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19 April 2004 Some properties of topological grayscale watersheds
Gilles Bertrand
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Proceedings Volume 5300, Vision Geometry XII; (2004) https://doi.org/10.1117/12.526740
Event: Electronic Imaging 2004, 2004, San Jose, California, United States
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.
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Gilles Bertrand "Some properties of topological grayscale watersheds", Proc. SPIE 5300, Vision Geometry XII, (19 April 2004); https://doi.org/10.1117/12.526740
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KEYWORDS
Algorithms
Electronic imaging
Vision geometry
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