Topo-geometric Shape Model for 3d Object Representation

We propose a new method for representing the topology and geometry of 2D compact surfaces embedded in a three-dimensional space. Topology is modeled through a skeletal graph, where a distance function is employed as a Morse function. Invariance to rigid transformations follows directly from this choice of Morse function. Geometry is captured by modeling the evolution of level curves of the distance function along topologically homogenous parts of the surface, which in turn correspond to various graph edges. Combining topological and geometric information leads to a weighted skeletal graph representation of a surface, which is sufficient for reconstructing the original surface. The uniqueness and completeness of representation make the method particularly suitable for shape recognition applications, where weighted graph isomorphism may be employed.