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Energy Minimization with Label Costs and Applications in Multi-Model Fitting

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The a-expansion algorithm has had a significant impact in computer vision due to its generality, effectiveness, and speed. Recently, various extensions of a-expansion were proposed that in addition to data fidelity and spatial smoothness can optimize ``label costs’’ with certain optimality guarantees. An energy with label costs can penalize a solution based on the set of labels that appear in it. The simplest special case is to penalize the number of labels in the solution, but the proposed energy is significantly more general than this. Usefulness of label costs is demonstrated by a number of specific applications in vision that appeared in the last couple of years.

Our work (CVPR2010, IJCV accepted) studies label costs from a general perspective, including discussion of multiple algorithms, optimality bounds, extensions, and fast special cases (e.g. UFL heuristics). In this talk we focus on natural generic applications of label costs is multi-model fitting and demonstrate several examples: homography estimation, rigid motion detection, unsupervised image segmentation, lossless and lossy compression, and FMM . Our general approach is juxtaposed with classical K-means and EM. We also discuss a method for effective exploration of the continuum of labels – an important practical obstacle for discrete a-expansion algorithm in fitting models with continuous parameters. We compare our optimization-based approach to multi-model fitting with standard extensions of RANSAC currently dominant in vision.

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