Shape representation based on mathematical morphology

This paper presents a novel shape representation algorithm based on mathematical morphology. It consists of two steps. Firstly, an input shape is decomposed into a union of meaningful convex subparts by a recursive scheme. Each subpart is obtained by repeatedly applying condition expansion to a seed, which is selected by utilizing the skeleton information. Secondly, the shape of each subpart is approximated by a morphological dilation of basic structuring elements. The location and direction of the subpart are represented respectively by two parameters. Thus the given shape is represented by a union set of a number of three-dimensional vectors. Experiments show that the new algorithm is immune to noise and occlusion, and invariant under rotation, translation and scaling. Compared to other algorithms, it achieves more natural looking shape components and more concise representation at lower computation costs and coding costs.