The waterfall hierarchy on weighted graphs

Abstract : We study and present two new algorithms for constructing the waterfall hierarchy of a topographic surface. The first models a topographic surface as a flooding graph, each node representing a lake filling a catchment basin up to its lowest pass point ; each edge representing such a pass point. It It makes use of the equivalence of node and edge weighted graphs, passing from one type to the other during as the algorithm proceeds. The second algorithm produces the waterfall partition in one pass through the edges of a minimum spanning tree of the region adjacency graph associated to a topographic surface.