Watershed algorithms

Abstract

© The Author(s) 2014. The watershed approach has been developed in image processing for segmenting grey-level images, i.e., two-dimensional scalar fields modeled as regular grids. It directly extends to higher dimensions. Few watershed algorithms are defined for simplicial models. In general, the input for a watershed algorithm is a graph describing the connectivity structure of either the input mesh (i.e., nodes correspond to vertices), or of its dual mesh (i.e., nodes correspond to cells of maximum dimension), with field values associated with its nodes. The output is a classification of the graph nodes as belonging to the catchment basin (ascending cell) of a certain minimum, or as belonging to the boundary between catchment basins. In this chapter, we present the main approaches to watershed computation, namely, by simulated immersion (Sect. 4.1), by topographic distance (Sect. 4.2), and by rain falling (Sect. 4.3), as well as a comparison among the different approaches (Sect. 4.4).