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Proceedings Paper

Some properties of topological grayscale watersheds
Author(s): Gilles Bertrand
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Paper Abstract

In this paper, we investigate topological watersheds. For that purpose we introduce a notion of “separation between two points” of an image. One of our main results is a necessary and sufficient condition for a map G to be a watershed of a map F, this condition is based on the notion of separation. A consequence of the theorem is that there exists a (greedy) polynomial time algorithm to decide whether a map G is a watershed of a map F or not. We also show that, given an arbitrary total order on the minima of a map, it is possible to define a notion of “degree of separation of a minimum” relative to this order. This leads to another necessary and sufficient condition for a map G to be a watershed of a map F. At last we derive, from our framework, a new definition for the dynamics of a minimum.

Paper Details

Date Published: 19 April 2004
PDF: 11 pages
Proc. SPIE 5300, Vision Geometry XII, (19 April 2004); doi: 10.1117/12.526740
Show Author Affiliations
Gilles Bertrand, Groupe ESIEE (France)


Published in SPIE Proceedings Vol. 5300:
Vision Geometry XII
Longin Jan Latecki; David M. Mount; Angela Y. Wu, Editor(s)

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