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65
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 40 (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.
Effective component tree computation with application to pattern recognition in astronomical imaging
 in Proc. IEEE Int. Conf. Image Processing 2007
"... In this paper a new algorithm to compute the component tree is presented. As compared to the state of the art, this algorithm does not use excessive memory and is able to work efficiently on images whose values are highly quantized or even with images having floating values. We also describe how it ..."
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Cited by 23 (6 self)
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In this paper a new algorithm to compute the component tree is presented. As compared to the state of the art, this algorithm does not use excessive memory and is able to work efficiently on images whose values are highly quantized or even with images having floating values. We also describe how it can be applied to astronomical data to identify relevant objects.
On the equivalence between hierarchical segmentations and ultrametric watersheds
 JMIV
, 2010
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Concurrent Computation of Attribute Filters on Shared Memory Parallel Machines
, 2008
"... Morphological attribute filters have not previously been parallelized mainly because they are both global and nonseparable. We propose a parallel algorithm that achieves efficient parallelism for a large class of attribute filters, including attribute openings, closings, thinnings, and thickenings, ..."
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Cited by 17 (0 self)
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Morphological attribute filters have not previously been parallelized mainly because they are both global and nonseparable. We propose a parallel algorithm that achieves efficient parallelism for a large class of attribute filters, including attribute openings, closings, thinnings, and thickenings, based on Salembier’s MaxTrees and Mintrees. The image or volume is first partitioned in multiple slices. We then compute the Maxtrees of each slice using any sequential MaxTree algorithm. Subsequently, the Maxtrees of the slices can be merged to obtain the Maxtree of the image. A Cimplementation yielded good speedups on both a 16processor MIPS 14000 parallel machine and a dualcore Opteronbased machine. It is shown that the speedup of the parallel algorithm is a direct measure of the gain with respect to the sequential algorithm used. Furthermore, the concurrent algorithm shows a speed gain of up to 72 percent on a singlecore processor due to reduced cache thrashing.
Volumetric Attribute Filtering and Interactive Visualization using the MaxTree Representation
"... Abstract—The MaxTree, designed for morphological attribute filtering in image processing, is a data structure in which the nodes represent connected components for all threshold levels in a data set. Attribute filters compute some attribute describing the shape or size of each connected component, ..."
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Cited by 13 (5 self)
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Abstract—The MaxTree, designed for morphological attribute filtering in image processing, is a data structure in which the nodes represent connected components for all threshold levels in a data set. Attribute filters compute some attribute describing the shape or size of each connected component, and then decide which components to keep or to discard. In this paper, we augment the basic MaxTree data structure such that interactive volumetric filtering and visualization becomes possible. We introduce extensions that allow (i) direct, splattingbased, volume rendering, (ii) representation of the MaxTree on graphics hardware, and (iii) fast active cell selection for isosurface generation. In all three cases, we can use the MaxTree representation for visualization directly, without needing to reconstruct the volumetric data explicitly. We show that both filtering and visualization can be performed at interactive frame rates, ranging between 2.4 and 32 frames per seconds. In contrast, a standard texturebased volume visualization method manages only between 0.5 and 1.8 frames per second. For isovalue browsing, the experimental results show that the performance is comparable to the performance of an interval tree, where our method has the advantage that both filter threshold browsing and isolevel browsing are fast. It is shown that the methods using graphics hardware can be extended to other connected filters. Index Terms—MaxTree, nonlinear filtering, mathematical morphology, volume visualization, connected filters I.
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.
Incremental algorithm for hierarchical minimum spanning forests and saliency of watershed cuts
, 2011
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Hyperconnected attribute filters based on kflat zones
 IEEE Transactions on Pattern Analysis and Machine Intelligence
"... Abstract—In this paper, we present a new method for attribute filtering, combining contrast and structural information. Using hyperconnectivity based on kflat zones, we improve the ability of attribute filters to retain internal details in detected objects. Simultaneously, we improve the suppressio ..."
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Cited by 7 (1 self)
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Abstract—In this paper, we present a new method for attribute filtering, combining contrast and structural information. Using hyperconnectivity based on kflat zones, we improve the ability of attribute filters to retain internal details in detected objects. Simultaneously, we improve the suppression of small, unwanted detail in the background. We extend the theory of attribute filters to hyperconnectivity and provide a fast algorithm to implement the new method. The new version is only marginally slower than the standard MaxTree algorithm for connected attribute filters, and linear in the number of pixels or voxels. It is two orders of magnitude faster than anisotropic diffusion. The method is implemented in the form of a filtering rule suitable for handling both increasing (size) and nonincreasing (shape) attributes. We test this new framework on nonincreasing shape filters on both 2D images from astronomy, document processing, and microscopy, and 3D CT scans, and show increased robustness to noise while maintaining the advantages of previous methods.
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.
Surface reconstruction using Power Watershed
"... Abstract. Surface reconstruction from a set of noisy point measurements has been a well studied problem for several decades. Recently, variational and discrete optimization approaches have been applied to solve it, demonstrating good robustness to outliers thanks to a global energy minimization sche ..."
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Cited by 5 (5 self)
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Abstract. Surface reconstruction from a set of noisy point measurements has been a well studied problem for several decades. Recently, variational and discrete optimization approaches have been applied to solve it, demonstrating good robustness to outliers thanks to a global energy minimization scheme. In this work, we use a recent approach embedding several optimization algorithms into a common framework named power watershed. We derive a specific watershed algorithm for surface reconstruction which is fast, robust to markers placement, and produces smooth surfaces. Experiments also show that our proposed algorithm compares favorably in terms of speed, memory requirement and accuracy with existing algorithms.