Self-validated labeling of Markov random fields for image segmentation.

This paper addresses the problem of self-validated labeling of Markov random fields (MRFs), namely to optimize an MRF with unknown number of labels. We present graduated graph cuts (GGC), a new technique that extends the binary s-t graph cut for self-validated labeling. Specifically, we use the split-and-merge strategy to decompose the complex problem to a series of tractable subproblems. In terms of Gibbs energy minimization, a suboptimal labeling is gradually obtained based upon a set of cluster-level operations. By using different optimization structures, we propose three practical algorithms: tree-structured graph cuts (TSGC), net-structured graph cuts (NSGC), and hierarchical graph cuts (HGC). In contrast to previous methods, the proposed algorithms can automatically determine the number of labels, properly balance the labeling accuracy, spatial coherence, and the labeling cost (i.e., the number of labels), and are computationally efficient, independent to initialization, and able to converge to good local minima of the objective energy function. We apply the proposed algorithms to natural image segmentation. Experimental results show that our algorithms produce generally feasible segmentations for benchmark data sets, and outperform alternative methods in terms of robustness to noise, speed, and preservation of soft boundaries.