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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Journal of Mathematical Imaging and Vision, Springer Verlag, 2014, 50 (3), pp.261-285. 〈10.1007/s10851-014-0498-z〉
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Dernière modification le : lundi 29 septembre 2014 - 10:38:30
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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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