Watershed and skeleton by influence zones: A distance-based approach

Abstract

The concept of Euclidean and geodesic distance is of great importance in binary mathematical morphology (MM), and the grey-level MM deals mainly with neighborhood configuration analysis. This paper presents a novel approach to grey-level MM based on the concept of a distance function relative to topographical surfaces. By introducing the notions of connection cost and deviation cost, this paper defines the topographical and differential distances and develops a powerful theoretical framework for establishing the equivalence between the two fundamental notions of skeleton by influence zones (SKIZ) and watershed: the SKIZ of the set of the minima of a grey-level image f with respect to the differential distance function is exactly the watershed of f. This leads to a duality between binary and grey-level images and to new fast algorithms for computing the SKIZ and the watershed.