@conference {Marquez-Neila2014,
	title = {Non-parametric higher-order random fields for image segmentation},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {8694 LNCS},
	number = {PART 6},
	year = {2014},
	pages = {269{\textendash}284},
	abstract = {Models defined using higher-order potentials are becoming increasingly popular in computer vision. However, the exact representation of a general higher-order potential defined over many variables is computationally unfeasible. This has led prior works to adopt parametric potentials that can be compactly represented. This paper proposes a non-parametric higher-order model for image labeling problems that uses a patch-based representation of its potentials. We use the transformation scheme of [11, 25] to convert the higher-order potentials to a pair-wise form that can be handled using traditional inference algorithms. This representation is able to capture structure, geometrical and topological information of labels from training data and to provide more precise segmentations. Other tasks such as image denoising and reconstruction are also possible. We evaluate our method on denoising and segmentation problems with synthetic and real images. {\textcopyright} 2014 Springer International Publishing.},
	keywords = {biomedical image analysis, higher-order models, image denoising, Image segmentation, random fields, structured prediction},
	isbn = {9783319105987},
	issn = {16113349},
	doi = {10.1007/978-3-319-10599-4_18},
	author = {M{\'a}rquez-Neila, Pablo and Kohli, Pushmeet and Carsten Rother and Baumela, Luis}
}
@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}
}
@article {Kohli2012,
	title = {User-centric learning and evaluation of interactive segmentation systems},
	journal = {International Journal of Computer Vision},
	volume = {100},
	number = {3},
	year = {2012},
	month = {dec},
	pages = {261{\textendash}274},
	abstract = {Many successful applications of computer vision to image or video manipulation are interactive by nature. However, parameters of such systems are often trained neglecting the user. Traditionally, interactive systems have been treated in the same manner as their fully automatic counterparts. Their performance is evaluated by computing the accuracy of their solutions under some fixed set of user interactions. In this paper, we study the problem of evaluating and learning interactive segmentation systems which are extensively used in the real world. The key questions in this context are how to measure (1) the effort associated with a user interaction, and (2) the quality of the segmentation result as perceived by the user. We conduct a user study to analyze user behavior and answer these questions. Using the insights obtained from these experiments, we propose a framework to evaluate and learn interactive segmentation systems which brings the user in the loop. The framework is based on the use of an active robot user-a simulated model of a human user. We show how this approach can be used to evaluate and learn parameters of state-of-the-art interactive segmentation systems. We also show how simulated user models can be integrated into the popular max-margin method for parameter learning and propose an algorithm to solve the resulting optimisation problem. {\textcopyright} 2012 The Author(s).},
	keywords = {Image segmentation, Interactive systems, Learning},
	issn = {09205691},
	doi = {10.1007/s11263-012-0537-4},
	author = {Kohli, Pushmeet and Nickisch, Hannes and Carsten Rother and Rhemann, Christoph}
}
@article {Meister2012,
	title = {When can we use KinectFusion for ground truth acquisition?},
	journal = {Proc Workshop on \ldots},
	year = {2012},
	pages = {3{\textendash}8},
	abstract = {Abstract{\textemdash}KinectFusion is a method for real-time capture of dense 3D geometry of the physical environment using a depth sensor. The system allows capture of a large dataset of 3D scene reconstructions at very low cost. In this paper we discuss the properties of the ...$\backslash$n},
	url = {http://meshlab.sourceforge.net/ http://www.msr-waypoint.net/en-us/um/people/pkohli/papers/mikhrk_iros_dataset_2012.pdf\%5Cnpapers3://publication/uuid/2615CF9D-C632-4E39-B1C4-B32A4A5D339C},
	author = {Meister, Stephan and Izadi, Shahram and Kohli, Pushmeet and M H{\"a}mmerle}
}
@conference {Nowozin2011a,
	title = {Decision tree fields},
	booktitle = {Proceedings of the IEEE International Conference on Computer Vision},
	year = {2011},
	pages = {1668{\textendash}1675},
