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Conditional Random Fields (CRFs) are one of the core technologies in computer vision, and have been applied to a wide variety of tasks. Conventional CRFs typically define edges between neighboring image pixels, resulting in a sparse graph over which inference can be performed efficiently. However, these CRFs fail to model more complex priors such as long-range contextual relationships. Fully-connected CRFs have thus been proposed. While there are efficient approximate inference methods for such CRFs, usually they are sensitive to initialization and make strong assumptions. In this work, we develop an efficient, yet general SDP algorithm for inference on fully-connected CRFs. The core of the proposed algorithm is a tailored quasi-Newton method, which solves a specialized SDP dual problem and takes advantage of the low-rank matrix approximation for fast computation. Experiments demonstrate that our method can be applied to fully-connected CRFs that could not previously be solved, such as those arising in pixel-level image co-segmentation.

Efficient SDP inference for fully-connected CRFs based on low-rank decomposition