Te-Won Lee, Thomas Wachtler, Terrence J. Sejnowski
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 . 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