The Gestalt Computational Model by Persistent Homology

TL;DR

This paper introduces a computational model based on persistent homology that quantifies and unifies Gestalt principles, providing a mathematical foundation for visual perception theories in cognitive psychology.

Contribution

It develops the first unified computational model of Gestalt principles using persistent homology, offering quantitative support and theoretical coherence.

Findings

Provides a quantitative framework for Gestalt principles

Demonstrates uniform calculation of principles via persistent homology

Enhances understanding of visual perception in computational psychology

Abstract

Widely employed in cognitive psychology, Gestalt theory elucidates basic principles in visual perception. However, the Gestalt principles are validated mainly by psychological experiments, lacking quantitative research supports and theoretical coherence. In this paper, we utilize persistent homology, a mathematical tool in computational topology, to develop a unified computational model for Gestalt principles, addressing the challenges of quantification and computation. On the one hand, the Gestalt computational model presents quantitative supports for Gestalt theory. On the other hand, it shows that the Gestalt principles can be uniformly calculated using persistent homology, thus developing a coherent theory for Gestalt principles in computation. Moreover, it is anticipated that the Gestalt computational model can serve as a significant computational model in the field of computational psychology, and help the understanding of human being visual perception.