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Collapses and watersheds in pseudomanifolds of arbitrary dimension

Abstract : This work is settled in the framework of abstract simplicial complexes. We propose a definition of a watershed and of a collapse (i.e., a homotopic retraction) for maps defined on pseudomanifolds of arbitrary dimension. Then, we establish two important results linking watersheds and homotopy. The first one generalizes a property known for distance transforms in a continuous setting to any map on pseudomanifolds: a watershed of any map is a subset of an ultimate collapse of the support of this map. The second result establishes, through an equivalence theorem, a deep link between watershed and collapse of maps: any watershed of any map can be straightforwardly obtained from an ultimate collapse of this map, and conversely any ultimate collapse of the initial map straightforwardly induces a watershed.
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Contributor : Jean Cousty <>
Submitted on : Tuesday, January 21, 2014 - 11:36:16 AM
Last modification on : Monday, June 29, 2020 - 10:33:56 PM
Document(s) archivé(s) le : Tuesday, April 22, 2014 - 9:52:26 AM


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Jean Cousty, Gilles Bertrand, Michel Couprie, Laurent Najman. Collapses and watersheds in pseudomanifolds of arbitrary dimension. Journal of Mathematical Imaging and Vision, Springer Verlag, 2014, 50 (3), pp.261-285. ⟨10.1007/s10851-014-0498-z⟩. ⟨hal-00871498v2⟩



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