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 to image analysis and computer vision. We show how to take into account such higher-order terms systematically in view of computational inference, and present results of a comprehensive and competitive numerical evaluation of a variety of dedicated cutting-plane algorithms. Our results reveal ways to evaluate a significant subset of models globally optimal, with-out compromising runtime. Polynomially solvable relaxations are studied as well, along with advanced rounding schemes for post-processing.

Although shown to be a very powerful tool in computer vision, existing higher-order models are mostly restricted to computing MAP configuration for specific energy functions. In this thesis, we propose a multi-class model along with a variational marginal inference formulation for capturing higher-order log-supermodular interactions. Our modeling technique utilizes set functions by incorporating constraints that each variable is assigned to exactly one class. Marginal inference for our model can be done efficiently by either Frank-Wolfe or a soft-move-making algorithm, both of which are easily parallelized. To simutaneously address the associated MAP problem, we extend marginal inference formulation to a parameterized version as smoothed MAP inference. Accompanying the extension, we present a rigorous analysis on the efficiency and accuracy trade-off by varying the smoothing strength. We evaluate the scalability and the effectiveness of our approach in the task of natural scene image segmentation, demonstrating state-of-the-art performance for both

We propose a new family of discrete energy minimiza-tion problems, which we call parsimonious labeling. Our energy function consists of unary potentials and high-order clique potentials. While the unary potentials are arbitrary, the clique potentials are proportional to the diversity of the set of unique labels assigned to the clique. Intuitively, our energy function encourages the labeling to be parsimo-nious, that is, use as few labels as possible. This in turn allows us to capture useful cues for important computer vi-sion applications such as stereo correspondence and image denoising. Furthermore, we propose an efficient graph-cuts based algorithm for the parsimonious labeling problem that provides strong theoretical guarantees on the quality of the solution. Our algorithm consists of three steps. First, we approximate a given diversity using a mixture of a novel hierarchical Pn Potts model. Second, we use a divide-and-conquer approach for each mixture component, where each subproblem is solved using an efficient α-expansion algo-rithm. This provides us with a small number of putative la-belings, one for each mixture component. Third, we choose the best putative labeling in terms of the energy value. Us-ing both synthetic and standard real datasets, we show that our algorithm significantly outperforms other graph-cuts based approaches. 1.