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Abstract:

In this overview talk, we address certain concepts of motion and deformation between image frames.
In particular, we are interested in optical flow, optimal transport, metamorphosis and large diffeomorphic metric mappings. While optical flow aims to find a motion field between images based on a gray-value constancy assumption by minimizing a cost function which is often convex and non-smooth, optimal transport aims to find an optimal transport plan between images considered as density functions of associated measures. Metamorphosis  minimizes the path energy between images in a nonlinear Riemannian manifold  of images and is related to LDDMM via a control problem formulation. We introduce the mathematical concepts, efficient solution strategies and demonstrate their behavior by numerical examples.