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

This paper describes a variational approach for estimating a discontinuous optical flow from a sequence of images. Defined as the apparent motion of the image brightness pattern, the optical flow is very important in the computer vision community, where its accurate estimation is strongly needed. After a short overview of existing methods, we present a new variational method that we study in the space of bounded variations. We first present an integral representation of the optical flow problem which appears to be not lower semicontinuous. The relaxed functional is then calculated. We conclude by challenging questions about the possible numerical analysis of the abstract results.