{"title": "A model of transparent motion and non-transparent motion aftereffects", "book": "Advances in Neural Information Processing Systems", "page_first": 837, "page_last": 843, "abstract": null, "full_text": "A  model of transparent  motion and \nnon-transparent motion aftereffects \n\nAlexander  Grunewald* \n\nMax-Planck Institut fur  biologische Kybernetik \n\nSpemannstrafie 38 \n\nD-72076 Tubingen,  Germany \n\nAbstract \n\nA  model  of  human  motion  perception  is  presented.  The  model \ncontains two stages of direction selective units.  The first stage con(cid:173)\ntains  broadly  tuned  units,  while  the  second  stage  contains  units \nthat are  narrowly  tuned.  The  model  accounts  for  the  motion  af(cid:173)\ntereffect  through  adapting  units  at  the  first  stage  and  inhibitory \ninteractions at the second stage.  The model explains how two pop(cid:173)\nulations of dots moving in slightly different directions are perceived \nas  a  single  population  moving  in  the  direction of the  vector  sum, \nand how two populations moving in strongly different directions are \nperceived as  transparent motion.  The model also explains why the \nmotion aftereffect in both cases appears as non-transparent motion. \n\n1 \n\nINTRODUCTION \n\nTransparent motion can be studied using displays which contain two populations of \nmoving dots.  The dots within each population have the same direction  of motion, \nbut directions can differ between the two populations.  When the two directions are \nvery similar, subjects report seeing dots moving in the average direction (Williams & \nSekuler, 1984).  However, when the difference  between the two directions gets large, \nsubjects  perceive  two  overlapping  sheets  of  moving  dots.  This  percept  is  called \ntransparent motion.  The occurrence of transparent motion cannot be explained by \ndirection averaging, since that would result in a single direction of perceived motion. \n\nRather than just being a  quirk of the human visual system,  transparent motion is \nan important issue in motion processing.  For example,  when a robot is  moving its \n\n\u2022  Present address:  Caltech,  Mail  Code 216-76,  Pasadena,  CA 91125. \n\n\f838 \n\nA.  GRUNEWALD \n\nmotion  leads  to  a  velocity  field.  The ability  to  detect  transparent  motion  within \nthat velocity field enables the robot to detect other moving objects at the same time \nthat the  velocity field  can be used  to estimate the heading  direction of the robot. \nWithout  the  ability  to  code  mUltiple  directions  of  motion  at  the  same  location, \ni.e.  without  the  provision  for  transparent  motion,  this  capacity  is  not  available. \nTraditional algorithms have failed  to properly  process  transparent motion,  mainly \nbecause they assigned a  unique velocity signal to each location, instead of allowing \nthe  possibility  for  multiple  motion  signals  at  a  single  location.  Consequently,  the \nstudy of transparent motion has  recently enjoyed widespread interest. \n\nSTIMULUS \n\nPERCEPT \n\nTest \n\nFigure  1:  Two populations of dots  moving in  different  directions  during  an adap(cid:173)\ntation phase are perceived as transparent motion.  Subsequent viewing of randomly \nmoving dots during a test phase leads to an illusory percept of unidirectional motion, \nthe motion aftereffect  (MAE).  Stimulus and percept in both phases are shown. \n\nAfter prolonged exposure to an adaptation display containing dots moving in one di(cid:173)\nrection, randomly moving dots in a  test display appear to be moving in the opposite \ndirection (Hiris &  Blake, 1992; Wohlgemuth,  1911).  This illusory percept of motion \nis  called the motion aftereffect  (MAE).  Traditionally this is  explained by  assuming \nthat pairs of oppositely  tuned direction selective  units  together  code the  presence \nof motion.  When  both are equally  active,  no motion is  seen.  Visual  motion leads \nto stronger activation of one unit, and thus an imbalance in the activity  of the two \nunits.  Consequently,  motion  is  perceived.  Activation  of that unit  causes  it to fa(cid:173)\ntigue, which means its response weakens.  After motion offset,  the previously active \nunit sends out a  reduced  signal  compared  to its  partner due  to  adaptation.  