nI  I  1-------\n111------(cid:173)\nI  I  1-------\n11 1------\n111-----(cid:173)\nI  I  1-------\n111-------\n111-------\n111-------\n111-------\n\n---------1 I \n----------1 I \n- - - - - - - - - 1 I \n----------1 I \n---------- I  I \n---------1 I \n- - - - - - - - - I  I \n---------- 1 I \n---------1 I \n----------1 I \n- - - - - - - - - - I  I \n----------1 I \n--------11 \n\nIII \nIII \nIII \nIII \nIII \nIII \nIII \nIII \nIII \nIII \nIII \nIII \n\nI  1--------(cid:173)\nI 1--------(cid:173)\nI  I --------(cid:173)\nI  1---------\nI 1---------\n1--------\n11-------(cid:173)\nI  1--------(cid:173)\nI  1--------(cid:173)\nI  1--------(cid:173)\nI  1--------(cid:173)\nI 1---------\n11---------\n\n-------------1 I 1- ------------\n- - ----------- 1 I 1-------------\n------------- 1 I 1-------------\n------------- 1 I 1-------------\n-------------1  I 1-------------\n-------------1 I 1-------------\n-------------1 I 1-------------\n-------------1 I 1-------------\n- - -----------1 I 1-------------\n-------------1 I 1-------------\n-------------1 I 1-------------\n-------------1 I 1-------------\n------------- 1 I 1-------------\n\nFigure 3:  Dependence  on  the size  of the figure.  The figure-ground  effect  is  most \nevident  only  for  small  figures,  and the  medial  axis  effect  is  most  evident  only  for \nfigures  of finite  and appropriate sizes. \n\nsuppression from  the border the border  suppression  region,  which  is  significant  and \nvisible  in  Fig.  (2B).  This  region  can  reach  no  further  than  the  longest  length  of \nthe  horizontal  connenctions  (mediating  the  sup presion)  from  the  effective  border \nregion.  Consequently,  texture bars right outside the border suppression region  not \nonly escape the stronger suppression from  the border,  but also  experience weaker \niso-orientation  suppression  from  the  weakened  texture  bars  in  the  nearby  border \nsuppression region.  As  a result, a second saliency peak appears -\nthe ripple effect, \nand we  can hence conclude that the ripple wavelength is  of the same order of mag(cid:173)\nnitude as the longest connection length of the cortical lateral connections mediating \nintra-cortical interactions. \n\nFig.  3 shows  that for  very  small figures,  the whole figure  belongs  to the effective \nborder region and is highlighted in the Vl responses.  As the figure size increases, the \nresponses in the inside of the figure become smaller than the responses in the border \nregion.  However, when the size of the figure is appropriate, namely about twice the \nripple wavelength, the center of the figure induces a secondary response highlight.  In \nthis  case,  the ripples  or the secondary saliency peaks from  both borders superpose \nonto  each  other  at  the  same  spatial  location  at  the  center  of the  figure.  This \nreinforces the saliency peak at this  medial axis since it has two border suppression \nregions (from two opposite borders), one on each side of it, as its contextual stimuli. \nFor even larger figures,  the medial  axis  effect  diminishes  because  the ripples from \n\n\fCan  VI  Mechanisms Account for Figure-Ground and Medial Axis Effects? \n\n141 \n\nModel Input \n\nModel Output \n\nI \nI \n\n11111111111111111 \n11111111111111111 \n11111111111111111 \n11111111111111111 \n1---------------1 \n1---------------1 \n1---------------1 \n1---------------1 \n1---------------1 \n1---------------1 \n1---------------1 \n1---------------1 \n1---------------1 \n1---------------1 \n1---------------1 \n1---------------1 \n1---------------1 \n1---------------1 \n111111111IIII11I1 \n11111111111111111 \n11111111111111111 \n11111111111111111 \n11111111111111111 \n11111111111111111 \n11111111111111111 \n\nIII \n\n\"1\" \n\n1111111111111111111 \n\"1\"11111111111111 \nII  111'111\"1111'11 \nI  III  1111  I \n'I' \nI \n111111 \n................. \nI \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 \n11:::::::::::::::11 \n11:::::::::::::::1' \n11---------------11 \n.