The Gestalt computational model by persistent homology

As a classic theory 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. This Gestalt computational model provides a quantitative approach to several key Gestalt principles, and it shows that these 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 visual perception.