Meaningful 3D shape partitioning using Morse functions

To simplify the matching and recognition of 3D objects, we propose to decompose a complex 3D shape into simpler primitive parts. Our partitioning of objects relies on their topological Reeb graphs. Taking advantage of the properties of Morse theory, we detect the critical points of the global geodesic function. These points define the levels at which the segmentation happens. To preserve the geometry of objects, we choose to use level curves instead of intervals. To proceed with object matching, we propose a kernel-based technique to register Reeb graphs. This optimal positioning of two Reeb graphs prepares for a pairwise comparison of the geometry of their primitives.