Self validated and spatially coherent clustering with ns mrf and graph cuts
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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
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


Outline
Outline

  • Motivation

  • Related Work

  • Proposed Method

  • Results

  • Discussion

18th Intl. Conf. Pattern Recognition


Clustering in low level vision
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


Motivation
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


Related work
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


Solving binary mrf with graph mincut
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


Feature samples representation
Feature Samples Representation

  • Non-parametric representation:

18th Intl. Conf. Pattern Recognition


Energy assignment
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


Ns mrf
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


Energy assignment for ns mrf
Energy Assignment for NS-MRF

  • Cluster Remaining Energy:

  • Cluster Merging Energy:

  • Cluster Splitting Energy:

  • Cluster Coherence Energy:

18th Intl. Conf. Pattern Recognition


Optimal cluster evolution
Optimal Cluster Evolution

18th Intl. Conf. Pattern Recognition


Cluster evolution
Cluster Evolution

18th Intl. Conf. Pattern Recognition


Image segmentation via ns mrf
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


Image segmentation via ns mrf1
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


More results
More Results

18th Intl. Conf. Pattern Recognition


More results1
More Results

18th Intl. Conf. Pattern Recognition


More results2
More Results

18th Intl. Conf. Pattern Recognition


More results3
More Results

18th Intl. Conf. Pattern Recognition


More results4
More Results

18th Intl. Conf. Pattern Recognition


Discussion
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


Thanks!

18th Intl. Conf. Pattern Recognition


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