@conference {Kluger2020,
	title = {CONSAC: Robust Multi-Model Fitting by Conditional Sample Consensus},
	booktitle = {CVPR 2020},
	year = {2020},
	month = {01/2020},
	abstract = {We present a robust estimator for fitting multiple parametric models of the same form to noisy measurements. Applications include finding multiple vanishing points in man-made scenes, fitting planes to architectural imagery, or estimating multiple rigid motions within the same sequence. In contrast to previous works, which resorted to hand-crafted search strategies for multiple model detection, we learn the search strategy from data. A neural network conditioned on previously detected models guides a RANSAC estimator to different subsets of all measurements, thereby finding model instances one after another. We train our method supervised as well as self-supervised. For supervised training of the search strategy, we contribute a new dataset for vanishing point estimation. Leveraging this dataset, the proposed algorithm is superior with respect to other robust estimators as well as to designated vanishing point estimation algorithms. For self-supervised learning of the search, we evaluate the proposed algorithm on multi-homography estimation and demonstrate an accuracy that is superior to state-of-the-art methods.},
	url = {http://arxiv.org/abs/2001.02643},
	author = {Kluger, Florian and Brachmann, Eric and Ackermann, Hanno and Carsten Rother and Yang, Michael Ying and Rosenhahn, Bodo}
}
@conference {Mackowiak2019,
	title = {CEREALS - Cost-Effective REgion-based Active Learning for Semantic Segmentation},
	booktitle = {British Machine Vision Conference 2018, BMVC 2018},
	year = {2019},
	abstract = {State of the art methods for semantic image segmentation are trained in a supervised fashion using a large corpus of fully labeled training images. However, gathering such a corpus is expensive, due to human annotation effort, in contrast to gathering unlabeled data. We propose an active learning-based strategy, called CEREALS, in which a human only has to hand-label a few, automatically selected, regions within an unlabeled image corpus. This minimizes human annotation effort while maximizing the performance of a semantic image segmentation method. The automatic selection procedure is achieved by: a) using a suitable information measure combined with an estimate about human annotation effort, which is inferred from a learned cost model, and b) exploiting the spatial coherency of an image. The performance of CEREALS is demonstrated on Cityscapes, where we are able to reduce the annotation effort to 17\%, while keeping 95\% of the mean Intersection over Union (mIoU) of a model that was trained with the fully annotated training set of Cityscapes.},
	author = {Mackowiak, Radek and Lenz, Philip and Ghori, Omair and Ferran Diego and Lange, Oliver and Carsten Rother}
}
@article {Arnab2018,
	title = {Conditional Random Fields Meet Deep Neural Networks for Semantic Segmentation},
	journal = {Cvpr},
	volume = {XX},
	number = {Xx},
	year = {2018},
	pages = {1{\textendash}15},
	abstract = {{\textemdash}Semantic Segmentation is the task of labelling every pixel in an image with a pre-defined object category. It has numer-ous applications in scenarios where the detailed understanding of an image is required, such as in autonomous vehicles and medical diagnosis. This problem has traditionally been solved with probabilistic models known as Conditional Random Fields (CRFs) due to their ability to model the relationships between the pixels being predicted. However, Deep Neural Networks (DNNs) have recently been shown to excel at a wide range of computer vision problems due to their ability to learn rich feature representations automatically from data, as opposed to traditional hand-crafted features. The idea of combining CRFs and DNNs have achieved state-of-the-art results in a number of domains. We review the literature on combining the modelling power of CRFs with the representation-learning ability of DNNs, ranging from early work that combines these two techniques as independent stages of a common pipeline to recent approaches that embed inference of probabilistic models directly in the neural network itself. Finally, we summarise future research directions.},
	keywords = {conditional random fields, deep learning, seman-},
