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269
An Experimental Comparison of MinCut/MaxFlow Algorithms for Energy Minimization in Vision
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2001
"... After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in lowlevel vision. The combinatorial optimization literature provides many mincut/maxflow algorithms with different polynomial time compl ..."
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Cited by 797 (48 self)
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After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in lowlevel vision. The combinatorial optimization literature provides many mincut/maxflow algorithms with different polynomial time complexity. Their practical efficiency, however, has to date been studied mainly outside the scope of computer vision. The goal of this paper
"GrabCut”  interactive foreground extraction using iterated graph cuts
 ACM TRANS. GRAPH
, 2004
"... The problem of efficient, interactive foreground/background segmentation in still images is of great practical importance in image editing. Classical image segmentation tools use either texture (colour) information, e.g. Magic Wand, or edge (contrast) information, e.g. Intelligent Scissors. Recently ..."
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Cited by 657 (31 self)
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The problem of efficient, interactive foreground/background segmentation in still images is of great practical importance in image editing. Classical image segmentation tools use either texture (colour) information, e.g. Magic Wand, or edge (contrast) information, e.g. Intelligent Scissors. Recently, an approach based on optimization by graphcut has been developed which successfully combines both types of information. In this paper we extend the graphcut approach in three respects. First, we have developed a more powerful, iterative version of the optimisation. Secondly, the power of the iterative algorithm is used to simplify substantially the user interaction needed for a given quality of result. Thirdly, a robust algorithm for “border matting ” has been developed to estimate simultaneously the alphamatte around an object boundary and the colours of foreground pixels. We show that for moderately difficult examples the proposed method outperforms competitive tools.
A comparative study of energy minimization methods for Markov random fields
 In ECCV
, 2006
"... Abstract. One of the most exciting advances in early vision has been the development of efficient energy minimization algorithms. Many early vision tasks require labeling each pixel with some quantity such as depth or texture. While many such problems can be elegantly expressed in the language of Ma ..."
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Cited by 241 (24 self)
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Abstract. One of the most exciting advances in early vision has been the development of efficient energy minimization algorithms. Many early vision tasks require labeling each pixel with some quantity such as depth or texture. While many such problems can be elegantly expressed in the language of Markov Random Fields (MRF’s), the resulting energy minimization problems were widely viewed as intractable. Recently, algorithms such as graph cuts and loopy belief propagation (LBP) have proven to be very powerful: for example, such methods form the basis for almost all the topperforming stereo methods. Unfortunately, most papers define their own energy function, which is minimized with a specific algorithm of their choice. As a result, the tradeoffs among different energy minimization algorithms are not well understood. In this paper we describe a set of energy minimization benchmarks, which we use to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods—graph cuts, LBP, and treereweighted message passing—as well as the wellknown older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching and interactive segmentation. We also provide a generalpurpose software interface that allows vision researchers to easily switch between optimization methods with minimal overhead. We expect that the availability of our benchmarks and interface will make it significantly easier for vision researchers to adopt the best method for their specific problems. Benchmarks, code, results and images are available at
Interactive Digital Photomontage
 ACM TRANS. GRAPH
, 2004
"... We describe an interactive, computerassisted framework for combining parts of a set of photographs into a single composite picture, a process we call "digital photomontage." Our framework makes use of two techniques primarily: graphcut optimization, to choose good seams within the constituent imag ..."
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Cited by 221 (17 self)
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We describe an interactive, computerassisted framework for combining parts of a set of photographs into a single composite picture, a process we call "digital photomontage." Our framework makes use of two techniques primarily: graphcut optimization, to choose good seams within the constituent images so that they can be combined as seamlessly as possible; and gradientdomain fusion, a process based on Poisson equations, to further reduce any remaining visible artifacts in the composite. Also central to the framework is a suite of interactive tools that allow the user to specify a variety of highlevel image objectives, either globally across the image, or locally through a paintingstyle interface. Image objectives are applied independently at each pixel location and generally involve a function of the pixel values (such as "maximum contrast") drawn from that same location in the set of source images. Typically, a user applies a series of image objectives iteratively in order to create a finished composite. The power of this framework lies in its generality; we show how it can be used for a wide variety of applications, including "selective composites" (for instance, group photos in which everyone looks their best), relighting, extended depth of field, panoramic stitching, cleanplate production, stroboscopic visualization of movement, and timelapse mosaics.
Computing geodesics and minimal surfaces via graph cuts
 in International Conference on Computer Vision
, 2003
"... Geodesic active contours and graph cuts are two standard image segmentation techniques. We introduce a new segmentation method combining some of their benefits. Our main intuition is that any cut on a graph embedded in some continuous space can be interpreted as a contour (in 2D) or a surface (in 3D ..."