	abstract = {This paper introduces a new formulation for discrete image labeling tasks, the Decision Tree Field (DTF), that combines and generalizes random forests and conditional random fields (CRF) which have been widely used in computer vision. In a typical CRF model the unary potentials are derived from sophisticated random forest or boosting based classifiers, however, the pairwise potentials are assumed to (1) have a simple parametric form with a pre-specified and fixed dependence on the image data, and (2) to be defined on the basis of a small and fixed neighborhood. In contrast, in DTF, local interactions between multiple variables are determined by means of decision trees evaluated on the image data, allowing the interactions to be adapted to the image content. This results in powerful graphical models which are able to represent complex label structure. Our key technical contribution is to show that the DTF model can be trained efficiently and jointly using a convex approximate likelihood function, enabling us to learn over a million free model parameters. We show experimentally that for applications which have a rich and complex label structure, our model achieves excellent results. {\textcopyright} 2011 IEEE.},
	isbn = {9781457711015},
	doi = {10.1109/ICCV.2011.6126429},
	author = {Nowozin, Sebastian and Carsten Rother and Bagon, Shai and Sharp, Toby and Yao, Bangpeng and Kohli, Pushmeet}
}
@conference {Bleyer2011,
	title = {Object stereo Joint stereo matching and object segmentation},
	booktitle = {Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition},
	year = {2011},
	pages = {3081{\textendash}3088},
	abstract = {This paper presents a method for joint stereo matching and object segmentation. In our approach a 3D scene is represented as a collection of visually distinct and spatially coherent objects. Each object is characterized by three different aspects: a color model, a 3D plane that approximates the object{\textquoteright}s disparity distribution, and a novel 3D connectivity property. Inspired by Markov Random Field models of image segmentation, we employ object-level color models as a soft constraint, which can aid depth estimation in powerful ways. In particular, our method is able to recover the depth of regions that are fully occluded in one input view, which to our knowledge is new for stereo matching. Our model is formulated as an energy function that is optimized via fusion moves. We show high-quality disparity and object segmentation results on challenging image pairs as well as standard benchmarks. We believe our work not only demonstrates a novel synergy between the areas of image segmentation and stereo matching, but may also inspire new work in the domain of automatic and interactive object-level scene manipulation. {\textcopyright} 2011 IEEE.},
	isbn = {9781457703942},
	issn = {10636919},
	doi = {10.1109/CVPR.2011.5995581},
	author = {Bleyer, Michael and Carsten Rother and Kohli, Pushmeet and Scharstein, Daniel and Sinha, Sudipta}
}
@conference {Pletscher2011,
	title = {Putting MAP back on the map},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {6835 LNCS},
	year = {2011},
	pages = {111{\textendash}121},
	abstract = {Conditional Random Fields (CRFs) are popular models in computer vision for solving labeling problems such as image denoising. This paper tackles the rarely addressed but important problem of learning the full form of the potential functions of pairwise CRFs. We examine two popular learning techniques, maximum likelihood estimation and maximum margin training. The main focus of the paper is on models such as pairwise CRFs, that are simplistic (misspecified) and do not fit the data well. We empirically demonstrate that for misspecified models maximum-margin training with MAP prediction is superior to maximum likelihood estimation with any other prediction method. Additionally we examine the common belief that MLE is better at producing predictions matching image statistics. {\textcopyright} 2011 Springer-Verlag.},
	isbn = {9783642231223},
	issn = {03029743},
	doi = {10.1007/978-3-642-23123-0_12},
	author = {Pletscher, Patrick and Nowozin, Sebastian and Kohli, Pushmeet and Carsten Rother}
}
@conference {Pletscher2011a,
	title = {Putting MAP back on the map},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {6835 LNCS},
	year = {2011},
	pages = {111{\textendash}121},