Thus \nadaptation  generates  an  imbalance  between  the  two  units,  and  therefore  illusory \nmotion,  the MAE,  is  perceived.  This is  the ratio  model (Sutherland,  1961). \n\nRecent  psychophysical  results  show  that  after  prolonged  exposure  to  transparent \nmotion,  observers perceive  a  MAE  of a  single direction of motion,  pointing in  the \nvector  average of the  adaptation directions  (Mather,  1980;  Verstraten,  Frederick(cid:173)\nsen,  &  van  de  Grind,  1994).  Thus  adaptation  to  transparent  motion  leads  to  a \nnon-transparent  MAE.  This  is  illustrated  in  Figure  1.  This  result  cannot  be  ac(cid:173)\ncounted for  by  the ratio model,  since  the non-transparent MAE  does  not point  in \nthe  direction  opposite  to either  of the  adaptation  directions.  Instead,  this  result \nsuggests that direction selective units of all  directions interact and thus contribute \nto the MAE.  This explanation is  called the  distribution-shift  model (Mather,  1980). \nHowever, thus far it has only been vaguely defined,  and no  demonstration has been \ngiven that shows how  this mechanism might  work. \n\n\fA Model of Transparent Motion and Non-transparent Motion Aftereffects \n\n839 \n\nThis study develops  a  model of human motion perception based on  elements from \nboth  the  ratio  and  the  distribution-shift  models  for  the  MAE.  The  model  is  also \napplicable  to the  situation  where  two  directions  of motion are present.  When  the \ndirections  differ  slightly,  only  a  single  direction  is  perceived.  When  the  directions \ndiffer  a  lot,  transparent motion is  perceived.  Both cases  lead to a  unitary MAE. \n\n2  OUTLINE OF THE MODEL \n\nThe  model  consists  of  two  stages.  Both  stages  contain  units  that  are  direction \nselective.  The architecture of the model is  shown in Figure 2. \n\n~----~--~,~r---~---'---\\ -, \nStage 2  CD080CD  86) \n+----+~--+~--~----~--~--~--~~ \n\nFigure 2:  The model contains two stages of direction selective units.  Units at stage \n1 excite  units  of like  direction  selectivity  at stage  2,  and  inhibit  units  of opposite \ndirections.  At  stage  2  recurrent  inhibition  sharpens  directional  motion  responses. \nThe grey level indicates the strength of interaction between units.  Strong influence \nis  indicated by  black arrows,  weak influence is  indicated by  light grey arrows. \n\nUnits in stage 1 are broadly tuned motion detectors.  In the present study the precise \nmechanism of motion detection is not central, and hence it has not been modeled.  It \nis assumed that the bandwidth of motion detectors at this stage is about 30 degrees \n(Raymond, 1993; Williams, Tweten, &  Sekuler, 1991).  In the absence of any visual \nmotion,  all  units are active at a  baseline level;  this is  equivalent to neuronal noise. \nWhenever  motion of a  particular  direction  is  present  in  the  input,  the  activity of \nthe  corresponding  unit  (Vi)  is  activated  maximally  (Vi  =  9),  and  units  of similar \ndirection selectivity are weakly  activated  (Vi  =  3).  The activities of all other units \ndecrease to zero.  Associated with each unit i  at stage 1 is  a weight Wi  that denotes \nthe adaptational state of unit i  to fire a unit at stage 2.  During prolonged exposure \nto motion these weights adapt, and their strength decreases. The equation governing \nthe strength of the weights is  given below: \n\ndWi \n-\ndt \n\n=  R(1- w\u00b7) - V\u00b7W \u00b7 \n~~, \n\n~ \n\nwhere  R  = 0.5  denotes  the  rate of recovery  to  the  baseline  weight.  When  Wi  = 1 \nthe corresponding unit is  not adapted.  The further  Wi  is  reduced from  1,  the more \n\n\f840 \n\nA.  GRUNEWALD \n\nthe corresponding unit  is  adapted.  The products ViWi  are transmitted to stage  2. \nEach unit of stage 1 excites  units coding similar directions at stage 2,  and inhibits \nunits  coding  opposite  directions  of motion.  The excitatory  and  inhibitory  effects \nbetween units at stages 1 and 2 are caused by kernels,  shown in Figure 3. \n\nFeedforward kernels \n\nexcitatory \n-------\ninhibitory \n\n---\n\n--\n\n--\n\n------\n\n1 \n\n0.8 \n\n0.6 \n\n0.4 \n\n0.2 \n\n0 \n\nFeedback kernels \nI \n\n1-\n\nexcitatory \n---~--- -\ninhibitory \n-\n\n-\n\n-\n\n------+  --------\n\n1 \n\n-\n\n0.8  -\n\n0 . 