Optical Flow on Moving Manifolds

Abstract. Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this article we study a Horn–Schunck type spatio-temporal regularization functional for image sequences that have a non-Euclidean, time varying image domain. To that end we con-struct a Riemannian metric that describes the deformation and structure of this evolving surface. The resulting functional can be seen as natural geo-metric generalization of previous work by Weickert and Schnörr (2001) and Lefèvre and Baillet (2008) for static image domains. In this work we show the existence and wellposedness of the corresponding optical flow problem and derive necessary and sufficient optimality conditions. The functionality of our approach is demonstrated in two numerical experiments