	url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.308.8889\&rep=rep1\&type=pdf\%0Ahttp://dx.doi.org/10.1109/CVPR.2012.6248050},
	author = {Arnab, Anurag and Zheng, Shuai and Jayasumana, Sadeep and Romera-paredes, Bernardino and Kirillov, Alexander and Savchynskyy, Bogdan and Carsten Rother and Kahl, Fredrik and Torr, Philip}
}
@conference {Schlesinger2017,
	title = {Crowd sourcing image segmentation with iaSTAPLE},
	booktitle = {Proceedings - International Symposium on Biomedical Imaging},
	year = {2017},
	pages = {401{\textendash}405},
	abstract = {We propose a novel label fusion technique as well as a crowdsourcing protocol to efficiently obtain accurate epithelial cell segmentations from non-expert crowd workers. Our label fusion technique simultaneously estimates the true segmentation, the performance levels of individual crowd workers, and an image segmentation model in the form of a pairwise Markov random field. We term our approach image-aware STAPLE (iaSTAPLE) since our image segmentation model seamlessly integrates into the well-known and widely used STAPLE approach. In an evaluation on a light microscopy dataset containing more than 5000 membrane labeled epithelial cells of a fly wing, we show that iaSTAPLE outperforms STAPLE in terms of segmentation accuracy as well as in terms of the accuracy of estimated crowd worker performance levels, and is able to correctly segment 99\% of all cells when compared to expert segmentations. These results show that iaSTAPLE is a highly useful tool for crowd sourcing image segmentation.},
	keywords = {Crowdsourcing, Epithelial cell segmentation, IaSTAPLE, Markovian Random Fields},
	isbn = {9781509011711},
	issn = {19458452},
	doi = {10.1109/ISBI.2017.7950547},
	author = {Schlesinger, Dmitrij and Jug, Florian and Myers, Gene and Carsten Rother and Kainmueller, Dagmar}
}
@conference {Mustikovela2016,
	title = {Can ground truth label propagation from video help semantic segmentation?},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {9915 LNCS},
	year = {2016},
	pages = {804{\textendash}820},
	abstract = {For state-of-the-art semantic segmentation task, training convolutional neural networks (CNNs) requires dense pixelwise ground truth (GT) labeling, which is expensive and involves extensive human effort. In this work, we study the possibility of using auxiliary ground truth, so-called pseudo ground truth (PGT) to improve the performance. The PGT is obtained by propagating the labels of a GT frame to its subsequent frames in the video using a simple CRF-based, cue integration framework. Our main contribution is to demonstrate the use of noisy PGT along with GT to improve the performance of a CNN. We perform a systematic analysis to find the right kind of PGT that needs to be added along with the GT for training a CNN. In this regard, we explore three aspects of PGT which influence the learning of a CNN: (i) the PGT labeling has to be of good quality; (ii) the PGT images have to be different compared to the GT images; (iii) the PGT has to be trusted differently than GT. We conclude that PGT which is diverse from GT images and has good quality of labeling can indeed help improve the performance of a CNN. Also, when PGT is multiple folds larger than GT, weighing down the trust on PGT helps in improving the accuracy. Finally, We show that using PGT along with GT, the performance of Fully Convolutional Network (FCN) on Camvid data is increased by 2.7\% on IoU accuracy. We believe such an approach can be used to train CNNs for semantic video segmentation where sequentially labeled image frames are needed. To this end, we provide recommendations for using PGT strategically for semantic segmentation and hence bypass the need for extensive human efforts in labeling.},
	isbn = {9783319494081},
	issn = {16113349},
	doi = {10.1007/978-3-319-49409-8_66},
	author = {Mustikovela, Siva Karthik and Yang, Michael Ying and Carsten Rother}
}
@conference {Royer2016,
	title = {Convexity shape constraints for image segmentation},
	booktitle = {Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition},
	volume = {2016-Decem},
	year = {2016},
	month = {sep},
	pages = {402{\textendash}410},
