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Power Watershed: A Unifying Graph-Based Optimization Framework
July 2011 (vol. 33 no. 7)
pp. 1384-1399
Camille Couprie, Université Paris-Est, ESIEE, Noisy-le-Grand
Leo Grady, Siemens Corporate Research, Princeton
Laurent Najman, Université Paris-Est, ESIEE, Noisy-le-Grand
Hugues Talbot, Université Paris-Est, ESIEE, Noisy-le-Grand
In this work, we extend a common framework for graph-based image segmentation that includes the graph cuts, random walker, and shortest path optimization algorithms. Viewing an image as a weighted graph, these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes. Introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watershed in this same framework. We then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm, which we term the power watershed. In particular, when q=2, the power watershed leads to a multilabel, scale and contrast invariant, unique global optimum obtained in practice in quasi-linear time. Placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watershed to optimize more general models of use in applications beyond image segmentation.

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Index Terms:
Combinatorial optimization, image segmentation, graph cuts, random walker, shortest paths, optimal spanning forests, Markov random fields.
Citation:
Camille Couprie, Leo Grady, Laurent Najman, Hugues Talbot, "Power Watershed: A Unifying Graph-Based Optimization Framework," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 33, no. 7, pp. 1384-1399, July 2011, doi:10.1109/TPAMI.2010.200
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