Computation of discontinuous optical flow by domain decomposition and shape optimization

摘要

A well-known method for the reconstruction of motion fields from noisy image data is to determine flow fields by the minimization of a quadratic functional. The first approach of this class has been proposed by Horn and Schunck (1981). A drawback of such approaches is that an explicit representation of the discontinuities of the motion field is lacking and that, in general, the resulting flow fields approximate the motion fields only badly at the corresponding locations in the image plane. In this article, we discuss the possibility to improve the results by hypothesizing the qualitative structure of the motion field in terms of certain parameters. We decompose the image plane into disjoint sets, restrict the domain of definition of the functionals to these sets, and use the hypotheses to deform and to move the boundaries of the sets within the image plane. We discuss the range of applicability of this new technique and illustrate the algorithm by numerical examples. This article is a revised and extended version of Schnörr (1990).