First-Order Modeling and Stability Analysis of Illusory Contours

In System Theory [20], input-output analysis has been a majo r tool for partial or complete identification of black-box systems. In cognitive vision science, t he study of various visual illusions follows exactly the same spirit. Cognitive scientists have designe d numerous intriguing inputs of image signals, so that the distorted or transformed outputs (as re ported by an average human observer) can help reveal some crucial latent properties of the human v ision system (see, e.g., the remarkable works of Adelson [1], Knill and Kersten [14, 16], and Kanizsa [11]). Illusory contours are such a well known class of visual illusions, and the current paper devel ops a mathematical model to characterize, analyze, and simulate generic illusory contours. Our w ork has been closely inspired by many existent modeling works, especially by Sarti, Malladi, and Sethian [24], and Zhu and Chan [30, 31]. Figure 1 shows two examples of illusory contours known as Kanizsa triangle and square [11, 24, 30].