	abstract = {Conditional Random Fields (CRFs) are popular models in computer vision for solving labeling problems such as image denoising. This paper tackles the rarely addressed but important problem of learning the full form of the potential functions of pairwise CRFs. We examine two popular learning techniques, maximum likelihood estimation and maximum margin training. The main focus of the paper is on models such as pairwise CRFs, that are simplistic (misspecified) and do not fit the data well. We empirically demonstrate that for misspecified models maximum-margin training with MAP prediction is superior to maximum likelihood estimation with any other prediction method. Additionally we examine the common belief that MLE is better at producing predictions matching image statistics. {\textcopyright} 2011 Springer-Verlag.},
	isbn = {9783642231223},
	issn = {03029743},
	doi = {10.1007/978-3-642-23123-0_12},
	author = {Pletscher, Patrick and Nowozin, Sebastian and Kohli, Pushmeet and Carsten Rother}
}
@conference {Rother2010,
	title = {Minimizing sparse higher order energy functions of discrete variables},
	year = {2010},
	pages = {1382{\textendash}1389},
	abstract = {Higher order energy functions have the ability to encode high level structural dependencies between pixels, which have been shown to be extremely powerful for image labeling problems. Their use, however, is severely hampered in practice by the intractable complexity of representing and minimizing such functions. We observed that higher order functions encountered in computer vision are very often {\textquotedblleft}sparse{\textquotedblright}, i.e. many labelings of a higher order clique are equally unlikely and hence have the same high cost. In this paper, we address the problem of minimizing such sparse higher order energy functions. Our method works by transforming the problem into an equivalent quadratic function minimization problem. The resulting quadratic function can be minimized using popular message passing or graph cut based algorithms for MAP inference. Although this is primarily a theoretical paper, it also shows how higher order functions can be used to obtain impressive results for the binary texture restoration problem.},
	doi = {10.1109/cvpr.2009.5206739},
	author = {Carsten Rother and Kohli, Pushmeet and Wei Feng and Jiaya Jia}
}
@conference {Rhemann2010,
	title = {A spatially varying PSF-based prior for alpha matting},
	booktitle = {Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition},
	year = {2010},
	pages = {2149{\textendash}2156},
	abstract = {In this paper we considerably improve on a state-of-theart alpha matting approach by incorporating a new prior which is based on the image formation process. In particular, we model the prior probability of an alpha matte as the convolution of a high-resolution binary segmentation with the spatially varying point spread function (PSF) of the camera. Our main contribution is a new and efficient deconvolution approach that recovers the prior model, given an approximate alpha matte. By assuming that the PSF is a kernel with a single peak, we are able to recover the binary segmentation with an MRF-based approach, which exploits flux and a new way of enforcing connectivity. The spatially varying PSF is obtained via a partitioning of the image into regions of similar defocus. Incorporating our new prior model into a state-of-the-art matting technique produces results that outperform all competitors, which we confirm using a publicly available benchmark. {\textcopyright}2010 IEEE.},
	isbn = {9781424469840},
	issn = {10636919},
	doi = {10.1109/CVPR.2010.5539894},
	author = {Rhemann, Christoph and Carsten Rother and Kohli, Pushmeet and Gelautz, Margrit}
}
@conference {Bleyer2010,
	title = {Surface stereo with soft segmentation},
	booktitle = {Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition},
	year = {2010},
	pages = {1570{\textendash}1577},
	abstract = {This paper proposes a new stereo model which encodes the simple assumption that the scene is composed of a few, smooth surfaces. A key feature of our model is the surface-based representation, where each pixel is assigned to a 3D surface (planes or B-splines). This representation enables several important contributions: Firstly, we formulate a higher-order prior which states that pixels of similar appearance are likely to belong to the same 3D surface. This enables to incorporate the very popular color segmentation constraint in a soft and principled way. Secondly, we use a global MDL prior to penalize the number of surfaces. Thirdly, we are able to incorporate, in a simple way, a prior which favors low curvature surfaces. Fourthly, we improve the asymmetric occlusion model by disallowing pixels of the same surface to occlude each other. Finally, we use the known fusion move approach which enables a powerful optimization of our model, despite the infinite number of possible labelings (surfaces). {\textcopyright}2010 IEEE.},
