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Self-Validated and Spatially Coherent Clustering with NS-MRF and Graph Cuts

Self-Validated and Spatially Coherent Clustering with NS-MRF and Graph Cuts. Wei Feng and Zhi-Qiang Liu Group of Media Computing School of Creative Media City University of Hong Kong. Outline. Motivation Related Work Proposed Method Results Discussion. Clustering in Low Level Vision.

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Self-Validated and Spatially Coherent Clustering with NS-MRF and Graph Cuts

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  1. Self-Validated and Spatially Coherent Clustering withNS-MRF and Graph Cuts Wei Feng and Zhi-Qiang Liu Group of Media Computing School of Creative Media City University of Hong Kong 18th Intl. Conf. Pattern Recognition

  2. Outline • Motivation • Related Work • Proposed Method • Results • Discussion 18th Intl. Conf. Pattern Recognition

  3. Clustering in Low Level Vision • Common problem: segmentation, stereo etc. • Two parts should be considered: • Accuracy (i.e., likelihood) • Spatial coherence (i.e., cost) • Bayesian framework: to minimize the Gibbs energy (equivalent form of MAP) 18th Intl. Conf. Pattern Recognition

  4. Motivation • Computational complexity remains a major weakness of the MRF/MAP scheme • How to determine the number of clusters (i.e., self-validation) 18th Intl. Conf. Pattern Recognition

  5. Related Work • Interactive segmentation [Boykov, ICCV’01] • Lazy snapping [Li, SIGGRAPH’03] • Mean shift [Comaniciu and Meer, 02] • TS-MRF [D’Elia, 03] • Graph based segmentation [Felzenszwalb, 04] • Spatial coherence clustering [Zabih, 04] • … 18th Intl. Conf. Pattern Recognition

  6. Solving Binary MRF with Graph Mincut • For a binary MRF , the optimal labeling can be achieved by graph mincut Coherence energy Likelihood energy 18th Intl. Conf. Pattern Recognition

  7. Feature Samples Representation • Non-parametric representation: 18th Intl. Conf. Pattern Recognition

  8. Energy Assignment • Based on the two components C0 and C1 and their corresponding subcomponents M0kand M1k, we can define likelihood energy and coherence energy in a nonparametric form. Modified Potts Model 18th Intl. Conf. Pattern Recognition

  9. NS-MRF • Net-Structured MRF • A powerful tool for labeling problems in low level vision • An efficient energy minimization scheme by graph cuts • Converting the K-class clustering into a sequence of K−1 much simpler binary clustering 18th Intl. Conf. Pattern Recognition

  10. Energy Assignment for NS-MRF • Cluster Remaining Energy: • Cluster Merging Energy: • Cluster Splitting Energy: • Cluster Coherence Energy: 18th Intl. Conf. Pattern Recognition

  11. Optimal Cluster Evolution 18th Intl. Conf. Pattern Recognition

  12. Cluster Evolution 18th Intl. Conf. Pattern Recognition

  13. Image Segmentation via NS-MRF • The preservation of soft edges: [2] [1] [1] P. F. Felzenszwalb and D. P. Huttenlocher. “Efficient graph based image segmentation”, IJCV 2004. [2] D. Comaniciu and P. Meer. “Mean shift: A robust approach towards feature space analysis”, PAMI 2002. 18th Intl. Conf. Pattern Recognition

  14. Image Segmentation via NS-MRF • The robustness to noise: [3] [1] [2] [1] C. D’Elia et al. “A tree-structured markov random field model for bayesian image segmentation”, IEEE Trans. Image Processing 2003. [2] P. F. Felzenszwalb and D. P. Huttenlocher. “Efficient graph based image segmentation”, IJCV 2004. [3] D. Comaniciu and P. Meer. “Mean shift: A robust approach towards feature space analysis”, PAMI 2002. 18th Intl. Conf. Pattern Recognition

  15. More Results 18th Intl. Conf. Pattern Recognition

  16. More Results 18th Intl. Conf. Pattern Recognition

  17. More Results 18th Intl. Conf. Pattern Recognition

  18. More Results 18th Intl. Conf. Pattern Recognition

  19. More Results 18th Intl. Conf. Pattern Recognition

  20. Discussion • NS-MRF is an efficient clustering method which is self-validated and guarantees stepwise global optimum. • It is ready to apply to a wide range of clustering problems in low-level vision. • Future work: • clustering bias • multi-resolution graph construction scheme for graph cuts based image modeling 18th Intl. Conf. Pattern Recognition

  21. Thanks! 18th Intl. Conf. Pattern Recognition

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