Abstract
We investigate the effectiveness of the divide set produced by watershed algorithms. We introduce the mosaic to retrieve the altitude of points along the divide set. A desirable property is that, when two minima are separated by a crest in the original image, they are still separated by a crest of the same altitude in the mosaic. Our main result states that this is the case if and only if the mosaic is obtained through a topological thinning.
Keywords
- segmentation
- graph
- mosaic
- (topologicall) watershed
- separation
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Najman, L., Couprie, M., Bertrand, G. (2005). Mosaics and Watersheds. In: Ronse, C., Najman, L., Decencière, E. (eds) Mathematical Morphology: 40 Years On. Computational Imaging and Vision, vol 30. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3443-1_17
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DOI: https://doi.org/10.1007/1-4020-3443-1_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3442-8
Online ISBN: 978-1-4020-3443-5
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