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50
What energy functions can be minimized via graph cuts
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2004
"... Abstract—In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph construction ..."
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Cited by 699 (21 self)
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Abstract—In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph constructions are complex and highly specific to a particular energy function, graph cuts have seen limited application to date. In this paper, we give a characterization of the energy functions that can be minimized by graph cuts. Our results are restricted to functions of binary variables. However, our work generalizes many previous constructions and is easily applicable to vision problems that involve large numbers of labels, such as stereo, motion, image restoration, and scene reconstruction. We give a precise characterization of what energy functions can be minimized using graph cuts, among the energy functions that can be written as a sum of terms containing three or fewer binary variables. We also provide a generalpurpose construction to minimize such an energy function. Finally, we give a necessary condition for any energy function of binary variables to be minimized by graph cuts. Researchers who are considering the use of graph cuts to optimize a particular energy function can use our results to determine if this is possible and then follow our construction to create the appropriate graph. A software implementation is freely available.
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 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].
Interactive Graph Cut Based Segmentation With Shape Priors
 IN CVPR, PAGES I: 755–762
, 2005
"... ... alternative to pure automatic segmentation in many applications. While automatic segmentation can be very challenging, a small amount of user input can often resolve ambiguous decisions on the part of the algorithm. In this work, we devise a graph cut algorithm for interactive segmentation which ..."
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Cited by 59 (0 self)
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... alternative to pure automatic segmentation in many applications. While automatic segmentation can be very challenging, a small amount of user input can often resolve ambiguous decisions on the part of the algorithm. In this work, we devise a graph cut algorithm for interactive segmentation which incorporates shape priors. While traditional graph cut approaches to interactive segmentation are often quite successful, they may fail in cases where there are diffuse edges, or multiple similar objects in close proximity to one another. Incorporation of shape priors within this framework mitigates these problems. Positive results on both medical and natural images are demonstrated.
Multilabel Random Walker Image Segmentation Using Prior Models
 In: IEEE Comp. Soc. Conf. Comp. Vision Pattern Recog
, 2005
"... The recently introduced random walker segmentation algorithm of [14] has been shown to have desirable theoretical properties and to perform well on a wide variety of images in practice. However, this algorithm requires userspecified labels and produces a segmentation where each segment is connected ..."
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Cited by 40 (4 self)
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The recently introduced random walker segmentation algorithm of [14] has been shown to have desirable theoretical properties and to perform well on a wide variety of images in practice. However, this algorithm requires userspecified labels and produces a segmentation where each segment is connected to a labeled pixel. We show that incorporation of a nonparametric probability density model allows for an extended random walkers algorithm that can locate disconnected objects and does not require userspecified labels. Finally, we show that this formulation leads to a deep connection with the popular graph cuts method of [8, 24]. 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 40 (4 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.
TVSeg  interactive total variation based image segmentation
 IN: BRITISH MACHINE VISION CONFERENCE (BMVC
, 2008
"... Interactive object extraction is an important part in any image editing software. We present a two step segmentation algorithm that first obtains a binary segmentation and then applies matting on the border regions to obtain a smooth alpha channel. The proposed segmentation algorithm is based on the ..."
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Cited by 38 (15 self)
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Interactive object extraction is an important part in any image editing software. We present a two step segmentation algorithm that first obtains a binary segmentation and then applies matting on the border regions to obtain a smooth alpha channel. The proposed segmentation algorithm is based on the minimization of the Geodesic Active Contour energy. A fast Total Variation minimization algorithm is used to find the globally optimal solution. We show how user interaction can be incorporated and outline an efficient way to exploit color information. A novel matting approach, based on energy minimization, is presented. Experimental evaluations are discussed, and the algorithm is compared to state of the art object extraction algorithms. The GPU based binaries are available online.
Random walks for interactive alphamatting
 IN PROCEEDINGS OF VIIP 2005
, 2005
"... Interactive, efficient, methods of foreground extraction and alphamatting are of increasing practical importance for digital image editing. Although several new approaches to this problem have recently been developed, many challenges remain. We propose a new technique based on random walks that h ..."
