First-Order Modeling and Stability Analysis of Illusory Contours

TL;DR

This paper introduces a first-order energy-based model for analyzing and simulating illusory contours in visual cognition, enabling rigorous geometric analysis and robust computation with potential cognitive insights.

Contribution

It proposes a novel, low-complexity first-order model for illusory contours, facilitating detailed geometric analysis and stable numerical simulation.

Findings

Model effectively captures geometric structures of illusory contours

Asymptotic approximation aligns with classical active contours

Robust level-set computation demonstrates practical applicability

Abstract

In visual cognition, illusions help elucidate certain intriguing latent perceptual functions of the human vision system, and their proper mathematical modeling and computational simulation are therefore deeply beneficial to both biological and computer vision. Inspired by existent prior works, the current paper proposes a first-order energy-based model for analyzing and simulating illusory contours. The lower complexity of the proposed model facilitates rigorous mathematical analysis on the detailed geometric structures of illusory contours. After being asymptotically approximated by classical active contours, the proposed model is then robustly computed using the celebrated level-set method of Osher and Sethian (J. Comput. Phys., 79:12-49, 1988) with a natural supervising scheme. Potential cognitive implications of the mathematical results are addressed, and generic computational examples are demonstrated and discussed.