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Cited by 180 (22 self)
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Geodesic active contours and graph cuts are two standard image segmentation techniques. We introduce a new segmentation method combining some of their benefits. Our main intuition is that any cut on a graph embedded in some continuous space can be interpreted as a contour (in 2D) or a surface (in 3D). We show how to build a grid graph and set its edge weights so that the cost of cuts is arbitrarily close to the length (area) of the corresponding contours (surfaces) for any anisotropic Riemannian metric. There are two interesting consequences of this technical result. First, graph cut algorithms can be used to find globally minimum geodesic contours (minimal surfaces in 3D) under arbitrary Riemannian metric for a given set of boundary conditions. Second, we show how to minimize metrication artifacts in existing graphcut based methods in vision. Theoretically speaking, our work provides an interesting link between several branches of mathematicsdifferential geometry, integral geometry, and combinatorial optimization. The main technical problem is solved using CauchyCrofton formula from integral geometry. 1.
Scene completion using millions of photographs
 ACM Transactions on Graphics (SIGGRAPH
, 2007
"... Figure 1: Given an input image with a missing region, we use matching scenes from a large collection of photographs to complete the image. What can you do with a million images? In this paper we present a new image completion algorithm powered by a huge database of photographs gathered from the Web. ..."
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Cited by 174 (10 self)
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Figure 1: Given an input image with a missing region, we use matching scenes from a large collection of photographs to complete the image. What can you do with a million images? In this paper we present a new image completion algorithm powered by a huge database of photographs gathered from the Web. The algorithm patches up holes in images by finding similar image regions in the database that are not only seamless but also semantically valid. Our chief insight is that while the space of images is effectively infinite, the space of semantically differentiable scenes is actually not that large. For many image completion tasks we are able to find similar scenes which contain image fragments that will convincingly complete the image. Our algorithm is entirely datadriven, requiring no annotations or labelling by the user. Unlike existing image completion methods, our algorithm can generate a diverse set of results for each input image and we allow users to select among them. We demonstrate the superiority of our algorithm over existing image completion approaches.
Seam carving for contentaware image resizing
 ACM Trans. Graph
, 2007
"... Figure 1: A seam is a connected path of low energy pixels in an image. On the left is the original image with one horizontal and one vertical seam. In the middle the energy function used in this example is shown (the magnitude of the gradient), along with the vertical and horizontal path maps used t ..."
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Cited by 163 (7 self)
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Figure 1: A seam is a connected path of low energy pixels in an image. On the left is the original image with one horizontal and one vertical seam. In the middle the energy function used in this example is shown (the magnitude of the gradient), along with the vertical and horizontal path maps used to calculate the seams. By automatically carving out seams to reduce image size, and inserting seams to extend it, we achieve contentaware resizing. The example on the top right shows our result of extending in one dimension and reducing in the other, compared to standard scaling on the bottom right. Effective resizing of images should not only use geometric constraints, but consider the image content as well. We present a simple image operator called seam carving that supports contentaware image resizing for both reduction and expansion. A seam is an optimal 8connected path of pixels on a single image from top to bottom, or left to right, where optimality is defined by an image energy function. By repeatedly carving out or inserting seams in one direction we can change the aspect ratio of an image. By applying these operators in both directions we can retarget the image to a new size. The selection and order of seams protect the content of the image, as defined by the energy function. Seam carving can also be used for image content enhancement and object removal. We support various visual saliency measures for defining the energy of an image, and can also include user input to guide the process. By storing the order of seams in an image we create multisize images, that are able to continuously change in real time to fit a given size.
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.
NearRegular Texture Analysis and Manipulation
, 2004
"... A nearregular texture deviates geometrically and photometrically from a regular congruent tiling. Although nearregular textures are ubiquitous in the manmade and natural world, they present computational challenges for state of the art texture analysis and synthesis algorithms. Using regular tili ..."
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Cited by 92 (12 self)
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A nearregular texture deviates geometrically and photometrically from a regular congruent tiling. Although nearregular textures are ubiquitous in the manmade and natural world, they present computational challenges for state of the art texture analysis and synthesis algorithms. Using regular tiling as our anchor point, and with userassisted lattice extraction, we can explicitly model the deformation of a nearregular texture with respect to geometry, lighting and color. We treat a deformation field both as a function that acts on a texture and as a texture that is acted upon, and develop a multimodal framework where each deformation field is subject to analysis, synthesis and manipulation. Using this formalization, we are able to construct simple parametric models to faithfully synthesize the appearance of a nearregular texture and purposefully control its regularity.
Minimizing nonsubmodular functions with graph cuts  a review
 TPAMI
, 2007
"... Optimization techniques based on graph cuts have become a standard tool for many vision applications. These techniques allow to minimize efficiently certain energy functions corresponding to pairwise Markov Random Fields (MRFs). Currently, there is an accepted view within the computer vision communi ..."
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Cited by 89 (6 self)
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Optimization techniques based on graph cuts have become a standard tool for many vision applications. These techniques allow to minimize efficiently certain energy functions corresponding to pairwise Markov Random Fields (MRFs). Currently, there is an accepted view within the computer vision community that graph cuts can only be used for optimizing a limited class of MRF energies (e.g. submodular functions). In this survey we review some results that show that graph cuts can be applied to a much larger class of energy functions (in particular, nonsubmodular functions). While these results are wellknown in the optimization community, to our knowledge they were not used in the context of computer vision and MRF optimization. We demonstrate the relevance of these results to vision on the problem of binary texture restoration.