	abstract = {Segmenting an image into multiple components is a central task in computer vision. In many practical scenarios, prior knowledge about plausible components is available. Incorporating such prior knowledge into models and algorithms for image segmentation is highly desirable, yet can be non-trivial. In this work, we introduce a new approach that allows, for the first time, to constrain some or all components of a segmentation to have convex shapes. Specifically, we extend the Minimum Cost Multicut Problem by a class of constraints that enforce convexity. To solve instances of this NP-hard integer linear program to optimality, we separate the proposed constraints in the branch-and-cut loop of a state-of-the-art ILP solver. Results on photographs and micrographs demonstrate the effectiveness of the approach as well as its advantages over the state-of-the-art heuristic.},
	isbn = {9781467388504},
	issn = {10636919},
	doi = {10.1109/CVPR.2016.50},
	url = {http://arxiv.org/abs/1509.02122},
	author = {Royer, Loic A. and Richmond, David L. and Carsten Rother and Bj{\"o}rn Andres and Kainmueller, Dagmar}
}
@article {kappes_15_comparative,
	title = {A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems},
	journal = {International Journal of Computer Vision},
	year = {2015},
	note = {1},
	pages = {1-30},
	doi = {10.1007/s11263-015-0809-x},
	author = {J{\"o}rg H. Kappes and Bj{\"o}rn Andres and Fred A. Hamprecht and Christoph Schn{\"o}rr and Nowozin, S. and Dhruv Batra and Kim, S. and Bernhard X. Kausler and Thorben Kr{\"o}ger and Lellmann, J. and Komodakis, N. and Savchynskyy, B. and Carsten Rother}
}
@article {Kappes2015,
	title = {A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems},
	journal = {Int.~J.~Comp.~Vision},
	year = {2015},
	note = {in press (preprint: arXiv:1404.0533)},
	author = {J{\"o}rg H. Kappes and Bj{\"o}rn Andres and Fred A. Hamprecht and Christoph Schn{\"o}rr and Nowozin, S. and Dhruv Batra and Kim, S. and Bernhard X. Kausler and Thorben Kr{\"o}ger and Lellmann, J. and Komodakis, N. and Savchynskyy, B. and Carsten Rother}
}
@article {Kappes2015b,
	title = {A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems},
	journal = {International Journal of Computer Vision},
	volume = {115},
	number = {2},
	year = {2015},
	pages = {155{\textendash}184},
	abstract = {Szeliski et al. published an influential study in 2006 on energy minimization methods for Markov random fields. This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the phenomenal success of random field models means that the kinds of inference problems that have to be solved changed significantly. Specifically, the models today often include higher order interactions, flexible connectivity structures, large label-spaces of different cardinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of more than 27 state-of-the-art optimization techniques on a corpus of 2453 energy minimization instances from diverse applications in computer vision. To ensure reproducibility, we evaluate all methods in the OpenGM 2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types.},
	keywords = {Benchmark, Combinatorial optimization, Discrete graphical models},
	issn = {15731405},
	doi = {10.1007/s11263-015-0809-x},
	author = {Kappes, J{\"o}rg H and Bj{\"o}rn Andres and Fred A. Hamprecht and Christoph Schn{\"o}rr and Nowozin, Sebastian and Dhruv Batra and Kim, Sungwoong and Kausler, Bernhard X and Kr{\"o}ger, Thorben and Lellmann, Jan and Komodakis, Nikos and Savchynskyy, Bogdan and Carsten Rother}
}
@article {Kappes2015a,
	title = {A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems},
	journal = {International Journal of Computer Vision},
	volume = {115},
	number = {2},
	year = {2015},
	pages = {155{\textendash}184},
	abstract = {Szeliski et al. published an influential study in 2006 on energy minimization methods for Markov random fields. This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the phenomenal success of random field models means that the kinds of inference problems that have to be solved changed significantly. Specifically, the models today often include higher order interactions, flexible connectivity structures, large label-spaces of different cardinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of more than 27 state-of-the-art optimization techniques on a corpus of 2453 energy minimization instances from diverse applications in computer vision. To ensure reproducibility, we evaluate all methods in the OpenGM 2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types.},