6  -\n\n0.4 r-\n\n0.2 f--\n\n0 \n\n-180 \n\n0 \n\n180 \n\n-180 \n\no \n\n180 \n\nFigure 3:  Kernels used in the model.  Left:  excitatory and inhibitory kernels between \nstages 1 and 2;  right:  excitatory and inhibitory feedback  kernels within stage 2. \n\nActivities  at stage  2 are  highly  tuned  for  the  direction  of motion.  The  broad ac(cid:173)\ntivation of motion signals at stage 1 is  directionally sharpened  at stage 2 through \nthe interactions between  recurrent excitation and inhibition.  Each unit in stage 2 \nexcites itself, and interacts with other units at stage 2 through recurrent inhibition. \nThis  inhibition  is  maximal  for  close  directions,  and  falls  off as  the  directions  be(cid:173)\ncome more dissimilar.  The kernels mediating excitatory and inhibitory interactions \nwithin  stage  2  are  shown  in  Figure  3.  Through  these  inhibitory  interactions  the \ndirectional tuning of units at stage 2 is sharpened; through the excitatory feedback \nit is  ensured that one unit will  be  maximally active.  Activities  of units  at stage 2 \nare given  by  Mi  =  max4 (mi' 0),  where the behavior of mi  is  governed by: \n\nF/ and Fi- denote the result of convolving the products of the activities  at stage \n1  and  the  corresponding  adaptation  level,  VjWj ,  with  excitatory  and  inhibitory \nfeedforward  kernels  respectively.  Similarly, Bt  and Bj denote the convolution of \nthe activities M j  at stage 2 with the feedback  kernels. \n\n3  SIMULATIONS  OF  PSYCHOPHYSICAL RESULTS \n\nIn the  simulations  there  were  24  units  at  each  stage.  The  model  was  simulated \ndynamically  by  integrating the differential  equations  using  a  fourth  order  Runge(cid:173)\nKutta method with stepsize H  =  0.01  time units.  The spacing of units in direction \nspace  was  15  degrees  at  both  stages.  Spatial  interactions  were  not  modeled.  In \nthe simulations  shown,  a  motion stimulus is  present until  t  =  3.  Then the motion \nstimulus ceases.  Activity at stage 2 after t =  3 corresponds to a  MAE. \n\n\fA Model  of Transparent Motion and Non-transparent  Motion Aftereffects \n\n841 \n\n3.1  UNIDIRECTIONAL  MOTION \n\nWhen  adapting  to  a  single  direction  of  motion,  the  model  correctly  generates  a \nmotion  signal  for  that  particular  direction  of motion.  After  offset  of  the  motion \ninput, the unit coding the opposite direction of motion is  activated, as in the MAE. \nA simulation of this is  shown in Figure 4. \n\nStage 1 \n\nStage 2 \n\nact \n\nact \n\n360 \n\n360 \n\nFigure  4:  Simulation  of single  motion  input  and  resulting  MAE.  Motion  input  is \npresented until  t  =  3. \n\nDuring adaptation the motion stimulus excites the corresponding units at stage 1, \nwhich  in turn activate units  at stage 2.  Due  to  recurrent inhibition only  one unit \nat stage  2  remains  active  (Grossberg,  1973),  and  thus  a  very  sharp  motion  signal \nis  registered  at stage  2.  During  adaptation the  weights  associated  with the  units \nthat receive a motion input decrease.  After motion offset,  all units receive the same \nbaseline input.  Since  the weights of the previously  active units are decreased,  the \ncorresponding cells at stage 2 receive less feedforward excitation.  At the same time, \nthe previously active units receive strong feedforward inhibition, since they receive \ninhibition from units tuned to very different directions of motion and whose weights \ndid not decay during adaptation.  Similarly, the units coding the opposite direction \nof motion  as  those  previously  active  receive  more  excitation  and  less  inhibition. \nThrough recurrent inhibition the unit at stage 2 coding the opposite direction to that \nwhich  was  active  during  adaptation is  activated  after  motion offset:  this  activity \ncorresponds to the MAE.  Thus the MAE is primarily an effect  of disinhibition. \n\n3.2  TRANSPARENT MOTION:  SIMILAR DIRECTIONS \n\nTwo  populations  of dots  moving  in  different,  but  very  similar,  directions  lead  to \nbimodal  activation  at stage  1.  Since  the  feedforward  excitatory  kernel  is  broadly \ntuned,  and since  the  directions  of motion  are  similar,  the ensuing  distribution  of \nactivities  at  stage  2  is  unimodal,  peaking  halfway  between  the  two  directions  of \nmotion.  