Local and global gestalt laws: A neurally based spectral approach
This work addresses the challenge of visual perception modeling for neuroscience and computer vision, but it appears incremental as it builds on existing gestalt theory and neural implementations.
The authors tackled the problem of figure-ground articulation by developing a mathematical model that integrates local and global gestalt laws, compatible with the primary visual cortex's architecture, and demonstrated its effectiveness through numerical simulations on various stimuli.
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.