A mathematical model of color and orientation processing in V1

Orientation processing in the primary visual cortex (V1) has been experimentally investigated in detail and reproduced in models, while color processing remains unclear. Thus, we have constructed a mathematical model of color and orientation processing in V1. The model is mainly based on the following experimental evidence concerning color blobs: A blob contains overlapping neuronal patches activated by different hues, so that each blob represents a full gamut of hue and might be structured with a loop (Xiao et al. in NeuroImage 35:771-786, 2007). The proposed model describes a set of orientation hypercolumns and color blobs, in which color and orientation preferences are represented by the poloidal and toroidal angles of a torus, correspondingly. The model consists of color-insensitive (CI) and color-sensitive (CS) neuronal populations, which are described by a firing-rate model. The set of CI neurons is described by the classical ring model (Ben-Yishai et al. in Proc Natl Acad Sci USA 92:3844-3848, 1995) with recurrent connections in the orientation space; similarly, the set of CS neurons is described in the color space and also receives input from CI neurons of the same orientation preference. The model predictions are as follows: (1) responses to oriented color stimuli are significantly stronger than those to non-oriented color stimuli; (2) the activity of CS neurons in total is higher than that of CI neurons; (3) a random color can be illusorily perceived in the case of gray oriented stimulus; (4) in response to two-color stimulus in the marginal phase, the network chooses either one of the colors or the intermediate color; (5) input to a blob has rather continual representation of a hue than discrete one (with two narrowly tuned opponent signals).