{"title": "Detection of First and Second Order Motion", "book": "Advances in Neural Information Processing Systems", "page_first": 801, "page_last": 807, "abstract": "", "full_text": "Detection of first  and second order motion \n\nAlexander  Grunewald \n\nDivision of Biology \n\nCalifornia Institute of Technology \n\nMail  Code 216-76 \n\nPasadena, CA  91125 \nalex@vis.caltech.edu \n\nHeiko  Neumann \n\nAbteilung  Neuroinformatik \n\nVniversitat VIm \n\n89069  VIm \nGermany \n\nhneumann@neuro.informatik.uni-ulm.de \n\nAbstract \n\nA  model  of  motion  detection  is  presented.  The  model  contains \nthree stages.  The first  stage is  unoriented and is  selective for  con(cid:173)\ntrast  polarities.  The  next  two  stages  work  in  parallel.  A  phase \ninsensitive stage pools across  different  contrast polarities through \na  spatiotemporal filter  and thus can detect  first  and second order \nmotion.  A phase sensitive stage keeps  contrast polarities separate, \neach of which is  filtered  through  a  spatiotemporal filter,  and thus \nonly first order motion can be detected.  Differential phase sensitiv(cid:173)\nity can therefore account for  the detection of first  and second order \nmotion.  Phase insensitive detectors correspond to cortical complex \ncells,  and phase sensitive detectors to simple  cells. \n\n1 \n\nINTRODUCTION \n\nIn our  environment  objects  are constantly  in  motion,  and the visual  system faces \nthe task of identifying the motion of objects.  This task can be subdivided into two \ncomponents:  motion detection and motion integration.  In this study we will look at \nmotion detection.  Recent psychophysics has made a useful distinction between first \nand second order motion.  In first order motion an absolute image feature is moving. \nFor  example,  a  bright  bar  moving  on  a  dark  background  is  an  absolute  feature \nbecause  luminance  is  moving.  In second  order  motion  a  relative  image  feature  is \nmoving,  for  example  a  contrast  reversing  bar.  No  longer  is  it  possible  to  identify \nthe moving object through its luminance,  but only that it has  different  luminance \nwith respect  to the  background.  Humans  are very  sensitive  to first  order  motion, \nbut  can  they  detect  second  order motion?  Chubb  &  Sperling  (1988)  showed  that \nsubjects  are in fact  able to detect  second  order motion.  These findings  have since \nbeen confirmed in many psychophysical experiments,  and it  has  become clear  that \nthe parameters that yield  detection of first  and second order motion  are different, \nsuggesting that separate motion detection systems exist. \n\n\f802 \n\nA.  Grunewald and H.  Neumann \n\n1.1  Detection of first  and  second  order motion \n\nFirst  order  motion,  which  is  what  we  encounter  in  our  daily  lives,  can  be  easily \ndetected by finding the peak in the Fourier energy distribution.  The motion energy \ndetector  developed  by  Adelson  &  Bergen  (1985)  does  this  explicitly,  and  it  turns \nout that it is also equivalent to a Reichardt detector (van Santen &  Sperling,  1985). \nHowever,  these  detectors  cannot  adequately  detect  second  order  motion,  because \nsecond order motion stimuli often contain the maximum  Fourier energy in  the op(cid:173)\nposite  direction  (possibly  at  a  different  velocity)  as  the  actual  motion.  In  other \nwords,  purely  linear  filters,  should  have  opposite  directional  tuning for  first  and \nsecond order motion.  This is  further  illustrated in Figure 1. \n\nFIRST ORDER MOTION \n\nStimulus \n\nEnergy \n\nReconstructed \n\n80 \n\nG)  60 \nE \n=40 \n\n20 \n\n0 \n\n80 \n\n~60 \n;:;40 \n\n20 \n\n0 \n\n20  4060  80100 \n\nspace \n\n20  40  60  80  100 \n\n20  40  60  80  100 \n\nSECOND ORDER MOTION \n\nStimulus \n\nEnergy \n\nReconstructed \n\n80 \n\n60 \n\n40 \n\n20 \n\n0 \n\n20  40  60  80  100 \n\nspace \n\n20  40  60  80  100 \n\n20  40  60  80  100 \n\nFigure  1:  Schematic  of first  and  second  order  motion,  their  peak  Fourier  energy, \nand  the  reconstruction.  The peak Fourier energy is  along the  direction  of motion \nfor  first  order motion,  and  in the  opposite  direction for  second order  motion.  For \nthis reason a  linear filter  cannot detect second order motion. \n\nOne way to account  for  second  order motion detection is  to  transform  the  second \norder motion signal  into  a  first  order signal.  