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

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.

References in corpus (4)

• A geometric model of multi-scale orientation preference maps via Gabor functions
• Uniqueness of viscosity mean curvature flow solution in two sub-Riemannian structures
• Coherent states of the Euclidean group and activation regions of primary visual cortex
• Cortical spatio-temporal dimensionality reduction for visual grouping

Cited by in corpus (5)

• Coherence resonance in neuronal populations: mean-field versus network model
• Gabor frames from contact geometry in models of the primary visual cortex
• A cortical-inspired sub-Riemannian model for Poggendorff-type visual illusions
• Multi-frequency image completion via a biologically-inspired sub-Riemannian model with frequency and phase
• Cortically based optimal transport