Color Opponency Constitutes a Sparse Representation for the Chromatic Structure of Natural Scenes
Authors: Thomas Wachtler, Terrence J. Sejnowski Te-Won Lee
Published in: Advances in Neural Information Processing Systems 13  (NIPS 2000) (Main Conference Track), 2000

Abstract: The human visual system encodes the chromatic signals  conveyed  by the  three types  of retinal  cone  photoreceptors  in  an  opponent  fashion.  This  color  opponency  has  been  shown  to  constitute  an  efficient encoding by spectral decorrelation of the receptor signals.  We analyze the spatial and chromatic structure of natural scenes by  decomposing the spectral images into a set of linear basis functions  such  that  they  constitute  a  representation  with  minimal  redun(cid:173) dancy.  Independent  component  analysis  finds  the  basis  functions  that  transforms  the  spatiochromatic  data  such  that  the  outputs  (activations)  are statistically as independent  as  possible,  i.e.  least  redundant.  The  resulting  basis functions  show  strong  opponency  along  an  achromatic  direction  (luminance  edges),  along  a  blue(cid:173) yellow  direction,  and along  a red-blue direction.  Furthermore, the  resulting activations have very sparse distributions, suggesting that  the use  of color  opponency in the human visual system achieves a  highly  efficient  representation of colors.  Our findings  suggest that  color opponency is a result of the properties of natural spectra and  not  solely  a  consequence of the overlapping cone spectral sensitiv(cid:173) ities. 
1  Statistical structure of natural scenes 
Efficient  encoding of visual  sensory information is  an important  task for  informa(cid:173) tion processing systems  and  its  study  may  provide  insights  into  coding  principles  of biological visual  systems.  An  important goal  of sensory information  processing 
Electronic  version available  at www. cnl. salk . edu/ ""tewon. 
is  to transform the  input  signals  such  that the  redundancy  between  the  inputs  is  reduced.  In natural scenes, the image intensity is  highly predictable from neighbor(cid:173) ing  measurements  and  an  efficient  representation  preserves  the  information  while  the  neuronal output  is  minimized.  Recently,  several methods  have been  proposed  for finding efficient codes for  achromatic images of natural scenes  [1,  2,  3, 4].  While  luminance dominates the structure of the visual world, color vision provides impor(cid:173) tant  additional  information  about  our  environment.  Therefore,  we  are  interested  in efficient,  i.e.  redundancy reducing representations for  the chromatic structure of  natural scenes. 
2  Learning  efficient  representation for  chromatic image 
Our goal was to find  efficient  representations of the chromatic sensory information  such that its spatial and chromatic redundancy is reduced significantly.  The method  we  used for  finding  statistically efficient  representations is  independent  component  analysis  (ICA).  ICA  is  a  way of finding  a linear non-orthogonal co-ordinate system  in multivariate data that minimizes mutual information among the axial projections  of the data.  The directions of the axes of this co-ordinate system  (basis functions)  are determined by both second and higher-order statistics of the original data, com(cid:173) pared to Principal Component Analysis  (PCA) which is used solely in second order  statistics  and  has  orthogonal  basis  functions.  The  goal  of ICA  is  to  perform  a  linear transform which  makes the resulting source outputs as  statistically indepen(cid:173) dent  from  each  other  as  possible  [5].  ICA  assumes  an  unknown  source  vector  s  with mutually independent  components Si.  A small patch of the observed image is  stretched into a vector x  that can be represented as a linear combination of sources  components Si  such that