Mathematical study of the relaxed optical flow problem in the space BV (Omega)

This paper describes a variational approach for estimating a discontinuous optical flow from a sequence of images. Defined as the apparent motion of t he image brightness pattern, the optical flow is very important in the comp uter vision community, where its accurate estimation is strongly needed. Af ter a short overview of existing methods, we present a new variational meth od that we study in the space of bounded variations. We first present an in tegral representation of the optical flow problem which appears to be not l ower semicontinuous. The relaxed functional is then calculated. We conclude by challenging questions about the possible numerical analysis of the abst ract results.