3D open-surface shape correspondence for statistical shape modeling: Identifying topologically consistent landmarks

Shape correspondence, which aims at accurately identifying corresponding landmarks from a given population of shape instances, is a very challenging step in constructing a statistical shape model such as the Point Distribution Model. The state-of-the-art methods such as MDL and SPHARM are primarily focused on closed-surface shape correspondence. In this paper we develop a novel method aimed at identifying accurately corresponding landmarks on 3D open-surfaces with a closed boundary. In particular, we enforce explicit topology consistency on the identified landmarks to ensure that they form a simple, consistent triangle mesh to more accurately model the correspondence of the underlying continuous shape instances. The proposed method also ensures the correspondence of the boundary of the open surfaces. For our experiments, we test the proposed method by constructing a statistical shape model of the human diaphragm from 26 shape instances.