Gilles Bertrand

Discrete Morse functions and watersheds

By Gilles Bertrand, Nicolas Boutry, Laurent Najman


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.

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Gradient vector fields of discrete morse functions and watershed-cuts

By Nicolas Boutry, Gilles Bertrand, Laurent Najman


In Proceedings of the IAPR international conference on discrete geometry and mathematical morphology (DGMM)


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