ABSTRACT
This chapter describes the basic operators of binary mathematical morphology (MM) in terms of Euclidean and geodesic distances and presents specific examples of MM segmentation exploiting the information generated by a distance function. It introduces the connection cost concept, discusses its main properties, defines the topographical distance function, and explains some topological properties. The chapter aims to develop a topographical MM, and shows a first relationship between skeleton by influence zone (SKIZ) and watershed (WS). It presents the differential distance based on the deviation cost concept and establishing the complete equivalence between SKIZ and WS, and deals with the algorithmic aspects of the developed concepts. Whereas MM dealing with binary images exploits widely the information on distance to a set or to its complement relative to the whole space or to a subset of it, gray-level MM is mainly based on the analysis of neighborhood configurations.
