A sub-Riemannian model of the visual cortex with frequency and phase

The Journal of Mathematical Neuroscience

A. Sarti¹  E. Baspinar²  G. Citti³ 

[1] EHESS, CAMS, Paris, France;MathNeuro Team, INRIA Sophia Antipolis, Valbonne, France;MathNeuro Team, INRIA Sophia Antipolis, Valbonne, France;Department of Mathematics, University of Bologna, Bologna, Italy;

关键词: Sub-Riemannian geometry;    Neurogeometry;    Differential geometry;    Gabor functions;    Visual cortex;    Image enhancement;   

DOI  :  10.1186/s13408-020-00089-6

来源: Springer

【 摘 要 】

In this paper, we present a novel model of the primary visual cortex (V1) based on orientation, frequency, and phase selective behavior of V1 simple cells. We start from the first-level mechanisms of visual perception, receptive profiles. The model interprets V1 as a fiber bundle over the two-dimensional retinal plane by introducing orientation, frequency, and phase as intrinsic variables. Each receptive profile on the fiber is mathematically interpreted as rotated, frequency modulated, and phase shifted Gabor function. We start from the Gabor function and show that it induces in a natural way the model geometry and the associated horizontal connectivity modeling of the neural connectivity patterns in V1. We provide an image enhancement algorithm employing the model framework. The algorithm is capable of exploiting not only orientation but also frequency and phase information existing intrinsically in a two-dimensional input image. We provide the experimental results corresponding to the enhancement algorithm.

【 授权许可】

CC BY