Geometric Models with Weighted Topology

This paper introduces the concept of weighted topology to model a 3D object whose connectivity and metric depend on a novel notion of weighted arc-length. The weighted arc-length between any two points of the shape takes into account the fact that a part of the object may be either weakly or strongly connected to another part. The new model is useful to treat problems which are intrinsically not robust to small topological changes. We describe an example implementation of the model and show how it can be exploited to (1) extend the applicability domain of existing segmentation algorithms and (2) improve the performances of a shape descriptor in a 3D object retrieval scenario.