H second  order motion  is  defined  by \ncontrast reversals,  then  detecting  contrast edges  and  then  rectifying  the  resulting \nsignal of contrast will  yield a first order motion signal.  Thus this approach includes \nthree steps:  orientation detection, rectification and finally motion detection (Wilson \net al.,  1992) . \n\n\fDetection of First and Second Order Motion \n\n803 \n\n1.2  Visual physiology \n\nCells  in the retina and the  lateral geniculate  nucleus  (LGN)  have  concentric  (and \nhence  unoriented)  receptive  fields  which  are  organized  in  an  opponent  manner. \nWhile the center of such an ON cell is excited by a light increment, the surround is \nexcited by a  light decrement,  and vice versa for  OFF cells.  It is only at the cortex \nthat direction and orientation selectivity arise.  Cortical simple cells  are sensitive to \nthe phase of the stimulus, while  complex cells  are not  (Hubel  &  Wiesel,  1962). \n\nMost  motion  models  take  at  least  partial  inspiration  from  known  physiology  and \nanatomy,  by relating the kernels of the motion detectors to the physiology of corti(cid:173)\ncal  cells.  The motion energy model in particular detects orientation and first  order \nmotion at the same time.  Curiously, all motion models essentially ignore the concen(cid:173)\ntric opponency of receptive fields  in the LG N.  This is  usually justified  by  pointing \nto the  linearity  of simple  cells  with  respect  to  stimulus  parameters.  However,  it \nhas  been  shown  that  simple  cells  in fact  exhibit  strong  nonlinearities  (Hammond \n&  MacKay,  1983).  Moreover,  motion detection  does  require  at least  one  stage of \nnonlinearity  (Poggio &  Reichardt,  1973).  The present  study  develops  a  model  of \nfirst and second order motion detection which explicitly includes an unoriented pro(cid:173)\ncessing stage,  and phase sensitive  and phase insensitive motion  detectors  are built \nfrom  these  unoriented  signals.  The  former  set  of detectors  only responds  to first \norder motion,  while  the second set of detectors responds  to both types of motion. \nWe further show the analogies that can be drawn between these detector types and \nsimple and complex cells  in cat visual  cortex. \n\n2  MODEL DESCRIPTION \n\nThe model is two-dimensional, one dimension is  space, which means that space has \nbeen  collapsed onto  a  line,  and the other  dimension  is  time.  The input  image  to \nthe  model  is  a  space-time  matrix  of  luminances,  as  shown  in  figure  1.  At  each \nprocessing  stage  essentially  the  same  operations  are  performed.  First  the  input \nsignal is  convolved  with  the  appropriate  kernel.  At  each  stage  there  are  multiple \nkernels,  to  generate  the  different  signal  types  at  that  stage.  For  example,  there \nare  ON  and  OFF  signals  at  the  unoriented  stage.  Next  the  convolved  responses \nare subtracted from  each other.  At  the unoriented stage this means  ON-OFF  and \nOFF-ON. In the final step these results are half-wave rectified to only yield positive \nsignals. \n\nUnoriented \n\nPhase insensitive \n\nPhase sensitive \n\nspace \n\nFigure 2:  The kernels in the model.  For the unoriented (left plot) and phase sensitive \n(right  plot)  kernel  plots black indicates  OFF regions,  white  ON  regions,  and grey \nzero input.  For the phase insensitive plot (middle)  grey denotes ON and OFF input, \nand black denotes zero input. \n\n\f804 \n\nA.  Grunewald and H. Neumann \n\nAt  the  unoriented stage  the input pattern is  convolved with  a  difference  of Gaus(cid:173)\nsians kernel.  This kernel  has only  a  spatial dimension,  no  temporal dimension  (see \nfigure  2).  As  described  earlier,  competition  is  between  ON  and  OFF signals,  fol(cid:173)\nlowed by half-wave rectification.  This ensures that at each location only one set of \nunoriented signals is  present.  A simulation of the signals at the unoriented stage is \nshown in figure  3.  For first order motion, ON signals are at locations corresponding \nto the inside of the  moving  bar.  With each shift  of the  bar the signals  also  move. \nSimilarly, the OFF signals correspond to the outside of the bar, and also move with \nthe bar.  For  second  order motion the  contrast polarity reverses.  Thus ON  signals \ncorrespond to the inside when the bar is  bright, and to the outside when the bar is \ndark,  and vice  versa for  OFF signals.  