Shape correspondence, which aims at accurately identifying corresponding landmarks from the given population of shape instances, is a major challenge in constructing a statistical shape model, such as the popular Point Distribution Model (PDM). In this talk, we present a newly developed 3D shape-correspondence method. Different from the available state-of-the-art 3D shape-correspondence methods, such as MDL and SPHARM, the proposed method bears two unique and important properties. First, while available methods are primarily focused on closed-surface shape correspondence, the proposed method aims to address open-surface shape correspondence, where each shape instance is an open surface with a closed boundary. Second, the proposed method explicitly enforces the topology consistency of the identified landmarks in a way that they constitute consistent and accurate triangulated meshes for the input shape instances. This way, the correspondence of the identified landmarks more accurately reflects the correspondence of the underlying continuous shape instances. In our experiments, we test the proposed method on 18 human diaphragm shape instances.