First-order modeling and stability analysis of illusory contours

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 [S. Osher, J.A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations, J. Comput. Phys., 79 (12) (1988) 12–49] with a natural supervising scheme. Potential cognitive implications of the mathematical results are addressed, and generic computational examples are demonstrated and discussed.