	keywords = {Benchmark, Combinatorial optimization, Discrete graphical models},
	isbn = {25164671.25},
	issn = {15731405},
	doi = {10.1007/s11263-015-0809-x},
	author = {Kappes, J{\"o}rg H and Bj{\"o}rn Andres and Fred A. Hamprecht and Christoph Schn{\"o}rr and Nowozin, Sebastian and Dhruv Batra and Kim, Sungwoong and Kausler, Bernhard X and Kr{\"o}ger, Thorben and Lellmann, Jan and Komodakis, Nikos and Savchynskyy, Bogdan and Carsten Rother}
}
@article {Kappes2015,
	title = {A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems},
	journal = {International Journal of Computer Vision},
	volume = {115},
	number = {2},
	year = {2015},
	pages = {155{\textendash}184},
	abstract = {Szeliski et al. published an influential study in 2006 on energy minimization methods for Markov random fields. This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the phenomenal success of random field models means that the kinds of inference problems that have to be solved changed significantly. Specifically, the models today often include higher order interactions, flexible connectivity structures, large label-spaces of different cardinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of more than 27 state-of-the-art optimization techniques on a corpus of 2453 energy minimization instances from diverse applications in computer vision. To ensure reproducibility, we evaluate all methods in the OpenGM 2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types.},
	keywords = {Benchmark, Combinatorial optimization, Discrete graphical models},
	issn = {15731405},
	doi = {10.1007/s11263-015-0809-x},
	url = {http://hci.iwr.uni-heidelberg.de/opengm2/},
	author = {Kappes, J{\"o}rg H and Bj{\"o}rn Andres and Fred A. Hamprecht and Christoph Schn{\"o}rr and Nowozin, Sebastian and Dhruv Batra and Kim, Sungwoong and Kausler, Bernhard X and Kr{\"o}ger, Thorben and Lellmann, Jan and Komodakis, Nikos and Savchynskyy, Bogdan and Carsten Rother}
}
@article {kappes_14_comparative,
	title = {A Comparative Study of Modern Inference Techniques for Structured
Discrete Energy Minimization Problems},
	journal = {CoRR},
	year = {2014},
	note = {1},
	url = {http://arxiv.org/abs/1404.0533},
	author = {J{\"o}rg H. Kappes and Bj{\"o}rn Andres and Fred A. Hamprecht and Christoph Schn{\"o}rr and Nowozin, S. and Dhruv Batra and Kim, S. and Bernhard X. Kausler and Thorben Kr{\"o}ger and Lellmann, J. and Komodakis, N. and Savchynskyy, B. and Carsten Rother}
}
@article {kappes-1014-bench-arxiv,
	title = {A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems},
	journal = {CoRR},
	volume = {abs/1404.0533},
	year = {2014},
	url = {http://hci.iwr.uni-heidelberg.de/opengm2/},
	author = {J{\"o}rg H. Kappes and Bj{\"o}rn Andres and Fred A. Hamprecht and Christoph Schn{\"o}rr and Nowozin, Sebastian and Dhruv Batra and Kim, Sungwoong and Bernhard X. Kausler and Thorben Kr{\"o}ger and Lellmann, Jan and Komodakis, Nikos and Savchynskyy, Bogdan and Carsten Rother}
}
@conference {kappes_13_comparative,
	title = {A Comparative Study of Modern Inference Techniques for Discrete Energy Minimization Problems},
	booktitle = {CVPR 2013. Proceedings},
	year = {2013},
	note = {1},
	doi = {10.1109/CVPR.2013.175},
	author = {J{\"o}rg H. Kappes and Bj{\"o}rn Andres and Fred A. Hamprecht and Christoph Schn{\"o}rr and Nowozin, S. and Dhruv Batra and Sungwoong, K. and Bernhard X. Kausler and Lellmann, J. and Komodakis, N. and Carsten Rother}
}
@conference {Kappes-2013-benchmark,
	title = {A Comparative Study of Modern Inference Techniques for Discrete Energy Minimization Problem},
	booktitle = {CVPR},
	year = {2013},
	author = {J{\"o}rg H. Kappes and Bj{\"o}rn Andres and Fred A. Hamprecht and Christoph Schn{\"o}rr and Nowozin, Sebastian and Dhruv Batra and Kim, Sungwoong and Bernhard X. Kausler and Lellmann, Jan and Komodakis, Nikos and Carsten Rother}
}
@conference {Shekhovtsov2012,
	title = {Curvature prior for MRF-based segmentation and shape inpainting},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {7476 LNCS},
	year = {2012},
	pages = {41{\textendash}51},
