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Multi-class labeling is one of the core problems in image analysis. We show how this combinatorial problem can be approximately solved using tools from convex optimization. We suggest a novel functional based on a multidimensional total variation formulation, allowing for a broad range of data terms. Optimization is carried out in the operator splitting(More)
We propose a novel method to obtain a part of an optimal non-relaxed integral solution for energy minimization problems with Potts interactions, known also as the minimal partition problem. The method empirically outperforms previous approaches like MQPBO and Kovtun's method in most of our test instances and especially in hard ones. As a starting point our(More)
Seven years ago, Szeliski et al. published an influential study on energy minimization methods for Markov random fields (MRF). This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the phenominal success of random field models means that the(More)
Discrete graphical models (also known as discrete Mar-kov random fields) are a major conceptual tool to model the structure of optimization problems in computer vision. While in the last decade research has focused on fast approximative methods, algorithms that provide globally optimal solutions have come more into the research focus in the last years.(More)
The detection and extraction of complex anatomical structures usually involves a trade-off between the complexity of local feature extraction and classification, and the complexity and performance of the subsequent structural inference from the viewpoint of combinatorial optimization. Concerning the latter, computationally efficient methods are of(More)
OpenGM is a C++ template library for defining discrete graphical models and performing inference on these models, using a wide range of state-of-the-art algorithms. No restrictions are imposed on the factor graph to allow for higher-order factors and arbitrary neighborhood structures. Large models with repetitive structure are handled efficiently because(More)
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(More)
Approximate inference by decomposition of discrete graphical models and Lagrangian relaxation has become a key technique in computer vision. The resulting dual objective function is convenient from the optimization point-of-view, in principle. Due to its inherent non-smoothness, however, it is not directly amenable to efficient convex optimization. Related(More)
Multicuts enable to conveniently represent discrete graphical models for unsupervised and supervised image segmentation, based on local energy functions that exhibit symmetries. The basic Potts model and natural extensions thereof to higher-order models provide a prominent class of representatives, that cover a broad range of segmentation problems relevant(More)
The design of inference algorithms for discrete-valued Markov Random Fields constitutes an ongoing research topic in computer vision. Large state-spaces, none-submodular energy-functions, and highly-connected structures of the underlying graph render this problem particularly difficult. Established techniques that work well for sparsely connected(More)