Collapses and Watersheds in Pseudomanifolds

This work is settled in the framework of abstract simplicial complexes. We propose a definition of a watershed and of a collapse for maps defined on pseudomanifolds of arbitrary dimension. Through an equivalence theorem, we establish a deep link between these two notions: any watershed can be obtained by collapse iterated until idempotence, and conversely any collapse iterated until idempotence induces a watershed. We also state an equivalence result which links the notions of a watershed and of a collapse with the one of a minimum spanning forest.

• Type: Conference
• Year: 2009
• Where: IWCIA
• Authors: Jean Cousty, Gilles Bertrand, Michel Couprie, Laurent Najman
• Keywords: Abstract Simplicial Complexes, Arbitrary Dimension, Equivalence Theorem, Image, IWCIA 2009