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Power Watershed: A Unifying GraphBased Optimization Framework
, 2011
"... In this work, we extend a common framework for graphbased 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 ..."
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Cited by 42 (8 self)
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In this work, we extend a common framework for graphbased 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 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 quasilinear 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.
Power watersheds: A new image segmentation framework extending graph cuts, random walker and optimal spanning forest
"... In this work, we extend a common framework for seeded 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 pa ..."
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Cited by 40 (11 self)
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In this work, we extend a common framework for seeded 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 watersheds 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 power watersheds. Placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watersheds to optimize more general models of use in application beyond image segmentation. 1.
Fusion graphs: merging properties and watersheds
"... This paper deals with mathematical properties of watersheds in weighted graphs linked to region merging methods, as used in image analysis. In a graph, a cleft (or a binary watershed) is a set of vertices that cannot be reduced, by point removal, without changing the number of regions (connected com ..."
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Cited by 12 (7 self)
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This paper deals with mathematical properties of watersheds in weighted graphs linked to region merging methods, as used in image analysis. In a graph, a cleft (or a binary watershed) is a set of vertices that cannot be reduced, by point removal, without changing the number of regions (connected components) of its complement. To obtain a watershed adapted to morphological region merging, it has been shown that one has to use the topological thinnings introduced by M. Couprie and G. Bertrand. Unfortunately, topological thinnings do not always produce thin clefts. Therefore, we introduce a new transformation on vertex weighted graphs, called Cwatershed, that always produces a cleft. We present the class of perfect fusion graphs, for which any two neighboring regions can be merged, while preserving all other regions, by removing from the cleft the points adjacent to both. An important theorem of this paper states that, on these graphs, the Cwatersheds are topological thinnings and the corresponding divides are thin clefts. We propose a lineartime immersionlike monotone algorithm to compute Cwatersheds on perfect fusion graphs, whereas, in general, a lineartime topological thinning algorithm does not exist. Finally, we derive some characterizations of perfect fusion graphs based on thinness properties of both Cwatersheds and topological watersheds.
Regionbased 3D artwork indexing and classification. In: 3DTV
, 2008
"... We present a method for 3D surface segmentation based on watershed cuts computed on local curvatures. The segmentation algorithm is applied to artwork database classification by mean of a search engine based on 3D region descriptor bags. The comparison with a search engine based on global descriptor ..."
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Cited by 6 (2 self)
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We present a method for 3D surface segmentation based on watershed cuts computed on local curvatures. The segmentation algorithm is applied to artwork database classification by mean of a search engine based on 3D region descriptor bags. The comparison with a search engine based on global descriptors clearly shows an improvement of performances. Index Terms — 3D surface segmentation, watershed cut, 3D descriptors, region bags, artwork database, indexing. 1.
On watershed cuts and thinnings
 IN: PROC. OF DGCI
, 2008
"... We recently introduced the watershed cuts, a notion of watershed in edgeweighted graphs. In this paper, we propose a new thinning paradigm to compute them. More precisely, we introduce a new transformation, called border thinning, that lowers the values of edges that match a simple local configura ..."
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Cited by 1 (1 self)
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We recently introduced the watershed cuts, a notion of watershed in edgeweighted graphs. In this paper, we propose a new thinning paradigm to compute them. More precisely, we introduce a new transformation, called border thinning, that lowers the values of edges that match a simple local configuration until idempotence and prove the equivalence between the cuts obtained by this transformation and the watershed cuts of a map. We discuss the possibility of parallel algorithms based on this transformation and give a sequential implementation that runs in linear time whatever the range of the input map.
Author manuscript, published in "Proceedings of the IEEE 3DTVCon Conference, Istanbul: Turkey (2008)" REGIONBASED 3D ARTWORK INDEXING AND CLASSIFICATION
, 2009
"... We present a method for 3D surface segmentation based on watershed cuts computed on local curvatures. The segmentation algorithm is applied to artwork database classification by mean of a search engine based on 3D region descriptor bags. The comparison with a search engine based on global descriptor ..."
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We present a method for 3D surface segmentation based on watershed cuts computed on local curvatures. The segmentation algorithm is applied to artwork database classification by mean of a search engine based on 3D region descriptor bags. The comparison with a search engine based on global descriptors clearly shows an improvement of performances. Index Terms — 3D surface segmentation, watershed cut, 3D descriptors, region bags, artwork database, indexing. 1.
Indexing of 3D Models Based on Graph of Surfacic Regions Sylvie PhilippFoliguet
"... We present a search engine dedicated to 3D object databases. The originality of the method is to represent models by adjacency graphs of surfacic regions. After segmentation of the 3D surface of a model, regions are described by various shape descriptors. The similarity between graphs is computed ..."
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We present a search engine dedicated to 3D object databases. The originality of the method is to represent models by adjacency graphs of surfacic regions. After segmentation of the 3D surface of a model, regions are described by various shape descriptors. The similarity between graphs is computed by kernels on graphs computed from kernels on walks. These kernel functions take into account both the similarity between regions and their spatial relationship. The search engine performs interactive research in a database from a query object, by using semisupervised classification. The system is applied to a database of 3D high resolution artwork models. We show that a graph representation outperforms a global description of the objects, when using the same descriptors.