Reconciling Landmarks and Level Sets

Shape warping is a key problem in statistical shape analysis. This paper proposes a framework for geometric shape warping based on both shape distances and landmarks. Our method is compatible with implicit representations and a matching between shape surfaces is provided at no additional cost. It is, to our knowledge, the first time that landmarks and shape distances are reconciled in a pure geometric level set framework. The feasibility of the method is demonstrated with two- and three-dimensional examples. Combining shape distance and landmarks, our approach reveals to need only a small number of landmarks to obtain improvements on both warping and matching