	abstract = {Most image labeling problems such as segmentation and image reconstruction are fundamentally ill-posed and suffer from ambiguities and noise. Higher-order image priors encode high-level structural dependencies between pixels and are key to overcoming these problems. However, in general these priors lead to computationally intractable models. This paper addresses the problem of discovering compact representations of higher-order priors which allow efficient inference. We propose a framework for solving this problem that uses a recently proposed representation of higher-order functions which are encoded as lower envelopes of linear functions. Maximum a Posterior inference on our learned models reduces to minimizing a pairwise function of discrete variables. We show that our framework can learn a compact representation that approximates a low curvature shape prior and demonstrate its effectiveness in solving shape inpainting and image segmentation problems. {\textcopyright} 2012 Springer-Verlag.},
	isbn = {9783642327162},
	issn = {03029743},
	doi = {10.1007/978-3-642-32717-9_5},
	author = {Shekhovtsov, Alexander and Kohli, Pushmeet and Carsten Rother}
}
@conference {Shekhovtsov2012a,
	title = {Curvature prior for MRF-based segmentation and shape inpainting},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {7476 LNCS},
	year = {2012},
	pages = {41{\textendash}51},
	abstract = {Most image labeling problems such as segmentation and image reconstruction are fundamentally ill-posed and suffer from ambiguities and noise. Higher-order image priors encode high-level structural dependencies between pixels and are key to overcoming these problems. However, in general these priors lead to computationally intractable models. This paper addresses the problem of discovering compact representations of higher-order priors which allow efficient inference. We propose a framework for solving this problem that uses a recently proposed representation of higher-order functions which are encoded as lower envelopes of linear functions. Maximum a Posterior inference on our learned models reduces to minimizing a pairwise function of discrete variables. We show that our framework can learn a compact representation that approximates a low curvature shape prior and demonstrate its effectiveness in solving shape inpainting and image segmentation problems. {\textcopyright} 2012 Springer-Verlag.},
	isbn = {9783642327162},
	issn = {03029743},
	doi = {10.1007/978-3-642-32717-9_5},
	url = {www.research.microsoft.com/vision/cambridge http://www.cs.ucl.ac.uk/staff/V.Kolmogorov/papers/StereoSegmentation_PAMI06.pdf\%5Cnpapers3://publication/uuid/F008E9F4-510D-4478-A3C0-1BFB22F6AEA0},
	author = {Shekhovtsov, Alexander and Kohli, Pushmeet and Carsten Rother}
}
@conference {Shekhovtsov2012b,
	title = {Curvature prior for MRF-based segmentation and shape inpainting},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {7476 LNCS},
	year = {2012},
	month = {sep},
	pages = {41{\textendash}51},
	abstract = {Most image labeling problems such as segmentation and image reconstruction are fundamentally ill-posed and suffer from ambiguities and noise. Higher-order image priors encode high-level structural dependencies between pixels and are key to overcoming these problems. However, in general these priors lead to computationally intractable models. This paper addresses the problem of discovering compact representations of higher-order priors which allow efficient inference. We propose a framework for solving this problem that uses a recently proposed representation of higher-order functions which are encoded as lower envelopes of linear functions. Maximum a Posterior inference on our learned models reduces to minimizing a pairwise function of discrete variables. We show that our framework can learn a compact representation that approximates a low curvature shape prior and demonstrate its effectiveness in solving shape inpainting and image segmentation problems. {\textcopyright} 2012 Springer-Verlag.},
	isbn = {9783642327162},
	issn = {03029743},
	doi = {10.1007/978-3-642-32717-9_5},
	url = {http://arxiv.org/abs/1109.1480},
	author = {Shekhovtsov, Alexander and Kohli, Pushmeet and Carsten Rother}
}
@conference {Vicente2010,
	title = {Cosegmentation revisited: Models and optimization},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {6312 LNCS},
	number = {PART 2},
	year = {2010},
	pages = {465{\textendash}479},
