A mathematical analysis of the motion coherence theory

摘要

In motion perception, there are a number of important phenomena involving coherence. Examples include motion capture and motion cooperativity. We propose a theoretical model, called the motion coherence theory, that gives a possible explanation for these effects [1,2]. In this framework, the aperture problem can also be thought of as a problem of coherence and given a similar explanation. We propose the concept of a velocity field defined everywhere in the image, even where there is no explicit motion information available. Theough a cost function, the model imposes smoothness on the velocity field in a more general way than in previous theories. In this paper, we provide a detailed theoretical analysis of the motion coherence theory. We discuss its relations with previous theories and show that some of them are approximations to it. A second paper [3] provides extensions for temporal coherence and comparisons to psychophysical phenomena. The theory applies to both short-range and long-range motion. It places them in the same computational framework and provides a way to define interactions between the two processes.