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139
Interactive Graph Cuts for Optimal Boundary & Region Segmentation of Objects in ND Images
, 2001
"... In this paper we describe a new technique for general purpose interactive segmentation of Ndimensional images. The user marks certain pixels as “object” or “background” to provide hard constraints for segmentation. Additional soft constraints incorporate both boundary and region information. Graph ..."
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Cited by 1013 (20 self)
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In this paper we describe a new technique for general purpose interactive segmentation of Ndimensional images. The user marks certain pixels as “object” or “background” to provide hard constraints for segmentation. Additional soft constraints incorporate both boundary and region information. Graph cuts are used to find the globally optimal segmentation of the Ndimensional image. The obtained solution gives the best balance of boundary and region properties among all segmentations satisfying the constraints. The topology of our segmentation is unrestricted and both “object” and “background” segments may consist of several isolatedparts. Some experimental results are presented in the context ofphotohideo editing and medical image segmentation. We also demonstrate an interesting Gestalt example. A fast implementation of our segmentation method is possible via a new mar$ow algorithm in [2].
Graph Cuts and Efficient ND Image Segmentation
, 2006
"... Combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics. This paper focusses on possibly the simplest application of graphcuts: segmentation of objects in image data. Despite its simplicity, this application epitomizes the best features ..."
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Cited by 304 (7 self)
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Combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics. This paper focusses on possibly the simplest application of graphcuts: segmentation of objects in image data. Despite its simplicity, this application epitomizes the best features of combinatorial graph cuts methods in vision: global optima, practical efficiency, numerical robustness, ability to fuse a wide range of visual cues and constraints, unrestricted topological properties of segments, and applicability to ND problems. Graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes, geodesic active contours, and levelsets. The segmentation energies optimized by graph cuts combine boundary regularization with regionbased properties in the same fashion as MumfordShah style functionals. We present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s/t graph cuts. After the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in Boykov and Jolly (2001), this idea was widely studied in computer vision and graphics communities. We provide links to a large number of known extensions based on iterative parameter reestimation and learning, multiscale or hierarchical approaches, narrow bands, and other techniques for demanding photo, video, and medical applications.
A Seeded Image Segmentation Framework Unifying Graph Cuts And Random Walker Which Yields A New Algorithm
 ICCV
, 2007
"... In this work, we present a common framework for seeded image segmentation algorithms that yields two of the leading methods as special cases The Graph Cuts and the Random Walker algorithms. The formulation of this common framework naturally suggests a new, third, algorithm that we develop here. Spe ..."
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Cited by 96 (10 self)
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In this work, we present a common framework for seeded image segmentation algorithms that yields two of the leading methods as special cases The Graph Cuts and the Random Walker algorithms. The formulation of this common framework naturally suggests a new, third, algorithm that we develop here. Specifically, the former algorithms may be shown to minimize a certain energy with respect to either an ℓ1 or an ℓ2 norm. Here, we explore the segmentation algorithm defined by an ℓ ∞ norm, provide a method for the optimization and show that the resulting algorithm produces an accurate segmentation that demonstrates greater stability with respect to the number of seeds employed than either the Graph Cuts or Random Walker methods.
The image foresting transform: Theory, algorithms, and applications
 IEEE TPAMI
, 2004
"... The image foresting transform (IFT) is a graphbased approach to the design of image processing operators based on connectivity. It naturally leads to correct and efficient implementations and to a better understanding of how different operators relate to each other. We give here a precise definiti ..."
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Cited by 95 (31 self)
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The image foresting transform (IFT) is a graphbased approach to the design of image processing operators based on connectivity. It naturally leads to correct and efficient implementations and to a better understanding of how different operators relate to each other. We give here a precise definition of the IFT, and a procedure to compute it—a generalization of Dijkstra’s algorithm—with a proof of correctness. We also discuss implementation issues and illustrate the use of the IFT in a few applications.
Interactive organ segmentation using graph cuts
 In Medical Image Computing and ComputerAssisted Intervention
, 2000
"... Abstract. An Ndimensional image is divided into “object ” and “background” segments using a graph cut approach. A graph is formed by connecting all pairs of neighboring image pixels (voxels) by weighted edges. Certain pixels (voxels) have to be a priori identified as object or background seeds prov ..."
