On Model-based Diffeomorphic Shape Evolution and Diffeomorphic Shape Registration

Shape registration is fundamental in many applications. However, the shape registration problem is usually ill posed unless further information is provided. In this dissertation, we examine a scenario when one of the two shapes to be registered is assumed to have evolved from the other shape according to a known model. The shape registration problem is then formulated as a variational problem subject to the dynamics of the shape evolution model. We provide sufficient conditions on models so that diffeomorphic shape evolution and diffeomorphic shape registration are guaranteed theoretically. In addition, we illustrate this model-based registration by applications of piecewise-rigid motion and biological atrophy. Numerical experiments of the two applications are presented with a GPU-accelerated implementation