City University of Hong Kong 18 th Intl. Conf. Pattern Recognition Self-Validated and Spatially Coherent Clustering with NS-MRF and Graph Cuts Wei Feng

1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong

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


Outline

Motivation Related Work Proposed Method Results Discussion


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)

coherencelikelihoodEEE


Motivation

Computational complexity remains a major weakness of the MRF/MAP scheme

How to determine the number of clusters (i.e., self-validation)


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] …


Solving Binary MRF with Graph Mincut For a binary MRF , the optimal la

beling can be achieved by graph mincut

Likelihood energy

Coherence energy


Feature Samples Representation Non-parametric representation:


Energy Assignment

Based on the two components C0 and C1 and their corresponding subcomponents M0

k and M1

k , we can define likelihood energy and coherence energy in a nonparametric form.

Modified Potts Model


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


Energy Assignment for NS-MRF Cluster Remaining

Energy:

Cluster Merging Energy:

Cluster Splitting Energy:

Cluster Coherence Energy:


Optimal Cluster Evolution


Cluster Evolution


Image Segmentation via NS-MRF The preservation of soft edges:

[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.

[1] [2]


Image Segmentation via NS-MRF The robustness to noise:

[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.

[2] [3][1]


More Results


More Results


More Results


More Results


More Results


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


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Documents

City University of Hong Kong 18 th Intl. Conf. Pattern Recognition Self-Validated and Spatially Coherent Clustering with NS-MRF and Graph Cuts Wei Feng