@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 {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 {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 {rathke2015b,
	title = {A Computational Approach to Log-Concave Density Estimation},
	journal = {An. St. Univ. Ovidius Constanta},
	volume = {23},
	year = {2015},
	pages = {151-166},
	author = {Rathke, Fabian and Christoph Schn{\"o}rr}
}
@article {Rathke2015,
	title = {A Computational Approach to Log-Concave Density Estimation},
	journal = {An. St. Univ. Ovidius Constanta},
	volume = {23},
	number = {3},
	year = {2015},
	pages = {151-166},
	author = {Rathke, F. and Christoph Schn{\"o}rr}
}
@conference {Silvestri2015,
	title = {A Convex Relaxation Approach to the Affine Subspace Clustering Problem},
	booktitle = {Proc.~GCPR},
	year = {2015},
	author = {Silvestri, F. and Reinelt, G. and Christoph Schn{\"o}rr}
}
@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}
}
@article {lenzen_13_class,
	title = {A Class of Quasi-Variational Inequalities for Adaptive Image Denoising
and Decomposition},
	journal = {Computational Optimization and Applications (COAP)},
	volume = {54 (2)},
	year = {2013},
	note = {1},
	pages = {371-398},
	doi = {10.1007/s10589-012-9456-0},
	author = {Frank Lenzen and Florian Becker and Lellmann, J. and Stefania Petra and Christoph Schn{\"o}rr}
}
@article {Lenzen-et-al-13,
	title = {A class of quasi-variational inequalities for adaptive image denoising and decomposition},
	journal = {Computational Optimization and Applications},
	volume = {54},
	number = {2},
	year = {2013},
	pages = {371-398},
	publisher = {Springer Netherlands},
	issn = {0926-6003},
	url = {http://dx.doi.org/10.1007/s10589-012-9456-0},
	author = {Frank Lenzen and Florian Becker and Lellmann, Jan and Stefania Petra and Christoph Schn{\"o}rr}
}
@article {Breitenreicher2012,
	title = {COAL: a generic modelling and prototyping framework for convex optimization problems of variational image analysis},
	journal = {Optimization Methods and Software},
	volume = {28},
	number = {5},
	year = {2013},
	note = {Projectpage: http://sourceforge.net/projects/coalproject/},
	pages = {1081-1094},
	doi = {10.1080/10556788.2012.672571},
	url = {http://www.tandfonline.com/doi/abs/10.1080/10556788.2012.672571},
	author = {Breitenreicher, Dirk and Lellmann, Jan and Christoph Schn{\"o}rr}
}
@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}
}
@booklet {SchmitzerSchnoerr-ShapeMeasures2013,
	title = {Contour Manifolds and Optimal Transport},
	year = {2013},
	note = {preprint},
	author = {Bernhard Schmitzer and Christoph Schn{\"o}rr}
}
@article {SwobodaSchnoerr2013,
	title = {Convex Variational Image Restoration with Histogram Priors},
	journal = {SIAM J.~Imag.~Sci.},
	volume = {6},
	number = {3},
	year = {2013},
	pages = {1719-1735},
	author = {Swoboda, P. and Christoph Schn{\"o}rr}
}
@article {Petra2013,
	title = {Critical Parameter Values and Reconstruction Propertiesof Discrete Tomography: Application to Experimental FluidDynamics},
	journal = {Fundamenta Informaticae},
	volume = {125},
	year = {2013},
	pages = {285--312},
	author = {Stefania Petra and Christoph Schn{\"o}rr and Schr{\"o}der, A.}
}
@article {Lellmann-Schnoerr-SIIMS-11,
	title = {Continuous Multiclass Labeling Approaches and Algorithms},
	journal = {SIAM J.~Imag.~Sci.},
	volume = {4},
	number = {4},
	year = {2011},
	pages = {1049-1096},
	author = {Lellmann, J. and Christoph Schn{\"o}rr}
}
@article {Yuan-et-al-JMIV-09,
	title = {Convex Hodge Decomposition and Regularization of Image Flows},
	journal = {J.~Math.~Imag.~Vision},
	volume = {33},
	number = {2},
