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Random walks for image segmentation
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2006
"... 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 ..."
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Cited by 387 (21 self)
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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.
Isoperimetric graph partitioning for image segmentation
 IEEE TRANS. ON PAT. ANAL. AND MACH. INT
, 2006
"... Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an alternate idea that finds partitions with a small isoperimetric constant, requiring solution to a linear system rather than an eigenvector problem. This approach produces the high quality segmentations o ..."
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Cited by 74 (12 self)
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Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an alternate idea that finds partitions with a small isoperimetric constant, requiring solution to a linear system rather than an eigenvector problem. This approach produces the high quality segmentations of spectral methods, but with improved speed and stability.
The Piecewise Smooth MumfordShah Functional on an Arbitrary Graph
"... Abstract—The MumfordShah functional has had a major impact on a variety of image analysis problems including image segmentation and filtering and, despite being introduced over two decades ago, it is still in widespread use. Present day optimization of the MumfordShah functional is predominated by ..."
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Cited by 19 (8 self)
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Abstract—The MumfordShah functional has had a major impact on a variety of image analysis problems including image segmentation and filtering and, despite being introduced over two decades ago, it is still in widespread use. Present day optimization of the MumfordShah functional is predominated by active contour methods. Until recently, these formulations necessitated optimization of the contour by evolving via gradient descent, which is known for its overdependence on initialization and the tendency to produce undesirable local minima. In order to reduce these problems, we reformulate the corresponding MumfordShah functional on an arbitrary graph and apply the techniques of combinatorial optimization to produce a fast, lowenergy solution. In contrast to traditional optimization methods, use of these combinatorial techniques necessitates consideration of the reconstructed image outside of its usual boundary, requiring additionally the inclusion of regularization for generating these values. The energy of the solution provided by this graph formulation is compared with the energy of the solution computed via traditional gradient descentbased narrowband level set methods. This comparison demonstrates that our graph formulation and optimization produces lower energy solutions than the traditional gradient descent based contour evolution methods in significantly less time. Finally, we demonstrate the usefulness of the graph formulation to apply the MumfordShah functional to new applications such as point clustering and filtering of nonuniformly sampled images. Index Terms—Level sets, active contours, piecewise smooth MumfordShah, combinatorial optimization, graph reformulation I.
GPUCuts: Combinatorial Optimisation, Graphic Processing Units and Adaptive Object Extraction
, 2005
"... Object extraction is a core component of computer vision with application to segmentation, tracking, etc. In this paper we propose a GPU graphbased approach to object segmentation. The main contributions of our approach consist of an adaptive, evolving schema to update to statistical properties of ..."
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Cited by 13 (0 self)
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Object extraction is a core component of computer vision with application to segmentation, tracking, etc. In this paper we propose a GPU graphbased approach to object segmentation. The main contributions of our approach consist of an adaptive, evolving schema to update to statistical properties of the object and the use of a local variant pushrelabel algorithm to recover the global minimum of the designed cost function. Furthermore, we propose the implementation of the method on a graphics processing unit where each node of the graph is considered as an independent processor that is connected with the neighborhood nodes. Such a schema recovers segmentation in an optimal and progressive manner. Promising experimental results and important decrease on the computational complexity demonstrate the potentials of our approach.
Isoperimetric graph partitioning for data clustering and image segmentation
 Boston University
, 2003
"... Spectral methods of graph partitioning have been shown to provide a powerful approach to the image segmentation problem. In this paper, we adopt a different approach, based on estimating the isoperimetric constant of an image graph. Our algorithm produces the high quality segmentations and data clus ..."
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Cited by 9 (1 self)
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Spectral methods of graph partitioning have been shown to provide a powerful approach to the image segmentation problem. In this paper, we adopt a different approach, based on estimating the isoperimetric constant of an image graph. Our algorithm produces the high quality segmentations and data clustering of spectral methods, but with improved speed and stability. 1
COMBINATORIAL CONTINUOUS MAXIMUM FLOW
, 2011
"... Maximum flow (and minimumcut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of applications such as image segmentation, stereo, image stitching an ..."
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Cited by 6 (2 self)
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Maximum flow (and minimumcut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of applications such as image segmentation, stereo, image stitching and texture synthesis. Algorithms based on the classical formulation of maxflow defined on a graph are known to exhibit metrication artefacts in the solution. Therefore, a recent trend has been to instead employ a spatially continuous maximum flow (or the dual mincut problem) in these same applications to produce solutions with no metrication errors. However, known fast continuous maxflow algorithms have no stopping criteria or have not been proved to converge. In this work, we revisit the continuous maxflow problem and show that the analogous discrete formulation is different from the classical maxflow problem. We then apply an appropriate combinatorial optimization technique to this combinatorial continuous maxflow (CCMF) problem to find a nulldivergence solution that exhibits no metrication artefacts and may be solved exactly by a fast, efficient algorithm with provable convergence. Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the fact, already proved by Nozawa in the continuous setting, that the maxflow and the total variation problems are not always equivalent.
unknown title
"... Abstract. Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cut algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of applications such as image segmentation, stereo, image st ..."
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Abstract. Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cut algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of applications such as image segmentation, stereo, image stitching, and texture synthesis. Algorithms based on the classical formulation of maxflow defined on a graph are known to exhibit metrication artifacts in the solution. Therefore, a recent trend has been to instead employ a spatially continuous maximum flow (or the dual mincut problem) in these same applications to produce solutions with no metrication errors. However, known fast continuous maxflow algorithms have no stopping criteria or have not been proved to converge. In this work, we revisit the continuous maxflow problem and show that the analogous discrete formulation is different from the classical maxflow problem. We then apply an appropriate combinatorial optimization technique to this combinatorial continuous maxflow (CCMF) problem to find a nulldivergence solution that exhibits no metrication artifacts and may be solved exactly by a fast, efficient algorithm with provable convergence. Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the fact, already proved by Nozawa in the continuous setting, that the maxflow and the total variation problems are not always equivalent.