Local and global gestalt laws: A neurally based spectral approach

TL;DR

This paper introduces a spectral model of figure-ground perception that integrates local and global gestalt laws, aligning with V1 neural architecture, and demonstrates its effectiveness through numerical simulations.

Contribution

It presents a neurally plausible spectral approach combining local connectivity kernels and global spectral analysis for figure-ground segmentation.

Findings

Spectral analysis effectively groups local features into perceptual units.

Connectivity kernels derived from Lie group theory model V1 long-range connections.

Numerical simulations validate the model's ability to replicate perceptual grouping.

Abstract

A mathematical model of figure-ground articulation is presented, taking into account both local and global gestalt laws. The model is compatible with the functional architecture of the primary visual cortex (V1). Particularly the local gestalt law of good continuity is described by means of suitable connectivity kernels, that are derived from Lie group theory and are neurally implemented in long range connectivity in V1. Different kernels are compatible with the geometric structure of cortical connectivity and they are derived as the fundamental solutions of the Fokker Planck, the Sub-Riemannian Laplacian and the isotropic Laplacian equations. The kernels are used to construct matrices of connectivity among the features present in a visual stimulus. Global gestalt constraints are then introduced in terms of spectral analysis of the connectivity matrix, showing that this processing can be cortically implemented in V1 by mean field neural equations. This analysis performs grouping of local features and individuates perceptual units with the highest saliency. Numerical simulations are performed and results are obtained applying the technique to a number of stimuli.