Shape Segmentation and Matching with Flow Discretization

Geometric shapes are identified with their features. For computational purposes a concrete mathematical definition of features is required. In this paper we use a topological approach, namely dynamical systems, to define features of shapes. To exploit this definition algorithmically we assume that a point sample of the shape is given as input from which features of the shape have to be approximated. We translate our definition of features to the discrete domain while mimicking the set-up developed for the continuous shapes. The outcome of this approach is a clean mathematical definition of features that are efficiently computable with combinatorial algorithms. Experimental results show that our algorithms segment shapes in two and three dimensions into so-called features quite effectively. Further, we develop a shape matching algorithm that takes advantage of our robust feature segmentation step. Performance of this algorithm is exhibited with experimental results.