From receptive profiles to a metric model of V1

TL;DR

This paper develops a metric model of V1's functional architecture based on connectivity kernels derived from receptive profiles, capturing the geometry and perceptual properties of the visual cortex.

Contribution

It introduces a flexible method to construct connectivity kernels from receptive profiles, aligning with known V1 properties and applicable to learned filter banks.

Findings

Connectivity kernels reflect V1's long-range horizontal connections.

The model aligns with association field perceptual rules.

Applicable to both predefined and learned filter banks.

Abstract

In this work we show how to construct connectivity kernels induced by the receptive profiles of simple cells of the primary visual cortex (V1). These kernels are directly defined by the shape of such profiles: this provides a metric model for the functional architecture of V1, whose global geometry is determined by the reciprocal interactions between local elements. Our construction adapts to any bank of filters chosen to represent a set of receptive profiles, since it does not require any structure on the parameterization of the family. The connectivity kernel that we define carries a geometrical structure consistent with the well-known properties of long-range horizontal connections in V1, and it is compatible with the perceptual rules synthesized by the concept of association field. These characteristics are still present when the kernel is constructed from a bank of filters arising from an unsupervised learning algorithm.