Topographic distance and watershed lines

The watershed line is the basic tool for segmenting images in mathematical morphology. A rigorous definition is given in terms of a distance function called topographic distance. If the topographical function is itself a distance function, then the topographical distance becomes identical with the geodesic distance function and the watershed becomes identical with the skeleton by zone of influence. The classical shortest paths algorithms of the graph theory are then revisited in order to derive new watershed algorithms, which are either new or more easy to implement in hardware.