期刊
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
卷 31, 期 8, 页码 1362-1374出版社
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2008.173
关键词
Watershed; minimum spanning forest; minimum spanning tree; graph; mathematical morphology; image segmentation
资金
- ANR [SURF-NT05-2,45825]
We study the watersheds in edge-weighted graphs. We define the watershed cuts following the intuitive idea of drops of water flowing on a topographic surface. We first establish the consistency of these watersheds: They can be equivalently defined by their catchment basins (through a steepest descent property) or by the dividing lines separating these catchment basins (through the drop of water principle). Then, we prove, through an equivalence theorem, their optimality in terms of minimum spanning forests. Afterward, we introduce a linear-time algorithm to compute them. To the best of our knowledge, similar properties are not verified in other frameworks and the proposed algorithm is the most efficient existing algorithm, both in theory and in practice. Finally, the defined concepts are illustrated in image segmentation, leading to the conclusion that the proposed approach improves, on the tested images, the quality of watershed-based segmentations.
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