This corresponds to the vector  average of the directions of motion of the \ntwo populations of dots.  A simulation of this is shown in Figure 5. \n\nDuring adaptation the units at stage 1 corresponding to the input adapt.  As before \nthis means that after motion offset the previously active units receive less excitatory \ninput and more inhibitory input.  As during adaptation this signal is unimodal.  Also, \nthe  unit  at stage  2  coding  the  opposite  direction  to  that  of the stimulus  receives \n\n\fStage 1 \n\nStage 2 \n\nA.  GRUNEWALD \n\n842 \n\nact \n\n60 120  180 \n\ndirection  240 \n\n60 120 \n\n180 \n\ndirection  240 \n\nFigure 5:  Simulation of two close directions of motion.  Stage 2 of the network model \nregisters unitary motion and a unitary MAE. \n\nless  inhibition  and more  excitation.  Through the  recurrent activities  within  stage \n2,  that unit gets maximally activated.  A unimodal MAE results. \n\n3.3  TRANSPARENT MOTION:  DIFFERENT DIRECTIONS \n\nWhen the directions of the two populations of dots in a transparent motion display \nare sufficiently distinct, the distribution of activities at stage 2 is no longer unimodal, \nbut bimodal.  Thus, recurrent inhibition leads to activation of two units at stage 2. \nThey correspond to the two stimulus directions.  A simulation is shown in Figure 6. \n\nStage 1 \n\nStage 2 \n\nact \n\n60 120 \n\n180 \n\ndirection  240 \n\nFigure  6:  Simulation  of two  distinct  directions  of motion.  Stage  2  of the  model \nregisters transparent motion during adaptation, but the MAE is  unidirectional. \n\nFeedforward inhibition is tuned much broader than feedforward excitation, and as a \nconsequence the inhibitory signal during adaptation is unimodal, peaking at the unit \nof stage 2 coding the opposite direction of the average of the two previously active \ndirections.  Therefore that unit receives the least amount of inhibition after motion \noffset.  It receives the same activity from  stage 1 as units coding nearby directions, \nsince the corresponding weights at stage 1 did not adapt.  Due to recurrent activities \nat stage 2 that unit becomes active:  non-transparent motion is  registered. \n\n\fA Model of Transparent Motion and Non-transparent  Motion Aftereffects \n\n843 \n\n4  DISCUSSION \n\nRecently  Snowden,  Treue,  Erickson,  and  Andersen  (1991)  have  studied  the effect \nof transparent motion stimuli on neurons in areas VI  and MT of macaque monkey. \nThey simultaneously  presented two  populations of dots,  one of which  was  moving \nin the preferred direction of the neuron under study,  and the other population was \nmoving in a different direction.  They found  that neurons in VI were barely affected \nby the second population of dots.  Neurons in MT, on the other hand, were inhibited \nwhen  the direction  of the second population  differed  from  the preferred  direction, \nand inhibition was maximal when the second population was moving opposite to the \npreferred direction.  These results support key  mechanisms of the model.  At stage \n1 there is  no interaction between  opposing  directions  of motion.  The feedforward \ninhibition  between  stages  1  and  2 is  maximal  between  opposite  directions.  Thus \nactivities of units at stage 1 parallel neural activities recorded at VI, and activities \nof units at stage 2 parallels those neural activities recorded in area MT. \n\nAcknowledgments \n\nThis research was  carried out under HFSP grant SF-354/94. \n\nReference \n\nGrossberg, S. (1973).  Contour enhancement, short term memory, and constancies in \nreverberating neural networks.  Studies in Applied Mathematics,  LII, 213-257. \n\nHiris,  E., & Blake,  R.  (1992).  Another perspective in the visual motion  aftereffect. \n\nProceedings  of the National Academy  of Sciences  USA,  89,  9025-9028. \n\nMather,  G.  (1980).  The  movement  aftereffect  and  a  distribution-shift  model  for \n\ncoding the direction of visual  movement.  Perception,  9,  379-392. \n\nRaymond,  J.  E.  (1993).  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British  Journal  of \n\nPsychology  (Monograph  Supplement),  1,  1-117. \n\n\f", "award": [], "sourceid": 1025, "authors": [{"given_name": "Alexander", "family_name": "Grunewald", "institution": null}]}