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28
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.
Morphological operators in graph spaces
"... Abstract. We study some basic morphological operators acting on the lattice of all subgraphs of a (nonweighted) graph G. To this end, we consider two dual adjunctions between the edge set and the vertex set of G. This allows us (i) to recover the classical notion of a dilation/erosion of a subset o ..."
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Cited by 18 (10 self)
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Abstract. We study some basic morphological operators acting on the lattice of all subgraphs of a (nonweighted) graph G. To this end, we consider two dual adjunctions between the edge set and the vertex set of G. This allows us (i) to recover the classical notion of a dilation/erosion of a subset of the vertices of G and (ii) to extend it to subgraphs of G. Afterward, we propose several new erosions, dilations, granulometries and alternate filters acting (i) on the subsets of the edge and vertex set of G and (ii) on the subgraphs of G. 1
On the equivalence between hierarchical segmentations and ultrametric watersheds
 JMIV
, 2010
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A Multichannel EdgeWeighted Centroidal Voronoi Tessellation Algorithm for 3D Superalloy Image Segmentation
"... In material science and engineering, the grain structure inside a superalloy sample determines its mechanical and physical properties. In this paper, we develop a new Multichannel EdgeWeighted Centroidal Voronoi Tessellation (MCEWCVT) algorithm to automatically segment all the 3D grains from micro ..."
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Cited by 16 (7 self)
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In material science and engineering, the grain structure inside a superalloy sample determines its mechanical and physical properties. In this paper, we develop a new Multichannel EdgeWeighted Centroidal Voronoi Tessellation (MCEWCVT) algorithm to automatically segment all the 3D grains from microscopic images of a superalloy sample. Built upon the classical kmeans/CVT algorithm, the proposed algorithm considers both the voxelintensity similarity within each cluster and the compactness of each cluster. In addition, the same slice of a superalloy sample can produce multiple images with different grain appearances using different settings of the microscope. We call this multichannel imaging and in this paper, we further adapt the proposed segmentation algorithm to handle such multichannel images to achieve higher grainsegmentation accuracy. We test the proposed MCEWCVT algorithm on a 4channel Nibased 3D superalloy image consisting of 170 slices. The segmentation performance is evaluated against the manually annotated groundtruth segmentation and quantitatively compared with other six image segmentation/edgedetection methods. The experimental results demonstrate the higher accuracy of the proposed algorithm than the comparison methods. 1.
Ultrametric Watersheds
, 2009
"... We study hierachical segmentation in the framework of edgeweighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical edgesegmentations. Sep 2011 ..."
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Cited by 7 (6 self)
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We study hierachical segmentation in the framework of edgeweighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical edgesegmentations. Sep 2011
Morphological filtering on graphs
, 2013
"... We study some basic morphological operators acting on the lattice of all subgraphs of an arbitrary (unweighted) graph G. To this end, we consider two dual adjunctions between the edge set and the vertex set of G. This allows us (i) to recover the classical notion of a dilation/erosion of a subset of ..."
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Cited by 5 (2 self)
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We study some basic morphological operators acting on the lattice of all subgraphs of an arbitrary (unweighted) graph G. To this end, we consider two dual adjunctions between the edge set and the vertex set of G. This allows us (i) to recover the classical notion of a dilation/erosion of a subset of the vertices of G and(ii) to extend it to subgraphs of G. Afterward, we propose several new openings, closings, granulometries and alternate filters acting (i) on the subsets of the edge and vertex set of G and (ii) on the subgraphs of G. The proposed framework is then extended to functions that weight the vertices and edges of a graph. We illustrate with applications to binary and grayscale image denoising, for which, on the provided images, the proposed approach outperforms the usual one based on structuring elements.
Grain Segmentation of 3D Superalloy Images Using Multichannel EWCVT under Human Annotation Constraints
"... Abstract. Grain segmentation on 3D superalloy images provides superalloy’s microstructures, based on which many physical and mechanical properties can be evaluated. This is a challenging problem in senses of (1) the number of grains in a superalloy sample could be thousands or even more; (2) the in ..."
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Cited by 4 (2 self)
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Abstract. Grain segmentation on 3D superalloy images provides superalloy’s microstructures, based on which many physical and mechanical properties can be evaluated. This is a challenging problem in senses of (1) the number of grains in a superalloy sample could be thousands or even more; (2) the intensity within a grain may not be homogeneous; and (3) superalloy images usually contains carbides and noises. Recently, the Multichannel EdgeWeighted Centroid Voronoi Tessellation (MCEWCVT) algorithm [1] was developed for grain segmentation and showed better performance than many widely used image segmentation algorithms. However, as a generalpurpose clustering algorithm, MCEWCVT does not consider possible prior knowledge from material scientists in the process of grain segmentation. In this paper, we address this issue by defining an energy minimization problem which subject to certain constraints. Then we develop a Constrained Multichannel EdgeWeighted Centroid Voronoi Tessellation (CMEWCVT) algorithm to effectively solve this constrained minimization problem. In particular, manually annotated segmentation on a very small set of 2D slices are taken as constraints and incorporated into the whole clustering process. Experimental results demonstrate that the proposed CMEWCVT algorithm significantly improve the previous grainsegmentation performance. 1
Ultrametric watersheds: a bijection theorem for hierarchical edgesegmentation
"... Abstract. We study hierachical segmentation in the framework of edgeweighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical edgesegmentations. We end t ..."
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Cited by 4 (3 self)
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Abstract. We study hierachical segmentation in the framework of edgeweighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical edgesegmentations. We end this paper by showing how the proposed framework allows to see constrained connectivity as a classical watershedbased morphological scheme, which provides an efficient algorithm to compute the whole hierarchy.
Elucidating the relations among seeded image segmentation methods and their possible extensions
 IN PROCEEDINGS OF SIBGRAPI
, 2011
"... Many image segmentation algorithms have been proposed, specially for the case of binary segmentation (object/background) in which hard constraints (seeds) are provided interactively. Recently, several theoretical efforts were made in an attempt to unify their presentation and clarify their relatio ..."
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Cited by 2 (1 self)
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Many image segmentation algorithms have been proposed, specially for the case of binary segmentation (object/background) in which hard constraints (seeds) are provided interactively. Recently, several theoretical efforts were made in an attempt to unify their presentation and clarify their relations. These relations are usually pointed out textually or depicted in the form of a table of parameters of a general energy formulation. In this work we introduce a more general diagram representation which captures the connections among the methods, by means of conventional relations from set theory. We formally instantiate several methods under this diagram, including graph cuts, power watersheds, fuzzy connectedness, grow cut, distance cuts, and others, which are usually presented as unrelated methods. The proposed diagram representation leads to a more elucidated view of the methods, being less restrictive than the tabular representation. It includes new relations among methods, besides bringing together the connections gathered from different works. It also points out some promising unexplored intermediate regions, which can lead to possible extensions of the existing methods. We also demonstrate one of such possible extensions, which is used to effectively combine the strengths of region and local contrast features.