Efficient morphological shape representation with overlapping disk components

This paper proposes a new morphological shape representation algorithm, in which a two-dimensional (2-D) binary shape is represented as a union of certain disks contained in the given shape. The representative disks of different sizes may overlap. But excessive overlapping between them is avoided. The algorithm combines the advantages of the morphological skeleton transform (MST) and the morphological shape decomposition (MSD). The representative disks have simple and well-defined mathematical characterizations. The algorithm is simple and efficient to implement. The experimental results show that the number of representative disks used by our algorithm is significant lower than that used by the MSD. The overlapping level between the representative disks is much lower than that of the MST. A simple procedure can be used to combine the representative disks into more meaningful shape components. These shape components seem to correspond better to the natural shape parts than those generated by the MSD. It is also possible to build a good approximation for a given shape using only a small number of major components.