Shape decomposition and representation using a recursive morphological operation

Abstract

This paper presents a recursive morphological operation developed in order to perform efficient shape representation. This operation uses a structuring element as a geometrical primitive to evaluate the shape of an object. It results in a set of loci of the translated structuring elements that are included in the object but which do not overlap. The analysis of its computational complexity shows that it is usually less time-consuming than morphological erosion. By using this operation, an object decomposition algorithm is then developed for shape representation. It decomposes an object into a union of simple and non-overlapping object components. The object is represented by the sizes and loci of its object components. This representation is information preserving, shift and scale invariant, and non-rebundant. It has been compared with skeletons, morphological decomposition, chain codes and quatrees in terms of compression ability and image processing facility. Experimental results shows that it is very compact, especially if information loss is allowed. Because of the non-overlap between object components, many image processing tasks can be easily performed by directly using this shape representation.