Thus any ON or  OFF signals to the leading \nedge of the bar will  remain active after the bar moves. \n\nUnoriented \n\nON \n\nOFF \n\n80 \n\nStimulus \n\n.\" \n...-\n\n.:: \n.rl' \n\n20 \no \n\n20  40  60  80  100 \n\nspace \n\nStimulus \n\n20 \n\n40  60  80  100 \n\n20  40  60  80  100 \n\nON \n\nOFF \n\n80 \n\n60 \n\n40 \n\n20 \n\n0 \n\n20  40  60  80  100 \n\n20  40  60  80  100 \n\nspace \n\n20  40  60  80  100 \n\nFigure  3:  Unoriented signals  to first  and second order  motion.  ON  signals  are  at \nthe  bright side of any  contrast transition,  while  OFF signals  are  at  the dark side. \nIn first  order motion ON  and OFF move synchronously to the moving stimulus.  In \nsecond order motion  ON  and  OFF signals  persist,  since  the leading edge  becomes \nthe trailing edge,  and at the same  time the contrast reverses, which  means  that at \na particular spatial location the contrast remains constant. \n\nAt  the phase insensitive stage the unoriented ON  and OFF signals  are  added,  and \nthen  the  result  is  convolved  with  an  energy  detection  filter.- The  pooling  of ON \nand  OFF  signals  means  that  the  contrast  transitions  in  the  image  are  essentially \nfull-wave  rectified.  This  causes  phase  insensitivity.  These pooled  signals  are  then \nconvolved with a space-time oriented filter  (see figure 2).  Competition between op(cid:173)\nposite directions of motion ensures that only one direction is active.  A consequence \nof the  pooling of unoriented  ON  and  OFF signals  at this  stage  is  that  the result(cid:173)\ning  signals  are  invariant  to first  or  second  order motion.  Thus  phase  insensitivity \n\n\fDetection of First and Second Order Motion \n\n805 \n\nmakes  this  stage able  to detect  both first  and  second  order motion.  These  signals \nare shown in figure  4.  In a  two-dimensional extension of this model these detectors \nwould  also  be  orientation selective.  The simplest way  to obtain this would  be  via \nelongation along the preferred orientation. \n\nStimulus \n\nleft \n\nright \n\nPhase insensitive \n\n20  40  60  80  100 \n\nspace \n\nStimulus \n\n20  40  60  80  100 \n\nspace \n\n20  40  60  80  100 \n\n20  40  60  80  100 \n\nleft \n\n80 \n\n60 \n\n40 \n\n20 \no \n\n20  40  60  80  100 \n\n\u2022\u2022 \n\u2022 \n\u2022 \n\nright \n\n::  / \n\n20  40  60  80  100 \n\nFigure  4:  Phase  insensitive  signals  to  first  and  second  order  motion.  For  both \nstimuli there are no leftwards signals,  and robust rightwards signals. \n\nAt  the  phase  sensitive  stage  unoriented  ON  and  OFF  signals  are  separately  con(cid:173)\nvolved with space-time oriented kernels which are offset  with respect to each other \n(see  figure  2).  The separate treatment of ON  and OFF signals yields  phase sensi(cid:173)\ntivity.  At each location there are four kernels:  two for  the two directions of motion, \nand  two  for  the  two  phases.  Competition  occurs  between  signals  of opposite  di(cid:173)\nrection tuning,  and opposite phase preference.  To  avoid  activation in the opposite \ndirection of motion slightly removed from the location of the edge spatially broadly \ntuned inhibition is necessary.  This is provided by the phase insensitive signals, thus \navoiding feedback  loops  among  phase sensitive detectors.  First order  signals  from \nthe unoriented stage match the spatiotemporal filters in the preferred direction, and \nthus  phase sensitive signals  arise.  However,  due to their phase reversal, second or(cid:173)\nder motion input,  provides poor motion signals, which are quenched through phase \ninsensitive inhibition.  These signals are shown in figure  5. \nThese simulations show  that first  and second order motion are detected differently. \nFirst  order motion is  detected by phase sensitive  and phase insensitive  motion de(cid:173)\ntectors,  while  second  order  motion  is  only  detected  by  the  latter.  From  this  we \nconclude that first  order motion is  a more potent stimulus,  and that the detection \nof second order is  more restricted, since it depends on a single type of detector.  In \nparticular, the size of the stimulus and its velocity have to be matched to the energy \n\n\f806 \n\nA.  Grunewald and H.  Neumann \n\nStimulus \n\nDL left \n\nDL right \n\nPhase sensitive \n\n20  40  60  80  100 \n\nspace \n\nStimulus \n\n20  40  60  80  100 \n\nDL left \n\nDL right \n\n20  40  60  80  100 \n\nspace \n\n20  40  60  80  100 \n\n20  40  60  80  100 \n\nFigure 5:  Phase sensitive signals  to first  and second order motion.  