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Cited by 82 (1 self)
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Abstract. An Ndimensional image is divided into “object ” and “background” segments using a graph cut approach. A graph is formed by connecting all pairs of neighboring image pixels (voxels) by weighted edges. Certain pixels (voxels) have to be a priori identified as object or background seeds providing necessary clues about the image content. Our objective is to find the cheapest way to cut the edges in the graph so that the object seeds are completely separated from the background seeds. If the edge cost is a decreasing function of the local intensity gradient then the minimum cost cut should produce an object/background segmentation with compact boundaries along the high intensity gradient values in the image. An efficient, globally optimal solution is possible via standard mincut/maxflow algorithms for graphs with two terminals. We applied this technique to interactively segment organs in various 2D and 3D medical images. 1
Optimal surface segmentation in volumetric images  a graphtheoretic approach
 IEEE TRANS. PATTERN ANAL. MACHINE INTELL
, 2006
"... Efficient segmentation of globally optimal surfaces representing object boundaries in volumetric data sets is important and challenging in many medical image analysis applications. We have developed an optimal surface detection method capable of simultaneously detecting multiple interacting surfaces ..."
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Cited by 77 (5 self)
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Efficient segmentation of globally optimal surfaces representing object boundaries in volumetric data sets is important and challenging in many medical image analysis applications. We have developed an optimal surface detection method capable of simultaneously detecting multiple interacting surfaces, in which the optimality is controlled by the cost functions designed for individual surfaces and by several geometric constraints defining the surface smoothness and interrelations. The method solves the surface segmentation problem by transforming it into computing a minimum st cut in a derived arcweighted directed graph. The proposed algorithm has a loworder polynomial time complexity and is computationally efficient. It has been extensively validated on more than 300 computersynthetic volumetric images, 72 CTscanned data sets of differentsized plexiglas tubes, and tens of medical images spanning various imaging modalities. In all cases, the approach yielded highly accurate results. Our approach can be readily extended to higherdimensional image segmentation.
O(N) Implementation of the Fast Marching Algorithm
 Journal of Computational Physics
, 2005
"... In this note we present an implementation of the fast marching algorithm for solving Eikonal equations that reduces the original runtime from O(N log N) to linear. This lower runtime cost is obtained while keeping an error bound of the same order of magnitude as the original algorithm. This improv ..."
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Cited by 68 (11 self)
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In this note we present an implementation of the fast marching algorithm for solving Eikonal equations that reduces the original runtime from O(N log N) to linear. This lower runtime cost is obtained while keeping an error bound of the same order of magnitude as the original algorithm. This improvement is achieved introducing the straight forward untidy priority queue, obtained via a quantization of the priorities in the marching computation. We present the underlying framework, estimations on the error, and examples showing the usefulness of the proposed approach. Key words: Fast marching, HamiltonJacobi and Eikonal equations, distance functions, bucket sort, untidy priority queue.
The Ordered Queue And The Optimality Of The Watershed Approaches
 In Mathematical Morphology and its Applications to Image and Signal Processing
, 2000
"... This work reviews the watershed in the graph framework of a shortestpath forest problem using a lexicographic path cost formulation. This formulation reects the behavior of the ordered queuebased watershed algorithm. This algorithm is compared with our proposed shortestpath forest (IFT{Image Fore ..."
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Cited by 64 (23 self)
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This work reviews the watershed in the graph framework of a shortestpath forest problem using a lexicographic path cost formulation. This formulation reects the behavior of the ordered queuebased watershed algorithm. This algorithm is compared with our proposed shortestpath forest (IFT{Image Foresting Transform), concluding that the watershed is a special case of that. Recently many dierent watershed approaches are being used. We point out that in some cases the watershed algorithm does not keep the optimality of the shortestpath forest solution unless the IFT algorithm is used. The main dierence between the algorithms is related to permanently labeling a pixel when inserting or removing it from the queue. The watershed based on the pixel dissimilarity using IFT can segment onepixel width regions while keeping the optimality of the shortestpath forest solution.
Fast volume segmentation with simultaneous visualization using programmable graphics hardware
 in Proceedings of the IEEE Visualization
, 2003
"... ..."
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.