Self-Validated Labeling of Markov Random Fields for Image segmentation

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

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

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

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

5. Graph formulation of MRF-based segmentation • Image I • MRF • Observation • Graph formulation • Undirected graph . • second order neighborthood system

6. Graph formulation of MRF-based segmentation • Optimal Labeling • Minimizing the Gibbs Energy

7. Graph formulation of MRF-based segmentation • Minimizing the Gibbs Energy • (K-way) graph cut problemNP-complete • K=2graph mincut / maxflow problem

8. Optimal Binary Segmentation • Feature space representation • Energy assignment

9. Optimal Binary Segmentation • Potts model

10. Optimal Binary Segmentation • Mincut/Maxflow problem

11. Graduated Graph Cuts(GGC) • Four types of segment-level operation • Retaining • Splitting • Merging • Regrouping

12. Tree-structured graph cuts(TSGC) • Segment Retaining Energy • Segment Splitting Energy • Splittable

13. Tree-structured graph cuts(TSGC) • Algorithm unchange Input Image I Feature Model Splitting or Retaining One Segment Final Segment Seg(I) change Overpatitioning problem

14. Net-structured graph cuts(NSGC) • Nearest neighbor of • Segment merging energy

15. Net-structured graph cuts(NSGC) unchange Splitting, Retaining or marging Input Image I Feature Model One Segment Final Segment Seg(I) change

16. Hierarchical Graph Cuts(HGC) • Complexity of s-t graph cut is O(mn2) .(n vertices, m arcs) • Image pyramid(efficiency)

17. Graduated Graph Cuts(GGC)

18. Experimental results • Eight methods • Efficient graph-based segmentation(GBS) • MeanShift • Two K-way graph cuts methods: KGC-I (K-means +expansion) and KGC-II (K-means + swap) • Isoperimetric graph partitioning (IsoCut) • Tree-structured MRF (TS-MRF) • Data-driven Markov Chain Monte Carlo (DDMCMC) • Normalized cut (NCut) • CIE L*u*v*

19. Robustness to noise Preservation of long-range soft boundaries

20. Robustness to noise Preservation of long-range soft boundaries

21. Experimental results F-measure score to ground truth Average number of segments

22. Experimental results

23. 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.