Only the dark(cid:173)\nlight  signals  are  shown.  First  order  motion  causes  a  consistent  rightward  motion \nsignal,  while  second order motion does not. \n\nfilters  for  motion signals to arise. \n\n3  RELATION TO PHYSIOLOGY \n\nThe relationship between the model  and physiology is  straightforward.  Unoriented \nsignals  correspond to LGN  responses,  phase insensitive  signals to  complex  cell  re(cid:173)\nsponses,  and  phase sensitive signals to simple  cell  responses.  Thus  the model  sug(cid:173)\ngests that both simple and some complex cells receive direct LGN  input.  Moreover \nthese  complex  cells  inhibit  simple  cells.  With  an  additional  threshold  in  simple \ncells  this  inhibition  could  also  be  obtained via  complex  to  simple  cell  excitation. \nWe  stress  that  we  are not ruling  out that many complex  cells  receive  only simple \ncell  input.  Rather, the present research shows that if all  complex cells receive only \nsimple  cell  input,  second  order  motion  cannot  be  detected.  Hence  at  least  some \ncomplex  cell  responses  need  to  be  built  up  directly  from  LGN  responses.  Several \nlines of evidence from  cat physiology support this suggestion.  First, the mean laten(cid:173)\ncies of simple and complex cells are about equal (Bullier & Henry,  1979), suggesting \nthat  at least  some  complex  cells  receive  direct  LGN  input.  Second,  noise  stimuli \ncan selectively activate complex cells, without activation of simple cells  (Hammond, \n1991).  Third,  cross-correlation analyses show  that complex  cells  do  receive  simple \ncell  input  (Ghose  et  ai.,  1994). \nThe  present  model  predicts  that  some  cortical  complex  cells  should  respond  to \n\n\fDetection of First and Second Order Motion \n\n807 \n\nsecond order motion.  Zhou & Baker (1993)  investigated this,  and found  that some \ncomplex  cells  in  area  17  respond  to  second  order  motion.  Moreover,  they  found \nthat simple cells  of a  particular first  order motion preference  did  not reverse their \nmotion preference  when stimulated with second  order motion,  which  would  occur \nif  simple  cells  were  just  linear  filters.  We  interpret  this  as  further  evidence  that \ncomplex cells  provide inhibitory input to simple cells.  If complex cells  are built  up \nfrom  LGN  input,  then  orientation selectivity  in  two-dimensional  space  cannot  be \nobtained based on simple cell input, but rather requires complex cells with elongated \nreceptive  fields.  Thus  we  predict  that  there  ought  to  be  a  correlation in  complex \ncells  between elongated receptive fields  and dependence on direct LGN  input. \nIn conclusion we  have shown  how  the phase sensitivity of motion detectors can be \nmapped onto the ability to detect only first  order motion, or both first  and second \norder  motion.  This  suggests  that  it  is  not  necessary  to  introduce  a  orientation \ndetection stage before  motion detection can take place, thus simplifying the model \nof motion  detection.  Furthermore  we  have  shown  that  the  proposed  model  is  in \naccord with known physiology. \n\nAcknow ledgments \n\nThis  work  was  supported  by  the  McDonnell-Pew  program  in  Cognitive  Neuro(cid:173)\nscience. \n\nReferences \n\nAdelson,  E.  &  Bergen  (1985).  Spatiotemporal energy models for  the perception of \nmotion.  J.  Opt.  Soc.  Am.  A, 2,  284-299. \nBullier, J. & Henry, G. H.  (1979).  Ordinal position of neurons in cat striate cortex. \nJ.  Neurophys.,  42,  1251-1263. \nChubb,  C.  &  Sperling,  G.  (1988).  Drift-balanced random  stimuli:  a  general  basis \nfor  studying non-Fourier motion perception.  J.  Opt.  Soc.  Am.  A, 5,  1986-2007. \nGhose, G.  M.,  Freeman, R.  D.  &  Ohzawa, I.  {1994}.  Local intracortical connections \nin the cat's visual  cortex:  postnatal development and plasticity.  J.  Neurophys.,  12, \n1290-1303. \nHammond,  P.  (1991).  On the response of simple  and complex  cells to random  dot \npatterns.  Vis.  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Science,  261, 98-101. \n\n\f", "award": [], "sourceid": 1371, "authors": [{"given_name": "Alexander", "family_name": "Grunewald", "institution": null}, {"given_name": "Heiko", "family_name": "Neumann", "institution": null}]}