	abstract = {The problem of cosegmentation consists of segmenting the same object (or objects of the same class) in two or more distinct images. Recently a number of different models have been proposed for this problem. However, no comparison of such models and corresponding optimization techniques has been done so far. We analyze three existing models: the L1 norm model of Rother et al. [1], the L2 norm model of Mukherjee et al. [2] and the "reward" model of Hochbaum and Singh [3]. We also study a new model, which is a straightforward extension of the Boykov-Jolly model for single image segmentation [4]. In terms of optimization, we use a Dual Decomposition (DD) technique in addition to optimization methods in [1,2]. Experiments show a significant improvement of DD over published methods. Our main conclusion, however, is that the new model is the best overall because it: (i) has fewest parameters; (ii) is most robust in practice, and (iii) can be optimized well with an efficient EM-style procedure. {\textcopyright} 2010 Springer-Verlag.},
	isbn = {3642155510},
	issn = {16113349},
	doi = {10.1007/978-3-642-15552-9_34},
	author = {Vicente, Sara and Kolmogorov, Vladimir and Carsten Rother}
}
@article {Szeliski2008a,
	title = {A comparative study of energy minimization methods for Markov random fields with smoothness-based priors},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume = {30},
	number = {6},
	year = {2008},
	month = {jun},
	pages = {1068{\textendash}1080},
	abstract = {Among the most exciting advances in early vision has been the development of efficient energy minimization algorithms for pixel-labeling tasks such as depth or texture computation. It has been known for decades that such problems can be elegantly expressed as Markov random fields, yet the resulting energy minimization problems have been 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 top-performing stereo methods. However, the tradeoffs among different energy minimization algorithms are still not well understood. In this paper we describe a set of energy minimization benchmarks and use them to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods graph cuts, LBP, and tree-reweighted message passing in addition to the well-known older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching, interactive segmentation, and denoising. We also provide a general-purpose software interface that allows vision researchers to easily switch between optimization methods. Benchmarks, code, images, and results are available at http://vision.middlebury.edu/ MRF/. {\textcopyright} 2008 IEEE.},
	keywords = {Belief propagation, Global optimization, Graph Cuts, Markov random fields, Performance evaluation},
	issn = {01628828},
	doi = {10.1109/TPAMI.2007.70844},
	author = {Szeliski, Richard and Zabih, Ramin and Scharstein, Daniel and Veksler, Olga and Kolmogorov, Vladimir and Agarwala, Aseem and Tappen, Marshall and Carsten Rother}
}
@article {Szeliski2008,
	title = {A comparative study of energy minimization methods for Markov random fields with smoothness-based priors},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume = {30},
	number = {6},
	year = {2008},
	pages = {1068{\textendash}1080},
	publisher = {Springer-Verlag},
	abstract = {Among the most exciting advances in early vision has been the development of efficient energy minimization algorithms for pixel-labeling tasks such as depth or texture computation. It has been known for decades that such problems can be elegantly expressed as Markov random fields, yet the resulting energy minimization problems have been 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 top-performing stereo methods. However, the tradeoffs among different energy minimization algorithms are still not well understood. In this paper we describe a set of energy minimization benchmarks and use them to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods graph cuts, LBP, and tree-reweighted message passing in addition to the well-known older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching, interactive segmentation, and denoising. We also provide a general-purpose software interface that allows vision researchers to easily switch between optimization methods. Benchmarks, code, images, and results are available at http://vision.middlebury.edu/ MRF/. {\textcopyright} 2008 IEEE.},
	keywords = {Belief propagation, Global optimization, Graph Cuts, Markov random fields, Performance evaluation},
