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71
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 ..."
Abstract

Cited by 657 (14 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].
Random walks for image segmentation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2006
"... Abstract—A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with userdefined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach on ..."
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Cited by 218 (18 self)
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Abstract—A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with userdefined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a highquality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs. Index Terms—Image segmentation, interactive segmentation, graph theory, random walks, combinatorial Dirichlet problem, harmonic functions, Laplace equation, graph cuts, boundary completion. Ç 1
Combining topdown and bottomup segmentation
 In Proceedings IEEE workshop on Perceptual Organization in Computer Vision, CVPR
, 2004
"... In this work we show how to combine bottomup and topdown approaches into a single figureground segmentation process. This process provides accurate delineation of object boundaries that cannot be achieved by either the topdown or bottomup approach alone. The topdown approach uses object represen ..."
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Cited by 149 (2 self)
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In this work we show how to combine bottomup and topdown approaches into a single figureground segmentation process. This process provides accurate delineation of object boundaries that cannot be achieved by either the topdown or bottomup approach alone. The topdown approach uses object representation learned from examples to detect an object in a given input image and provide an approximation to its figureground segmentation. The bottomup approach uses imagebased criteria to define coherent groups of pixels that are likely to belong together to either the figure or the background part. The combination provides a final segmentation that draws on the relative merits of both approaches: The result is as close as possible to the topdown approximation, but is also constrained by the bottomup process to be consistent with significant image discontinuities. We construct a global cost function that represents these topdown and bottomup requirements. We then show how the global minimum of this function can be efficiently found by applying the sumproduct algorithm. This algorithm also provides a confidence map that can be used to identify image regions where additional topdown or bottomup information may further improve the segmentation. Our experiments show that the results derived from the algorithm are superior to results given by a pure topdown or pure bottomup approach. The scheme has broad applicability, enabling the combined use of a range of existing bottomup and topdown segmentations. 1.
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 149 (5 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.
Alpha Estimation in Natural Images
, 2000
"... Many boundaries between objects in the world project onto curves in an image. However, boundaries involving natural objects (e.g., trees, hair, water, smoke) are often unworkable under this model because many pixels receive light from more than one object. We propose a technique for estimating alpha ..."
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Cited by 101 (0 self)
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Many boundaries between objects in the world project onto curves in an image. However, boundaries involving natural objects (e.g., trees, hair, water, smoke) are often unworkable under this model because many pixels receive light from more than one object. We propose a technique for estimating alpha, the proportion in which two colors mix to produce a color at the boundary. The technique extends blue screen matting to backgrounds that have almost arbitrary color distributions, though coarse knowledge of the boundary's location is required. Results show a number of different objects moved from one image to another while maintaining naturalism. 1. Introduction The popularity of imagebased rendering techniques has led to increased interest in extracting objects from one image to be placed in another. When boundaries are in focus and are well modeled by a set of edges meeting at corners, a reasonable effect can be obtained by cutting and pasting followed by a smoothing operation along t...
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 58 (9 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.
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 56 (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
Jetstream: Probabilistic contour extraction with particles
 Proc. of ICCV
, 2001
"... The problem of extracting continuous structures from noisy or cluttered images is a difficult one. Successful extraction depends critically on the ability to balance prior constraints on continuity and smoothness against evidence garnered from image analysis. Exact, deterministic optimisation algori ..."
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Cited by 47 (2 self)
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The problem of extracting continuous structures from noisy or cluttered images is a difficult one. Successful extraction depends critically on the ability to balance prior constraints on continuity and smoothness against evidence garnered from image analysis. Exact, deterministic optimisation algorithms, based on discretized functionals, suffer from severe limitations on the form of prior constraint that can be imposed tractably. This paper proposes a sequential MonteCarlo technique, termed JetStream, that enables constraints on curvature, corners, and contour parallelism to be mobilized, all of which are infeasible under exact optimization. The power of JetStream is demonstrated in two contexts: (1) interactive cutout in photoediting applications, and (2) the recovery of roads in aerial photographs. 1.
Random walks for interactive organ segmentation in two and three dimensions: Implementation and validation
 In MICCAI
, 2005
"... Abstract. A new approach to interactive segmentation based on random walks was recently introduced that shows promise for allowing physicians more flexibility to segment arbitrary objects in an image. This report has two goals: To introduce a novel computational method for applying the random walker ..."
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Cited by 24 (4 self)
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Abstract. A new approach to interactive segmentation based on random walks was recently introduced that shows promise for allowing physicians more flexibility to segment arbitrary objects in an image. This report has two goals: To introduce a novel computational method for applying the random walker algorithm in 2D/3D using the Graphics Processing Unit (GPU) and to provide quantitative validation studies of this algorithm relative to different targets, imaging modalities and interaction strategies. 1