Neurogeometry of color vision

In neurogeometry, principles of differential geometry and neuron dynamics are used to model the representation of forms in the primary visual cortex, V1. This approach is well-suited for explaining the perception of illusory contours such as Kanizsa's figure (see Petitot (2008) for a review). In its current version, neurogeometry uses achromatic inputs to the visual system as the starting-point for form estimation. Here we ask how neurogeometry operates when the input is chromatic as in color vision. We propose that even when considering only the perception of form, the random nature of the cone mosaic must be taken into account. The main challenge for neurogeometry is to explain how achromatic information could be estimated from the sparse chromatic sampling provided by the cone mosaic. This article also discusses the non-linearity involved in a neural geometry for chromatic processing. We present empirical results on color discrimination to illustrate the geometric complexity for the discrimination contour when the adaptation state of the observer is not conditioned. The underlying non-linear geometry must conciliate both mosaic sampling and regulation of visual information in the visual system.