=:~~~~~~~=I \n.1---------------11 \n\u20221---------------1 \n1---------------1 \nI\u2022\u2022\u2022\u2022\u2022 .... \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 \n1111111.11111111111 \n1111111111111111111 \n'\"\"11\"'1\"1'1111 \n1111111111,11,1111, \n'111111111111111111 \n1111111111111111111 \n\n.. ---------------.. \n\n. . . . .  \"  . . . . . . . . . .  1 \n\n-------1 II  I  I  II  I  II  I  I  I 11-------\n:::::::1 I I I I II  I II  I I I I I::::::: \n:::::::1 II  I I II  I I I I I I I I::::::: \n:::::::1 II  I I I I I II  I I II  I::::::: \n-------1 II  I  I  I I  I  I I  I  I  I 11-------\n-------1 II  I  I  I I  I  I I  I  I 111-------\n-------1 II  I  I  I I  I  I I  I  I  I 11-------\n:::::::1 II  I I I I I II  I I I I I::::::: \n-------1 II  I  I  I I  I  II  I  I  II  1-------\n\n-------.111,,1 \u2022\u2022 , I 111.------\n------\u2022\u2022 11  \".1\"  1111.-------\n-------.11 I  I 11I1  I  I 111.-------\n:::::::11: I I 1IIII I III:::::::: \n-------\u00b7\u00b71 I I 'II1 I I  I '11------(cid:173)\n:::::=U  I  I. I  I  II  I I \n-------\u2022\u2022 1 I I ,.1\"  111.1-------\n-------.11  I I \".\"  I  I , \u2022\u2022 -------\n:::::::111 II 1III1  I III:::::::: \n-------\u2022\u2022 ,  I 111I11  I  I 1 \u2022\u2022 -------\n\n: : : : : : :  \n\n---------111111111111111---------\n----~-------1111111111111111111111111111111Ir:----=:-:--\n\n-::-:-:-:-=-1 I 11~1?71711 I 1--:-:-:-:-::=:-:-: \n-_-_-==_-_-_-:..-_-(j' ,',',I,',',',\"\"\"'if ___ -_-=_-===-_-___ \n::===-----:-,,',',1,',1,',',',',',',1,',',',','--=---==..-:-(cid:173)\n-----===------,',',',',',',',',',',',',',',',',',',------=.---: \n:--~-----11111111111111111111111111111111111_-:---==-----\u00ad\n-------1111 I I I I I I I I I I  1111 - - - - - - -\n- - - - - - -11  II I I I I I  t  III 1 111--------\n- - - - - - - -111  III1IIIII '11--------\n--------1111111111111111--------\n-_-_-===-_-_-_-_-_-_=.! ,',1,',',',',1,'.', !.=.,..-_-_-_-___ -===--_-_-_ \n---------1 I  I  I  I  I  I  I  I  I  I  I  I  1----------\n\n-----=-----_-~-..=..'_I_'-'_I~-::_-:-~-----\n\n\" \" \" ' / / / / / / / / / / / / / / / \" \" ' \"  \n\" \" \" ' / / / / / / / / ' / ' / / / / ' \" \" , ,  \n\n\" \" \" ' / / / ' / / / / / / ' / / / / ' \" \" , ,  \n\n\"\"\"'/'/','/'//'////'\"\",, \n\"\"\",'//'/'/\"/'////'\"\"\" \n\"\"\"\"'/'//','////'/'\"\",, \n\"\"\"'///'/'////'////'\"\",, \n\"\"\",'//'/\"/'/'//'\"\"\"\" \n\"\"\",'//'//////'///'\"\"\", \n\n\" \" \" ' / / / ' / / / / / / ' / / / / ' \" \" , ,  \n\n\" \" \" ' / / / ' / / / / / / / / / / / ' \" \" , ,  \n\" \" \" ' / / / / / / / / / / / / / / / \" \" ' \"  \n\" \" \" ' / / / / / / / / / / / / / / / \" \" ' \"  \n\nI  II II \nII II I \n\n1I1I1 \n1111 \nI '''' \n11111 \nII II I \nI1III \nII II I \nII II I \nII II I \n\n11---------------1 I  I  I  II  I \n11---------------1 I  I  I  II  I \n11---------------1 I  I  I  II  I \n11---------------1 I  I  I  II  I \n11---------------1 I  I  I  II  I \n11---------------1 I  I  I  II  I \n11:::::::::::::::1 I I I II  I \n11---------------1 I  I  I  II  I \n11---------------1 I  I  I  II  I \n11---------------11 I  I  II  I \n11---------------11 I  I  I I I \n11---------------11 I  I  II  I \n\n\"\"\"\"\"\"\"\"\"\"\"\"\"\", \n\"\"\"\"\"\"\"\"\"\"\"\"\"\", \n\"\"\"\"\"\"\"\"\"\"\"\"\"\", \n\"\"\"\"\"\"\"\"\"\"\"\"\"\", \n\"\"\"\"\"\"\"\"\"\"\"\"\"\", \n\"\"\"\"\"\"\"\"\"\"\"\"\"\", \n\"\"\"\"\"\"\"\"\"\"\"\"\"\", \n\"\"\"\"\"\"\"\"\"\"\"\"\"\", \n\"\"\"\"\"\"\"\"\"\"\"\"\"\", \n\"\"\"\"\"\"\"\"\"\"\"\"\"\", \n\"\"\"\"\"\"\"\"\"\"\"\"\"\", \n\"\"\"\"\"\"\"\"\"\"\"\"\"\", \n\"\"\"\"\"\"\"\"\"\"\"\"\"\", \nI I' I ,.1------------111 I I I  I \nI II I 111:::::::::::::::1.11 II  I \nI  II  I , \u2022\u2022 ------------- \u2022\u2022 ,  I II  I \n1111111===--=====111, : II \nI  II  I '.1--------------11' I  II  I \nI  I  I I  I \nI  I I I \"  -------------\nI II  1 111:::::::::::::::.11 I II  1 \nI II I 11::::::::::::::::111 I II I \nI  II  I , \u2022\u2022 -------------- \u2022\u2022 ,  I  II  I \n\nFigure 4:  Dependence on the shape and texture feature  of the figures. \n\nthe two opposite borders of the figure  no longer reinforce each other. \nFig.  4 demonstrates that the border effect and its consequences for  the medial axis \nalso  depend  on  the shape of the figures  and the nature of the texture they contain \n(eg  the  orientations  of the elements).  Bars  in  the  texture  parallel  to  the  border \ninduce stronger highlights,  and as  a  consequence,  cause stronger ripple effects  and \nmedial  axis highlights.  This comes from  the stronger co-linear,  contour enhancing, \ninputs these bars receive than bars not parallel to the border. \n\n\f142 \n\nZ.  Li \n\n3  Summary and Discussion \n\nThe model  of V1  was  originally proposed to account for  pre-attentive contour en(cid:173)\nhancement  and visual segmentation  (Li  1998,  1999,  1999b).  The contextual influ(cid:173)\nences mediated by intracortical interactions enable each V1 neuron to process inputs \nfrom  a  local  image area substantially larger than its  classical receptive field.  This \nenables  cortical  neurons  to detect  image  locations  where translation invariance  in \nthe input image breaks down,  and highlight these image locations with higher neu(cid:173)\nral activities, making them conspicuous.  These highlights mark candidate locations \nfor  image region  (or object surface)  boundaries, smooth contours and small figures \nagainst backgrounds, serving the purpose of pre-attentive segmentation. \n\nThis paper has shown that the figure-ground and medial axis effects observed in the \nrecent  experiments can be accounted for  using  a  purely V1  mechanism  for  border \nhighlighting, provided that the sizes of the figures  are small enough or of finite  and \nappropriate scale.  This has been the case in the existing experiments.  We therefore \nsuggest  that  feedbacks  from  higher  visual  areas  are  not  necessary  to  explain  the \nexperimental observations, although we  cannot, of course, exclude the possibilities \nthat they also contribute. \n\nReferences \n\n[1]  Lamme V.A.  (1995)  Journal  of Neuroscience  15(2), 1605-15. \n[2]  Lee  T.S,  Mumford  D,  Romero  R.  and  Lamme  V.  A.F.  (1998)  Vis.  Res.  38: \n\n2429-2454. \n\n[3]  Zipser K.,  Lamme V.  A.,  and Schiller P. H.  (1996)  J. Neurosci.  16 (22),  7376-\n\n89. \n\n[4]  Lamme V.  A.  F., Zipser K. and Spekreijse H.  Soc.  Neuroscience  Abstract 603.1, \n\n1997. \n\n[5]  Blum H.  (1973)  Biological shape and visual science J.  Theor.  Bioi. 38:  205-87. \n[6]  Gallant J.L.,  van  Essen D.C.,  and  Nothdurft  H.C.  (1995)  In  Early  vision  and \nbeyond eds. T. Papathomas, Chubb C,  Gorea A.,  and Kowler E.  (MIT  press), \npp 89-98. \n\n[7]  C. D.  Gilbert  (1992)  Neuron.  9(1),  1-13. \n[8]  C.  M.  Gray and W.  Singer  (1989)  Proc.  Natl.  Acad.  Sci.  USA  86, 1698-1702. \n[9]  M.  K.  Kapadia,  M.  Ito,  C.  D.  Gilbert,  and  G.  Westheimer  (1995)  Neuron. \n\n15(4), 843-56. \n\n[10]  J.  J.  Knierim and D.  C.  van Essen  (1992)  J.  Neurophysiol.  67,  961-980. \n[11]  Z.  Li  (1998)  Neural  Computation 10(4)  p  903-940. \n[12]  Z.  Li  (1999)  Network:  computations  in neural systems 10(2). p.  187-212. \n[13]  Z.  Li  (1999b)  Spatial  Vision 13(1)  p.  25-50. \n[14]  K.S.  Rockland and J.  S.  Lund  (1983)  J.  Compo  Neurol.  216, 303-318 \n[15]  E.  L.  White  (1989)  Cortical circuits (Birkhauser) . \n\n\f", "award": [], "sourceid": 1746, "authors": [{"given_name": "Zhaoping", "family_name": "Li", "institution": null}]}