	year = {2009},
	pages = {169-177},
	author = {Yuan, Jing and Christoph Schn{\"o}rr and Steidl, Gabriele}
}
@conference {Lellmann-et-al-09a,
	title = {Convex Multi-Class Image Labeling by Simplex-Constrained Total Variation},
	booktitle = {Scale Space and Variational Methods in Computer Vision (SSVM 2009)},
	volume = {5567},
	year = {2009},
	pages = {150-162},
	publisher = {Springer},
	organization = {Springer},
	author = {Lellmann, J. and J{\"o}rg H. Kappes and Yuan, J. and Florian Becker and Christoph Schn{\"o}rr},
	editor = {Tai, X.-C. and M{\'o}rken, K. and Lie, K.-A. and Lysaker, M.}
}
@conference {lellmann_09_convex2,
	title = {Convex Multi-Class Image Labeling by Simplex-Constrained Total Variation},
	booktitle = {Scale Space and Variational Methods in Computer Vision (SSVM 2009)},
	volume = {5567},
	year = {2009},
	note = {1},
	pages = {150-162},
	publisher = {Springer},
	organization = {Springer},
	doi = {10.1007/978-3-642-02256-2_13},
	author = {Lellmann, J. and J{\"o}rg H. Kappes and Yuan, J. and Florian Becker and Christoph Schn{\"o}rr and M{\'o}rken, K. and Lysaker, M.},
	editor = {Tai, X.-C. and Lie, K.-A.}
}
@conference {Lellmann2009a,
	title = {Convex Optimization for Multi-Class Image Labeling with a Novel Family of Total Variation Based Regularizers},
	booktitle = {IEEE International Conference on Computer Vision (ICCV)},
	year = {2009},
	pages = {646 -- 653},
	author = {Lellmann, J. and Florian Becker and Christoph Schn{\"o}rr}
}
@conference {lellmann_09_convex,
	title = {Convex Optimization for Multi-Class Image Labeling with a Novel Family
of Total Variation Based Regularizers},
	booktitle = {Proceedings of the IEEE Conference on Computer Vision (ICCV 09) Kyoto, Japan},
	year = {2009},
	note = {1},
	pages = {646-653},
	doi = {10.1109/ICCV.2009.5459176},
	author = {Lellmann, J. and Florian Becker and Christoph Schn{\"o}rr}
}
@conference {Fundana-Heyden-Gosch-Schnoerr-2008,
	title = {Continuous Graph Cuts for Prior-Based Object Segmentation},
	booktitle = {19th Int.~Conf.~Patt.~Recog.~(ICPR)},
	year = {2008},
	pages = {1--4},
	author = {Fundana, Ketut and Heyden, Anders and Gosch, Christian and Christoph Schn{\"o}rr}
}
@conference {Yuan-et-al-2008b,
	title = {Convex Hodge Decomposition of Image Flows},
	booktitle = {Pattern Recognition -- 30th DAGM Symposium},
	volume = {5096},
	year = {2008},
	pages = {416--425},
	publisher = {Springer Verlag},
	organization = {Springer Verlag},
	author = {Yuan, Jing and Steidl, Gabriele and Christoph Schn{\"o}rr}
}
@techreport {Lellmann2008,
	title = {Convex Multi-Class Image Labeling by Simplex-Constrained Total Variation},
	year = {2008},
	institution = {IWR, University of Heidelberg},
	url = {http://www.ub.uni-heidelberg.de/archiv/8759/},
	author = {Lellmann, J. and J{\"o}rg H. Kappes and Yuan, J. and Florian Becker and Christoph Schn{\"o}rr}
}
@conference {Heiler-Schnoerr-06a,
	title = {Controlling Sparseness in Non-negative Tensor Factorization},
	booktitle = {Computer Vision -- ECCV 2006},
	volume = {3951},
	year = {2006},
	pages = {56-67},
	publisher = {Springer},
	organization = {Springer},
	author = {Heiler, M. and Christoph Schn{\"o}rr}
}
@conference {Bruhn-et-al-02b,
	title = {Combining the Advantages of Local and Global Optic Flow Methods},
	booktitle = {Pattern Recognition, Proc. 24th DAGM Symposium},
	series = {lncs},
	volume = {2449},
	year = {2002},
	pages = {454{\textendash}462},
	publisher = {Springer},
	organization = {Springer},
	address = {Z{\"u}rich, Switzerland},
	author = {Bruhn, Andr{\'e}s and Weickert, Joachim and Christoph Schn{\"o}rr},
	editor = {van Gool, L.}
}
