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

TL;DR

This paper introduces a novel sub-Riemannian model of the primary visual cortex that incorporates orientation, frequency, and phase information, enabling advanced image enhancement by mimicking neural connectivity patterns.

Contribution

The paper presents a new geometric model of V1 based on Gabor functions with frequency and phase, extending previous orientation-only models and demonstrating its application in image enhancement.

Findings

Effective image enhancement exploiting frequency and phase.

Model aligns with neural connectivity patterns in V1.

Experimental results show improved image clarity.

Abstract

In this paper we present a novel model of the primary visual cortex (V1) based on orientation, frequency and phase selective behavior of the 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 2-dimensional retinal plane by introducing orientation, frequency and phase as intrinsic variables. Each receptive profile on the fiber is mathematically interpreted as a 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 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 2-dimensional input image. We provide the experimental results corresponding to the enhancement algorithm.