	issn = {01628828},
	doi = {10.1109/TPAMI.2007.70844},
	url = {http://vision.middlebury.edu/MRF.},
	author = {Szeliski, Richard and Zabih, Ramin and Scharstein, Daniel and Veksler, Olga and Kolmogorov, Vladimir and Agarwala, Aseem and Tappen, Marshall and Carsten Rother}
}
@conference {Kannan2007a,
	title = {Clustering appearance and shape by learning jigsaws},
	booktitle = {Advances in Neural Information Processing Systems},
	year = {2007},
	pages = {657{\textendash}664},
	abstract = {Patch-based appearance models are used in a wide range of computer vision applications. To learn such models it has previously been necessary to specify a suitable set of patch sizes and shapes by hand. In the jigsaw model presented here, the shape, size and appearance of patches are learned automatically from the repeated structures in a set of training images. By learning such irregularly shaped {\textquoteright}jigsaw pieces{\textquoteright}, we are able to discover both the shape and the appearance of object parts without supervision. When applied to face images, for example, the learned jigsaw pieces are surprisingly strongly associated with face parts of different shapes and scales such as eyes, noses, eyebrows and cheeks, to name a few. We conclude that learning the shape of the patch not only improves the accuracy of appearance-based part detection but also allows for shape-based part detection. This enables parts of similar appearance but different shapes to be distinguished; for example, while foreheads and cheeks are both skin colored, they have markedly different shapes.},
	isbn = {9780262195683},
	issn = {10495258},
	doi = {10.7551/mitpress/7503.003.0087},
	author = {Kannan, Anitha and Winn, John and Carsten Rother}
}
@conference {Kannan2007,
	title = {Clustering appearance and shape by learning jigsaws},
	booktitle = {Advances in Neural Information Processing Systems},
	year = {2007},
	pages = {657{\textendash}664},
	abstract = {Patch-based appearance models are used in a wide range of computer vision applications. To learn such models it has previously been necessary to specify a suitable set of patch sizes and shapes by hand. In the jigsaw model presented here, the shape, size and appearance of patches are learned automatically from the repeated structures in a set of training images. By learning such irregularly shaped {\textquoteright}jigsaw pieces{\textquoteright}, we are able to discover both the shape and the appearance of object parts without supervision. When applied to face images, for example, the learned jigsaw pieces are surprisingly strongly associated with face parts of different shapes and scales such as eyes, noses, eyebrows and cheeks, to name a few. We conclude that learning the shape of the patch not only improves the accuracy of appearance-based part detection but also allows for shape-based part detection. This enables parts of similar appearance but different shapes to be distinguished; for example, while foreheads and cheeks are both skin colored, they have markedly different shapes.},
	isbn = {9780262195683},
	issn = {10495258},
	doi = {10.7551/mitpress/7503.003.0087},
	author = {Kannan, Anitha and Winn, John and Carsten Rother}
}
@conference {Kolmogorov2006a,
	title = {Comparison of energy minimization algorithms for highly connected graphs},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {3952 LNCS},
	year = {2006},
	pages = {1{\textendash}15},
	abstract = {Algorithms for discrete energy minimization play a fundamental role for low-level vision. Known techniques include graph cuts, belief propagation (BP) and recently introduced tree-reweighted message passing (TRW). So far, the standard benchmark for their comparison has been a 4-connected grid-graph arising in pixel-labelling stereo. This minimization problem, however, has been largely solved: recent work shows that for many scenes TRW finds the global optimum. Furthermore, it is known that a 4-connecled grid-graph is a poor stereo model since it does not take occlusions into account. We propose the problem of stereo with occlusions as a new test bed for minimization algorithms. This is a more challenging graph since it has much larger connectivity, and it also serves as a better stereo model. An attractive feature of this problem is that increased connectivity does not result in increased