	isbn = {9781424469840},
	issn = {10636919},
	doi = {10.1109/CVPR.2010.5539783},
	author = {Bleyer, Michael and Carsten Rother and Kohli, Pushmeet}
}
@conference {Glocker2010,
	title = {TriangleFlow: Optical flow with triangulation-based higher-order likelihoods},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {6313 LNCS},
	number = {PART 3},
	year = {2010},
	pages = {272{\textendash}285},
	abstract = {We use a simple yet powerful higher-order conditional random field (CRF) to model optical flow. It consists of a standard photo-consistency cost and a prior on affine motions both modeled in terms of higher-order potential functions. Reasoning jointly over a large set of unknown variables provides more reliable motion estimates and a robust matching criterion. One of the main contributions is that unlike previous region-based methods, we omit the assumption of constant flow. Instead, we consider local affine warps whose likelihood energy can be computed exactly without approximations. This results in a tractable, so-called, higher-order likelihood function. We realize this idea by employing triangulation meshes which immensely reduce the complexity of the problem. Optimization is performed by hierarchical fusion moves and an adaptive mesh refinement strategy. Experiments show that we achieve high-quality motion fields on several data sets including the Middlebury optical flow database. {\textcopyright} 2010 Springer-Verlag.},
	isbn = {364215557X},
	issn = {16113349},
	doi = {10.1007/978-3-642-15558-1_20},
	url = {http://vision.middlebury.edu/flow/},
	author = {Glocker, Ben and Heibel, T. Hauke and Navab, Nassir and Kohli, Pushmeet and Carsten Rother}
}
@conference {Lempitsky2009,
	title = {Image segmentation with a bounding box prior},
	booktitle = {Proceedings of the IEEE International Conference on Computer Vision},
	year = {2009},
	pages = {277{\textendash}284},
	abstract = {User-provided object bounding box is a simple and popular interaction paradigm considered by many existing interactive image segmentation frameworks. However, these frameworks tend to exploit the provided bounding box merely to exclude its exterior from consideration and sometimes to initialize the energy minimization. In this paper, we discuss how the bounding box can be further used to impose a powerful topological prior, which prevents the solution from excessive shrinking and ensures that the user-provided box bounds the segmentation in a sufficiently tight way. The prior is expressed using hard constraints incorporated into the global energy minimization framework leading to an NP-hard integer program. We then investigate the possible optimization strategies including linear relaxation as well as a new graph cut algorithm called pinpointing. The latter can be used either as a rounding method for the fractional LP solution, which is provably better than thresholding-based rounding, or as a fast standalone heuristic. We evaluate the proposed algorithms on a publicly available dataset, and demonstrate the practical benefits of the new prior both qualitatively and quantitatively. {\textcopyright}2009 IEEE.},
	isbn = {9781424444205},
	doi = {10.1109/ICCV.2009.5459262},
	author = {Lempitsky, Victor and Kohli, Pushmeet and Carsten Rother and Sharp, Toby}
}
@conference {Rhemann2009b,
	title = {A perceptually motivated online benchmark for image matting},
	booktitle = {2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009},
	volume = {2009 IEEE},
	year = {2009},
	pages = {1826{\textendash}1833},
	abstract = {The availability of quantitative online benchmarks for low-level vision tasks such as stereo and optical flow has led to significant progress in the respective fields. This paper introduces such a benchmark for image matting. There are three key factors for a successful benchmarking system: (a) a challenging, high-quality ground truth test set; (b) an online evaluation repository that is dynamically updated with new results; (c) perceptually motivated error functions. Our new benchmark strives to meet all three criteria. We evaluated several matting methods with our benchmark and show that their performance varies depending on the error function. Also, our challenging test set reveals problems of existing algorithms, not reflected in previously reported results. We hope that our effort will lead to considerable progress in the field of image matting, and welcome the reader to visit our benchmark at www.alphamatting.com. {\textcopyright} 2009 IEEE.},
