self-validated labeling of markov random fields for image segmentation tzu-ting liao advisor:...
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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 NoiseK-labeling segmentationNormalize Cut(NCut)
Labeling qualityLabeling 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
• Image I
• MRF • Observation
• Graph formulation
• Undirected graph .
• • second order neighborthood system
Graph formulation of MRF-based segmentation
• Minimizing the Gibbs Energy
•(K-way) graph cut problemNP-complete
•K=2graph mincut / maxflow problem
𝑆1
𝑆2
𝑆𝑘
Graduated Graph Cuts(GGC)• Four types of segment-level operation
• Retaining• Splitting• Merging• Regrouping
Tree-structured graph cuts(TSGC)• Segment Retaining Energy
• Segment Splitting Energy
• Splittable
𝑆
𝑌𝐶0 (𝑆 )
𝐶1 (𝑆 )
𝑌
Tree-structured graph cuts(TSGC)• Algorithm
Input Image I One Segment
Splitting or Retaining
Feature Model
Final Segment Seg(I)
unchange
change
Overpatitioning problem
Net-structured graph cuts(NSGC)• Nearest neighbor of
• Segment merging energy
𝑆 𝑖 𝑆 𝑗
𝑌 𝑖 𝑌 𝑗
𝐶0 (𝑆𝑖 )
𝐶1 (𝑆 𝑖 )
𝐶0 (𝑆 𝑗 )
𝐶1 (𝑆 𝑗 )(𝐷𝑖𝑠𝑡 (𝐶0 ,𝐶1)=𝑚𝑖𝑛𝑖𝐷 (𝑀 𝑖
𝑡 ,𝐶1−𝑡 ))
Net-structured graph cuts(NSGC)
Input Image I One Segment
Splitting, Retaining
or marging
Feature Model
Final Segment Seg(I)
unchange
change
𝑆 𝑖 𝑆 𝑗 𝑆 𝑖 𝑆 𝑗
𝑆 𝑖 𝑆 𝑗 𝑆 𝑖 𝑆 𝑗
Hierarchical Graph Cuts(HGC)• Complexity of s-t graph cut is O(mn2) .(n vertices, m
arcs)
• Image pyramid(efficiency)
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*