Self-Validated Labeling of Markov Random Fields for Image segmentation Tzu-Ting Liao ADVISOR: SHENG-JYH WANG W. Feng, J. Y. Jia, and Z. Q. Liu, “Self-validated labeling of Markov random fields for image segmentation,” IEEE Transactions on PAMI, 2010.

K-labeling Image labeling Number of label K is known. 40 percent Gaussian Noise K-labeling segmentation Normalize Cut(NCut) Labeling quality Labeling Cost

Self-validated labeling Self-labeling segmentation (Previous methods) Self-labeling segmentation (This methods) Split-and-merge

Graph theoretic approach Greig: binary labeling problem(s-t graph mincut/maxflow) Boykov, Kolmogorov: K-labeling problem

Graph formulation of MRF-based segmentation

Optimal Binary Segmentation

Graduated Graph Cuts(GGC)

Tree-structured graph cuts(TSGC)

Algorithm Input Image I Splitting or Retaining Feature Model Final Segment Seg(I) unchange change Overpatitioning problem

Net-structured graph cuts(NSGC)

Input Image I Splitting, Retaining or marging Feature Model Final Segment Seg(I) unchange change

Hierarchical Graph Cuts(HGC) Complexity of s-t graph cut is O(mn 2 ).(n vertices, m arcs) Image pyramid(efficiency)

Graduated Graph Cuts(GGC)

Experimental results

Robustness to noise Preservation of long-range soft boundaries

Robustness to noise Preservation of long-range soft boundaries

Experimental results F-measure score to ground truthAverage number of segments

Experimental results

Conclusion Automatically determine the number of labels. Balance the labeling accuracy, spatial coherence, and the labeling cost. Computationally efficient. Independent to initialization. Converge to good local minima of the objective energy function.