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.
Document type :
Journal articles
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00871498
Contributor : Jean Cousty <>
Submitted on : Tuesday, January 21, 2014 - 11:36:16 AM
Last modification on : Thursday, July 5, 2018 - 2:25:26 PM
Document(s) archivé(s) le : Tuesday, April 22, 2014 - 9:52:26 AM

Files

SimplicialWatershed.pdf
Publisher files allowed on an open archive

Identifiers

Citation

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⟩

Share

Metrics

Record views

312

Files downloads

344