Discrete Morse functions and watersheds
In Journal of Mathematical Imaging and Vision
Abstract Any watershed, when defined on a stack on a normal pseudomanifold of dimension $d$, is a pure $(d-1)$-subcomplex that satisfies a drop-of-water principle. In this paper, we introduce Morse stacks, a class of functions that are equivalent to discrete Morse functions. We show that the watershed of a Morse stack on a normal pseudomanifold is uniquely defined, and can be obtained with a linear-time algorithm relying on a sequence of collapses.