A mathematical model of color and orientation processing in V1

A neural field model for color perception unifying assimilation and contrast

We address the question of color-space interactions in the brain, by proposing a neural field model of color perception with spatial context for the visual area V1 of the cortex. Our framework reconciles two opposing perceptual phenomena, known as simultaneous contrast and chromatic assimilation. They have been previously shown to act synergistically, so that at some point in an image, the color seems perceptually more similar to that of adjacent neighbors, while being more dissimilar from that of remote ones. Thus, their combined effects are enhanced in the presence of a spatial pattern, and can be measured as larger shifts in color matching experiments. Our model supposes a hypercolumnar structure coding for colors in V1, and relies on the notion of color opponency introduced by Hering. The connectivity kernel of the neural field exploits the balance between attraction and repulsion in color and physical spaces, so as to reproduce the sign reversal in the influence of neighboring points. The color sensation at a point, defined from a steady state of the neural activities, is then extracted as a nonlinear percept conveyed by an assembly of neurons. It connects the cortical and perceptual levels, because we describe the search for a color match in asymmetric matching experiments as a mathematical projection on color sensations. We validate our color neural field alongside this color matching framework, by performing a multi-parameter regression to data produced by psychophysicists and ourselves. All the results show that we are able to explain the nonlinear behavior of shifts observed along one or two dimensions in color space, which cannot be done using a simple linear model.

The color perception produced by an image heavily depends on the spatial distribution of its colors. From this “color in context” phenomenon, extensively studied in psychophysics for decades, has arisen the question in neuroscience of how color and space interact in the brain. Visual signals are indeed processed in such a way that neighboring pixels make the perception at some point different from its real color, inducing a color shift. In this work, we propose to emulate perception in context by modeling the activity of color sensitive neurons with a neural field. Our framework unifies two antagonistic effects, assimilation and contrast, which have been suggested to occur simultaneously but at different scales. We use the notion of color opponency inspired by the work of Hering, so as to express these effects as a combination of attraction and repulsion in physical and color spaces. We introduce the concept of “color sensation”, and show how to rigorously link the neural field model to perceptual shifts, by considering color matching as a mathematical projection on color sensations. The results show that our model is able to reproduce some nontrivial behaviors of the color shifts observed in experiments.