Motion–boundary illusions and their regularization

Humans use various cues to understand the structure of the world from images. One such cue is the contours of an object formed by occlusion or from surface discontinuities. It is known that contours in the image of an object provide various amounts of information about the shape of the object in view, depending on assumptions that the observer makes. Another powerful cue is motion. The ability of the hum an visual system to discern structure from a motion stimulus is well known and has a solid theoretical and experimental foundation. However, when hum ans interpret a visual scene they use various cues to understand what they observe, and the interpretation comes from combining the information acquired from the various modules devoted to specific cues. In such an integration of modules it seems that each cue carries a different weight and importance. We performed several experiments where we made sure that the only cues available to the observer were contour and motion. It turns out that when humans combine information from contour and motion to reconstruct the shape of an object in view, if the results of the two modules - shape from contour and structure from motion - are inconsistent, they experience a perceptual result which is due to the combination of the two modules, with the influence of the contour dominating, thus giving rise to the illusion. We describe here examples of such illusions and identify the conditions under which they happen. Finally, we introduce a computational theory for combining contour and motion using the theory of regularization. The theory explains such illusions and predicts many more. The same computational theory, when applied to retinal motion estimation, explains the effect of boundaries on the perception of motion that gives rise to a set of well-known illusions described by Wallach (1976).