Watersheds, extension maps, and the emergence paradigm

In this paper, we investigate the links between the flooding paradigm and the topological watershed. Guided by the analysis of a classical flooding algorithm, we introduce several notions that help us to understand the watershed: minima extension, extension map, and pass values. We investigate the possibility for a flooding to produce a topological watershed, and conclude that this is not feasible. This leads us to reverse the flooding paradigm, and to propose a notion of emergence. An emergence process is a transformation based on a topological criterion, in which points are processed in decreasing altitude order while preserving the number of connected components of lower cross-sections. Our main result states that any emergence watershed is a topological watershed, and more remarkably, that any topological watershed of a given image can be obtained as an emergence watershed of the image.