	isbn = {9781424439935},
	doi = {10.1109/CVPRW.2009.5206503},
	author = {Rhemann, Christoph and Carsten Rother and Wang, Jue and Gelautz, Margrit and Kohli, Pushmeet and Rott, Pamela}
}
@conference {Rhemann2009a,
	title = {A perceptually motivated online benchmark for image matting},
	booktitle = {2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009},
	volume = {2009 IEEE},
	year = {2009},
	pages = {1826{\textendash}1833},
	abstract = {The availability of quantitative online benchmarks for low-level vision tasks such as stereo and optical flow has led to significant progress in the respective fields. This paper introduces such a benchmark for image matting. There are three key factors for a successful benchmarking system: (a) a challenging, high-quality ground truth test set; (b) an online evaluation repository that is dynamically updated with new results; (c) perceptually motivated error functions. Our new benchmark strives to meet all three criteria. We evaluated several matting methods with our benchmark and show that their performance varies depending on the error function. Also, our challenging test set reveals problems of existing algorithms, not reflected in previously reported results. We hope that our effort will lead to considerable progress in the field of image matting, and welcome the reader to visit our benchmark at www.alphamatting.com. {\textcopyright} 2009 IEEE.},
	keywords = {Benchmark, Evaluation, Matting},
	isbn = {9781424439935},
	doi = {10.1109/CVPRW.2009.5206503},
	url = {www.alphamatting.com.},
	author = {Rhemann, Christoph and Carsten Rother and Wang, Jue and Gelautz, Margrit and Kohli, Pushmeet and Rott, Pamela}
}
@conference {Rhemann2009,
	title = {A perceptually motivated online benchmark for image matting},
	booktitle = {2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009},
	volume = {2009 IEEE},
	year = {2009},
	pages = {1826{\textendash}1833},
	abstract = {The availability of quantitative online benchmarks for low-level vision tasks such as stereo and optical flow has led to significant progress in the respective fields. This paper introduces such a benchmark for image matting. There are three key factors for a successful benchmarking system: (a) a challenging, high-quality ground truth test set; (b) an online evaluation repository that is dynamically updated with new results; (c) perceptually motivated error functions. Our new benchmark strives to meet all three criteria. We evaluated several matting methods with our benchmark and show that their performance varies depending on the error function. Also, our challenging test set reveals problems of existing algorithms, not reflected in previously reported results. We hope that our effort will lead to considerable progress in the field of image matting, and welcome the reader to visit our benchmark at www.alphamatting.com. {\textcopyright} 2009 IEEE.},
	isbn = {9781424439935},
	doi = {10.1109/CVPRW.2009.5206503},
	url = {www.alphamatting.com.},
	author = {Rhemann, Christoph and Carsten Rother and Wang, Jue and Gelautz, Margrit and Kohli, Pushmeet and Rott, Pamela}
}
@conference {Kohli2008,
	title = {On partial optimality in multi-label MRFs},
	booktitle = {Proceedings of the 25th International Conference on Machine Learning},
	year = {2008},
	pages = {480{\textendash}487},
	abstract = {We consider the problem of optimizing multilabel MRFs, which is in general NP-hard and ubiquitous in low-level computer vision. One approach for its solution is to formulate it as an integer linear programming and relax the integrality constraints. The approach we consider in this paper is to first convert the multi-label MRF into an equivalent binary-label MRF and then to relax it. The resulting relaxation can be efficiently solved using a maximum flow algorithm. Its solution provides us with a partially optimal labelling of the binary variables. This partial labelling is then easily transferred to the multi-label problem. We study the theoretical properties of the new relaxation and compare it with the standard one. Specifically, we compare tightness, and characterize a subclass of problems where the two relaxations coincide. We propose several combined algorithms based on the technique and demonstrate their performance on challenging computer vision problems. Copyright 2008 by the author(s)/owner(s).},
	isbn = {9781605582054},
	doi = {10.1145/1390156.1390217},
	author = {Kohli, Pushmeet and Shekhovtsov, Alexander and Carsten Rother and Kolmogorov, Vladimir and Torr, Philip}
}
