Learning to Predict Visibility and Invisibility from Occlusion Events
Authors: Jonathan A. Marshall, Richard K. Alley, Robert S. Hubbard
Published in: Advances in Neural Information Processing Systems 8  (NIPS 1995) (Main Conference Track), 1995

Abstract: Visual  occlusion  events  constitute  a  major source  of depth  information.  This paper presents a self-organizing neural network that learns to detect,  represent,  and predict the visibility and invisibility relationships that arise  during  occlusion  events,  after  a  period  of exposure  to  motion sequences  containing occlusion  and  disocclusion events.  The  network develops  two  parallel opponent  channels  or  "chains"  of lateral  excitatory  connections  for  every  resolvable  motion trajectory.  One  channel,  the  "On"  chain or  "visible"  chain, is  activated when a moving stimulus is visible.  The other  channel, the  "Off"  chain or  "invisible"  chain,  carries  a persistent,  amodal  representation that predicts the motion of a formerly visible stimulus that  becomes  invisible  due  to occlusion.  The  learning  rule  uses  disinhibition  from  the  On  chain  to  trigger  learning  in  the  Off  chain.  The  On  and  Off chain  neurons  can  learn  separate  associations  with  object  depth  or(cid:173) dering.  The results  are closely  related  to the  recent  discovery  (Assad  &  Maunsell,  1995)  of neurons in macaque monkey posterior  parietal cortex  that respond selectively to inferred  motion of invisible stimuli. 
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INTRODUCTION:  LEARNING ABOUT  OCCLUSION  EVENTS 
Visual  occlusion  events  constitute  a  major source  of depth  information.  Yet  lit(cid:173) tle  is  known  about  the  neural  mechanisms  by  which  visual  systems  use  occlusion  events  to infer  the  depth  relations  among visual objects.  What is  the structure  of  such  mechanisms?  Some possible  answers  to this question  are revealed  through  an  analysis of learning rules that can cause  such  mechanisms to self-organize. 
Evidence  from  psychophysics  (Kaplan,  1969;  Nakayama  &  Shimojo,  1992;  Nakayama,  Shimojo,  &  Silverman,  1989;  Shimojo,  Silverman,  &  Nakayama,  1988,  1989;  Yonas,  Craton,  &  Thompson,  1987)  and  neurophysiology  (Assad  &  Maunsell,  1995;  Frost,  1993)  suggests  that  the  process  of  determining  relative  depth  from  occlusion  events  operates  at  an early stage  of visual  processing.  Mar(cid:173) shall  (1991)  describes  evidence  that suggests  that the same early  processing  mech(cid:173) anisms maintain a representation of temporarily occluded objects for  some amount 
Learning to  Predict Visibility  and  Invisibility  from  Occlusion  Events 
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of time after  they  have  disappeared  behind  an  occluder,  and  that  these  represen(cid:173) tations of invisible objects  interact  with other  object  representations,  in  much  the  same  manner  as  do  representations  of visible  objects.  The  evidence  includes  the  phenomena of kinetic subjective contours (Kellman & Cohen,  1984), motion viewed  through a slit (Parks' Camel)  (Parks,  1965) , illusory occlusion  (Ramachandran, In(cid:173) ada, & Kiama, 1986) , and interocular occlusion sequencing  (Shimojo, Silverman, &  Nakayama, 1988).  2  PERCEPTION OF OCCLUSION  AND 
DISOCCLUSION  EVENTS:  AN ANALYSIS 
The neural network model exploits the visual changes that occur at occlusion bound(cid:173) aries to form a mechanism for detecting and representing object visibility/invisibility  information.  The set of learning  rules  used  in  this model is  an extended  version  of  one  that has  been  used  before  to describe  the  formation of neural  mechanisms for  a  variety  of other  visual  processing  functions  (Hubbard  &  Marshall,  1994;  Mar(cid:173) shall,  1989,  1990ac,  1991,  1992;  Martin &  Marshall,  1993). 
Our  analysis  is  derived  from  the  following  visual  predictivity principle,  which 
may be postulated  as  a  fundamental principle  of neural organization in visual sys(cid:173) tems:  Visual  systems  represent the  world in  terms of predictions of its  appearance,  and they reorganize themselves  to generate  better predictions.  To maximize the cor(cid:173) rectness  and completeness of its predictions, a visual system  would  need  to predict  the motions and visibility/invisibility of all objects in a scene.  Among other things,  it would  need  to predict the disappearance of an object moving behind an occluder  and the reappearance  of an object emerging from  behind  an occluder. 
A  consequence  of this  postulate  is  that occluded  objects  must,  at  some  level, 
continue  to  be  represented  even  though  they  are  invisible.  Moreover,  the  repre(cid:173) sentation of an  object  must  distinguish  whether  the  object  is  visible  or  invisible;  otherwise, the visual system could not determine whether its representations predict  visibility  or  invisibility,  which  would  contravene  the  predictivity  principle.  Thus,  simple single-channel prediction schemes like the one  described  by  Marshall (1989,  1990a)  are inadequate to represent  occlusion  and disocclusion events.  3  A  MODEL FOR GROUNDED LEARNING TO 
PREDICT VISIBILITY AND  INVISIBILITY 
The initial structure  of the  Visible/Invisible network  model is  given  in  Figure  1A.  The network self-organizes in  response  to a  training regime containing many input  sequences  representing motion with and without occlusion and disocclusion events.  After  a  period  of self-organization,  the  specific  connections  that  a  neuron  receives  (Figure  1B)  determine whether it responds  to visible or invisible objects.  A neuron  that  responds  to  visible  objects  would  have  strong  bottom-up input  connections,  and it would  also have strong time-delayed lateral excitatory input connections.  A  neuron that responds selectively to invisible objects would  not have strong bottom(cid:173) up connections, but it would have strong lateral excitatory input connections.  These  lateral inputs would transmit to the neuron evidence that a previously visible object  existed.  The neurons  that respond  to invisible objects  must operate in  a  way  that  allows lateral  input  excitation  alone  to activate  the  neurons  supraliminally, in  the  absence of bottom-up input excitation from  actual visible objects.  4  SIMULATION OF A  SIMPLIFIED  NETWORK  4.1 
INITIAL  NETWORK STRUCTURE 
The  simulated  network,  shown  in  Figure  2,  describes  a  simplified  one(cid:173) dimensional  subnetwork  (Marshall  &  Alley,  1993)  of  the  more  general  two(cid:173) dimensional  network.  Layer  1  is  restricted  to  a  set  of motion-sensitive  neurons  corresponding  to one rightward motion trajectory. 
The  L+  connections  in  the  simulation  have  a  signal  transmission  latency  of  one  time unit.  Restricting  the lateral connections  to  a  single  time delay  and  to a  single direction limits the simulation to representing  a single speed  and direction of  motion; these results are therefore preliminary. This restriction reduced the number  of connections  and  made the simulation much faster. 
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J. A. MARSHALL, R.  K. ALLEY, R. S. HUBBARD