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352
Fast approximate energy minimization via graph cuts
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when v ..."
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Cited by 2132 (62 self)
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In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when very large moves are allowed. The first move we consider is an αβswap: for a pair of labels α, β, this move exchanges the labels between an arbitrary set of pixels labeled α and another arbitrary set labeled β. Our first algorithm generates a labeling such that there is no swap move that decreases the energy. The second move we consider is an αexpansion: for a label α, this move assigns an arbitrary set of pixels the label α. Our second
What energy functions can be minimized via graph cuts?
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2004
"... 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 co ..."
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Cited by 1053 (23 self)
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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.
Pictorial Structures for Object Recognition
 IJCV
, 2003
"... In this paper we present a statistical framework for modeling the appearance of objects. Our work is motivated by the pictorial structure models introduced by Fischler and Elschlager. The basic idea is to model an object by a collection of parts arranged in a deformable configuration. The appearance ..."
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Cited by 819 (16 self)
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In this paper we present a statistical framework for modeling the appearance of objects. Our work is motivated by the pictorial structure models introduced by Fischler and Elschlager. The basic idea is to model an object by a collection of parts arranged in a deformable configuration. The appearance of each part is modeled separately, and the deformable configuration is represented by springlike connections between pairs of parts. These models allow for qualitative descriptions of visual appearance, and are suitable for generic recognition problems. We use these models to address the problem of detecting an object in an image as well as the problem of learning an object model from training examples, and present efficient algorithms for both these problems. We demonstrate the techniques by learning models that represent faces and human bodies and using the resulting models to locate the corresponding objects in novel images.
Shape modeling with front propagation: A level set approach
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... Abstract Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods ..."
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Cited by 804 (20 self)
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Abstract Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods and overcomes some of their limitations. Our techniques can be applied to model arbitrarily complex shapes, which include shapes with significant protrusions, and to situations where no a priori assumption about the object’s topology is made. A single instance of our model, when presented with an image having more than one object of interest, has the ability to split freely to represent each object. This method is based on the ideas developed by Osher and Sethian to model propagating solidhiquid interfaces with curvaturedependent speeds. The interface (front) is a closed, nonintersecting, hypersurface flowing along its gradient field with constant speed or a speed that depends on the curvature. It is moved by solving a “HamiltonJacob? ’ type equation written for a function in which the interface is a particular level set. A speed term synthesizpd from the image is used to stop the interface in the vicinity of object boundaries. The resulting equation of motion is solved by employing entropysatisfying upwind finite difference schemes. We present a variety of ways of computing evolving front, including narrow bands, reinitializations, and different stopping criteria. The efficacy of the scheme is demonstrated with numerical experiments on some synthesized images and some low contrast medical images. Index Terms Shape modeling, shape recovery, interface motion, level sets, hyperbolic conservation laws, HamiltonJacobi
Deformable models in medical image analysis: A survey
 Medical Image Analysis
, 1996
"... This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They hav ..."
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Cited by 591 (7 self)
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This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They have proven to be effective in segmenting, matching, and tracking anatomic structures by exploiting (bottomup) constraints derived from the image data together with (topdown) a priori knowledge about the location, size, and shape of these structures. Deformable models are capable of accommodating the significant variability of biological structures over time and across different individuals. Furthermore, they support highly intuitive interaction mechanisms that, when necessary, allow medical scientists and practitioners to bring their expertise to bear on the modelbased image interpretation task. This article reviews the rapidly expanding body of work on the development and application of deformable models to problems of fundamental importance in medical image analysis, includingsegmentation, shape representation, matching, and motion tracking.
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.
Intelligent Scissors for Image Composition
 In Computer Graphics, SIGGRAPH Proceedings
, 1995
"... We present a new, interactive tool called Intelligent Scissors which we use for image segmentation and composition. Fully automated segmentation is an unsolved problem, while manual tracing is inaccurate and laboriously unacceptable. However, Intelligent Scissors allow objects within digital images ..."
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Cited by 290 (8 self)
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We present a new, interactive tool called Intelligent Scissors which we use for image segmentation and composition. Fully automated segmentation is an unsolved problem, while manual tracing is inaccurate and laboriously unacceptable. However, Intelligent Scissors allow objects within digital images to be extracted quickly and accurately using simple gesture motions with a mouse. When the gestured mouse position comes in proximity to an object edge, a livewire boundary “snaps ” to, and wraps around the object of interest. Livewire boundary detection formulates discrete dynamic programming (DP) as a twodimensional graph searching problem. DP provides mathematically optimal boundaries while greatly reducing sensitivity to local noise or other intervening structures. Robustness is further enhanced with onthefly training which causes the boundary to adhere to the specific type of edge currently being followed, rather than simply the strongest edge in the neighborhood. Boundary cooling automatically freezes unchanging segments and automates input of additional seed points. Cooling also allows the user to be much more free with the gesture path, thereby increasing the efficiency and finesse with which boundaries can be extracted. Extracted objects can be scaled, rotated, and composited using livewire masks and spatial frequency equivalencing. Frequency equivalencing is performed by applying a Butterworth filter which matches the lowest frequency spectra to all other image components. Intelligent Scissors allow creation of convincing compositions from existing images while dramatically increasing the speed and precision with which objects can be extracted. 1.
Global Minimum for Active Contour Models: A Minimal Path Approach
, 1997
"... A new boundary detection approach for shape modeling is presented. It detects the global minimum of an active contour model’s energy between two end points. Initialization is made easier and the curve is not trapped at a local minimum by spurious edges. We modify the “snake” energy by including the ..."
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Cited by 236 (70 self)
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A new boundary detection approach for shape modeling is presented. It detects the global minimum of an active contour model’s energy between two end points. Initialization is made easier and the curve is not trapped at a local minimum by spurious edges. We modify the “snake” energy by including the internal regularization term in the external potential term. Our method is based on finding a path of minimal length in a Riemannian metric. We then make use of a new efficient numerical method to find this shortest path. It is shown that the proposed energy, though based only on a potential integrated along the curve, imposes a regularization effect like snakes. We explore the relation between the maximum curvature along the resulting contour and the potential generated from the image. The method is capable to close contours, given only one point on the objects’ boundary by using a topologybased saddle search routine. We show examples of our method applied to real aerial and medical images.
Efficient Matching of Pictorial Structures
 PROC. IEEE COMPUTER VISION AND PATTERN RECOGNITION CONF.
, 2000
"... A pictorial structure is a collection of parts arranged in a deformable configuration. Each part is represented using a simple appearance model and the deformable configuration is represented by springlike connections between pairs of parts. While pictorial structures were introduced a number of ye ..."
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Cited by 207 (11 self)
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A pictorial structure is a collection of parts arranged in a deformable configuration. Each part is represented using a simple appearance model and the deformable configuration is represented by springlike connections between pairs of parts. While pictorial structures were introduced a number of years ago, they have not been broadly applied to matching and recognition problems. This has been due in part to the computational difficulty of matching pictorial structures to images. In this paper we present an efficient algorithm for finding the best global match of a pictorial structure to an image. The running time of the algorithm is optimal and it it takes only a few seconds to match a model with five to ten parts. With this improved algorithm, pictorial structures provide a practical and powerful framework for qualitative descriptions of objects and scenes, and are suitable for many generic image recognition problems. We illustrate the approach using simple models of a person and a car.