complexity of message passing algorithms. Indeed, one contribution of this paper is to show that sophisticated implementations of BP and TRW have the same time and memory complexity as that of 4-connecled grid-graph stereo. The main conclusion of our experimental study is that for our problem graph cut outperforms both TRW and BP considerably. TRW achieves consistently a lower energy than BP. However, as connectivity increases the speed of convergence of TRW becomes slower. Unlike 4-connected grids, the difference between the energy of the best optimization method and the lower bound of TRW appears significant. This shows the hardness of the problem and motivates future research. {\textcopyright} Springer-Verlag Berlin Heidelberg 2006.},
	isbn = {3540338349},
	issn = {16113349},
	doi = {10.1007/11744047_1},
	author = {Kolmogorov, Vladimir and Carsten Rother}
}
@conference {Kolmogorov2006b,
	title = {Comparison of energy minimization algorithms for highly connected graphs},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {3952 LNCS},
	year = {2006},
	pages = {1{\textendash}15},
	abstract = {Algorithms for discrete energy minimization play a fundamental role for low-level vision. Known techniques include graph cuts, belief propagation (BP) and recently introduced tree-reweighted message passing (TRW). So far, the standard benchmark for their comparison has been a 4-connected grid-graph arising in pixel-labelling stereo. This minimization problem, however, has been largely solved: recent work shows that for many scenes TRW finds the global optimum. Furthermore, it is known that a 4-connecled grid-graph is a poor stereo model since it does not take occlusions into account. We propose the problem of stereo with occlusions as a new test bed for minimization algorithms. This is a more challenging graph since it has much larger connectivity, and it also serves as a better stereo model. An attractive feature of this problem is that increased connectivity does not result in increased complexity of message passing algorithms. Indeed, one contribution of this paper is to show that sophisticated implementations of BP and TRW have the same time and memory complexity as that of 4-connecled grid-graph stereo. The main conclusion of our experimental study is that for our problem graph cut outperforms both TRW and BP considerably. TRW achieves consistently a lower energy than BP. However, as connectivity increases the speed of convergence of TRW becomes slower. Unlike 4-connected grids, the difference between the energy of the best optimization method and the lower bound of TRW appears significant. This shows the hardness of the problem and motivates future research. {\textcopyright} Springer-Verlag Berlin Heidelberg 2006.},
	isbn = {3540338349},
	issn = {16113349},
	doi = {10.1007/11744047_1},
	author = {Kolmogorov, Vladimir and Carsten Rother}
}
@conference {Rother2006,
	title = {Cosegmentation of image pairs by histogram matching - Incorporating a global constraint into MRFs},
	booktitle = {Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition},
	volume = {1},
	year = {2006},
	pages = {994{\textendash}1000},
	abstract = {We introduce the term cosegmentation which denotes the task of segmenting simultaneously the common parts of an image pair. A generative model for cosegmentation is presented. Inference in the model leads to minimizing an energy with an MRF term encoding spatial coherency and a global constraint which attempts to match the appearance histograms of the common parts. This energy has not been proposed previously and its optimization is challenging and NP-hard. For this problem a novel optimization scheme which we call trust region graph cuts is presented. We demonstrate that this framework has the potential to improve a wide range of research: Object driven image retrieval, video tracking and segmentation, and interactive image editing. The power of the framework lies in its generality, the common part can be a rigid/non-rigid object (or scene), observed from different viewpoints or even similar objects of the same class. {\textcopyright} 2006 IEEE.},
	isbn = {0769525970},
	issn = {10636919},
	doi = {10.1109/CVPR.2006.91},
	url = {http://research.microsoft.com/vision/cambridge/},
	author = {Carsten Rother and Kolmogorov, Vladimir and Minka, Tom and Blake, Andrew}
}
