@article{3173,
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 general-purpose 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.},
author = {Vladimir Kolmogorov and Zabih, Ramin},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
number = {2},
pages = {147 -- 159},
publisher = {IEEE},
title = {{What energy functions can be minimized via graph cuts? }},
doi = {10.1109/TPAMI.2004.1262177},
volume = {26},
year = {2004},
}
@inproceedings{3177,
abstract = {Feature space clustering is a popular approach to image segmentation, in which a feature vector of local properties (such as intensity, texture or motion) is computed at each pixel. The feature space is then clustered, and each pixel is labeled with the cluster that contains its feature vector. A major limitation of this approach is that feature space clusters generally lack spatial coherence (i.e., they do not correspond to a compact grouping of pixels). In this paper, we propose a segmentation algorithm that operates simultaneously in feature space and in image space. We define an energy function over both a set of clusters and a labeling of pixels with clusters. In our framework, a pixel is labeled with a single cluster (rather than, for example, a distribution over clusters). Our energy function penalizes clusters that are a poor fit to the data in feature space, and also penalizes clusters whose pixels lack spatial coherence. The energy function can be efficiently minimized using graph cuts. Our algorithm can incorporate both parametric and non-parametric clustering methods. It can be applied to many optimization-based clustering methods, including k-means and k-medians, and can handle models which are very close in feature space. Preliminary results are presented on segmenting real and synthetic images, using both parametric and non-parametric clustering.},
author = {Zabih, Ramin and Vladimir Kolmogorov},
pages = {437 -- 444},
publisher = {IEEE},
title = {{Spatially coherent clustering using graph cuts}},
doi = {10.1109/CVPR.2004.1315196},
volume = {2},
year = {2004},
}
@article{3178,
abstract = {Minimum cut/maximum flow algorithms on graphs have emerged as an increasingly useful tool for exactor approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow 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 is to provide an experimental comparison of the efficiency of min-cut/max flow algorithms for applications in vision. We compare the running times of several standard algorithms, as well as a new algorithm that we have recently developed. The algorithms we study include both Goldberg-Tarjan style "push -relabel" methods and algorithms based on Ford-Fulkerson style "augmenting paths." We benchmark these algorithms on a number of typical graphs in the contexts of image restoration, stereo, and segmentation. In many cases, our new algorithm works several times faster than any of the other methods, making near real-time performance possible. An implementation of our max-flow/min-cut algorithm is available upon request for research purposes.},
author = {Boykov, Yuri and Vladimir Kolmogorov},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
number = {9},
pages = {1124 -- 1137},
publisher = {IEEE},
title = {{An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision}},
doi = {10.1109/TPAMI.2004.60},
volume = {26},
year = {2004},
}
@inproceedings{3179,
abstract = {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 graph-cut has been developed which successfully combines both types of information. In this paper we extend the graph-cut 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 alpha-matte around an object boundary and the colours of foreground pixels. We show that for moderately difficult examples the proposed method outperforms competitive tools.},
author = {Rother, Carsten and Vladimir Kolmogorov and Blake, Andrew},
number = {3},
pages = {309 -- 314},
publisher = {ACM},
title = {{"GrabCut" - Interactive foreground extraction using iterated graph cuts }},
doi = {10.1145/1015706.1015720},
volume = {23},
year = {2004},
}
@inproceedings{3208,
abstract = {A new technique for proving the adaptive indistinguishability of two systems, each composed of some component systems, is presented, using only the fact that corresponding component systems are non-adaptively indistinguishable. The main tool is the definition of a special monotone condition for a random system F, relative to another random system G, whose probability of occurring for a given distinguisher D is closely related to the distinguishing advantage ε of D for F and G, namely it is lower and upper bounded by ε and (1+ln1), respectively.
A concrete instantiation of this result shows that the cascade of two random permutations (with the second one inverted) is indistinguishable from a uniform random permutation by adaptive distinguishers which may query the system from both sides, assuming the components’ security only against non-adaptive one-sided distinguishers.
As applications we provide some results in various fields as almost k-wise independent probability spaces, decorrelation theory and computational indistinguishability (i.e., pseudo-randomness).},
author = {Maurer, Ueli M and Krzysztof Pietrzak},
pages = {410 -- 427},
publisher = {Springer},
title = {{Composition of random systems: When two weak make one strong}},
doi = {10.1007/978-3-540-24638-1_23},
volume = {2951},
year = {2004},
}