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Cited by 37 (2 self)
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Interactive, efficient, methods of foreground extraction and alphamatting are of increasing practical importance for digital image editing. Although several new approaches to this problem have recently been developed, many challenges remain. We propose a new technique based on random walks that has the following advantages: First, by leveraging a recent technique from manifold learning theory, we effectively use RGB values to set boundaries for the random walker, even in fuzzy or lowcontrast images. Second, the algorithm is straightforward to implement, requires specification of only a single free parameter (set the same for all images), and performs the segmentation and alphamatting in a single step. Third, the user may locally fine tune the results by interactively manipulating the foreground/background maps. Finally, the algorithm has an inherit parallelism that leads to a particularly efficient implementation via the graphics processing unit (GPU). Our method processes a 1024 × 1024 image at the interactive speed of 0.5 seconds and, most importantly, produces highquality results. We show that our algorithm can generate good segmentation and matting results at an interactive rate with minimal user interaction.
Shape priors in variational image segmentation: Convexity, lipschitz continuity and globally optimal solutions
 In IEEE Int. Conf. on Comp. Vision and Patt. Recog
, 2008
"... In this work, we introduce a novel implicit representation of shape which is based on assigning to each pixel a probability that this pixel is inside the shape. This probabilistic representation of shape resolves two important drawbacks of alternative implicit shape representations such as the level ..."
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Cited by 21 (3 self)
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In this work, we introduce a novel implicit representation of shape which is based on assigning to each pixel a probability that this pixel is inside the shape. This probabilistic representation of shape resolves two important drawbacks of alternative implicit shape representations such as the level set method: Firstly, the space of shapes is convex in the sense that arbitrary convex combinations of a set of shapes again correspond to a valid shape. Secondly, we prove that the introduction of shape priors into variational image segmentation leads to functionals which are convex with respect to shape deformations. For a large class of commonly considered (spatially continuous) functionals, we prove that – under mild regularity assumptions – segmentation and tracking with statistical shape priors can be performed in a globally optimal manner. In experiments on tracking a walking person through a cluttered scene we demonstrate the advantage of global versus local optimality. 1.
An energy minimization approach to the data driven editing of presegmented images/volumes
 IN: MEDICAL IMAGE COMPUTING AND COMPUTERASSISTED INTERVENTION – MICCAI. VOLUME 4191
, 2006
"... Fully automatic, completely reliable segmentation in medical images is an unrealistic expectation with today’s technology. However, many automatic segmentation algorithms may achieve a nearcorrect solution, incorrect only in a small region. For these situations, an interactive editing tool is requ ..."
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Cited by 11 (1 self)
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Fully automatic, completely reliable segmentation in medical images is an unrealistic expectation with today’s technology. However, many automatic segmentation algorithms may achieve a nearcorrect solution, incorrect only in a small region. For these situations, an interactive editing tool is required, ideally in 3D, that is usually left to a manual correction. We formulate the editing task as an energy minimization problem that may be solved with a modified version of either graph cuts or the random walker 3D segmentation algorithms. Both algorithms employ a seeded user interface, that may be used in this scenario for a user to seed erroneous voxels as belonging to the foreground or the background. In our formulation, it is unnecessary for the user to specify both foreground and background seeds.
Bayesian Parallel Imaging With EdgePreserving Priors
 MAGNETIC RESONANCE IN MEDICINE
, 2007
"... Existing parallel MRI methods are limited by a fundamental tradeoff in that suppressing noise introduces aliasing artifacts. Bayesian methods with an appropriately chosen image prior offer a promising alternative; however, previous methods with spatial priors assume that intensities vary smoothly o ..."
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Cited by 9 (1 self)
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Existing parallel MRI methods are limited by a fundamental tradeoff in that suppressing noise introduces aliasing artifacts. Bayesian methods with an appropriately chosen image prior offer a promising alternative; however, previous methods with spatial priors assume that intensities vary smoothly over the entire image, resulting in blurred edges. Here we introduce an edgepreserving prior (EPP) that instead assumes that intensities are piecewise smooth, and propose a new approach to efficiently compute its Bayesian estimate. The estimation task is formulated as an optimization problem that requires a nonconvex objective function to be minimized in a space with thousands of dimensions. As a result, traditional continuous minimization methods cannot be applied. This optimization task is closely related to some problems in the field of computer vision for which discrete optimization methods have been developed in the last few years. We adapt these algorithms, which are based on graph cuts, to address our optimization problem. The results of several parallel imaging experiments on brain and torso regions performed under challenging conditions with high acceleration factors are shown and compared with the results of conventional sensitivity encoding (SENSE) methods. An empirical analysis indicates that the proposed method visually improves overall quality compared to conventional methods.