Department of Communication, Computer and Systems Science,
University of Genoa, Via all'Opera Pia 11a, 16145, Genoa, Italy
Abstract
This paper discusses the representation of smooth planar shapes, which are formally defined as connected regularized point sets with "smooth" boundaries. The structure of shape is investigated and two complementary entities are singled out: a "main structure" and the overlying "details" or "texture". Accordingly, a complementarity principle for the discription of shape is proposed: "Shape requires discription at different levels of detail: global discriptions require low detail whereas local discriptions require higher detail. The relative emphasis depends on the application". It is suggested that the two entities can be separated in terms of frequency analysis, the low frequency component being associated with the main structure, and the high frequency component with details/textures. The prposed representation of shape consists of two complementary components: (i) the "skeletal representation" of the main structure, which uses the concept of Medial Axis Transformation, and (ii) the "zero-crossing represntation" of details/textures which extends to the contours of shapes the theorem by Logan already applied to problems of vision. The two representations are discussed with regard to problems of analysis and synthesis.