Ortega, Eric
Coauthors(s): Eric Ortega Gary Holt Bartlett W. Mel Biomedical Engineering Department University of Southern California
USC
Biomedical Engineering
Mail Code 1451 USC Los Angeles, CA 90089
lnc.usc.edu

Smart Center-Surround Receptive Fields: What Bayes May Say About the Neural Substrate for Color Constancy

Color constancy refers to the ability of a visual system to perceive the true colors (reflectances) of surfaces under light sources which themselves vary in color from situation to situation. In taking in a scene, therefore, the visual system must estimate the color of the illuminant in order to discount its colorizing effects on the objects and surfaces in the field of view. The main difficulty lies in the fact that the light reaching the eye from a given surface is a mixture of the color of the object and the color of the light source, where neither component is known independently. The key principle underlying many color constancy algorithms entails that the color of the illuminant can be estimated at a given point A in the image by measuring the average color over a moderately large region surrounding A, and then “normalizing out” this color estimate from the measured color at A. Assuming a “grey world”, in which every area of the visual field contains an unbiased collection of surface reflectances, this normalization step leads to a truer report of the surface color at A than a direct report of the unprocessed color value at A. The appeal of this type of scheme as a neural algorithm lies in the fact that the center-surround normalization operation seems to fit well with the widespread distribution of center-surround (e.g. color opponent) receptive fields in the color-processing areas of visual cortex. One puzzle which arises from the naive mapping of color normalization processes onto conventional “dumb” center-surround receptive fields, however, is that the degree of color correction induced perceptually at any given point in the image in actuality depends on a variety of complex geometric factors, including local contour and junction structure, and the local gamut of surface colors from which the color of the illuminant must be deduced---none of which can be accounted for by a simple center-surround organization. As a simple example, an “unenlightened” center-surround operator will necessarily deplete the color saturation in the interior of a large region of constant color---a perceptual phenomenon which does not in fact occur in human subjects. In this work we consider how Bayes implies the need for smart center-surround receptive fields for color-constant perception. We focus on one variable which exerts a powerful nonlinear influence on the magnitude of the color correction induced at a given point in the image: the color gamut, or range of different colors, contained within the surround. Assuming simple gaussian priors for one-dimensional illuminant (brightness) and reflectance probabilities, we show analytically and in monte carlo simulations that the variance of the posterior distribution of the illuminant p(illuminant | {m_1, m_2, ... m_n}) given one or more measurements m_i falls very rapidly as the number of independent color patches in the surround is increased. This observation implies that surrounds containing only a single color, such as within large homogeneous regions, lead to highly unreliable estimates of the illuminant---and therefore should be “permitted” to make only small color color corrections. In regions containing a large gamut of color patches, such as are commonly used in color induction illusions, the posterior distribution over illuminants is made extremely narrow, permitting far larger color corrections than in the low-gamut case. We discuss how cortical circuitry could effect this type of nonlinear center-surround organization.