city university of hong kong 18 th intl. conf. pattern recognition self-validated and spatially...
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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
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
Outline
Motivation Related Work Proposed Method Results Discussion
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
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
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
Motivation
Computational complexity remains a major weakness of the MRF/MAP scheme
How to determine the number of clusters (i.e., self-validation)
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
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] …
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
Solving Binary MRF with Graph Mincut For a binary MRF , the optimal la
beling can be achieved by graph mincut
Likelihood energy
Coherence energy
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
Feature Samples Representation Non-parametric representation:
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
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
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
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
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
Energy Assignment for NS-MRF Cluster Remaining
Energy:
Cluster Merging Energy:
Cluster Splitting Energy:
Cluster Coherence Energy:
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
Optimal Cluster Evolution
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
Cluster Evolution
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
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]
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
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]
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
More Results
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
More Results
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
More Results
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
More Results
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
More Results
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
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
1818thth Intl. Conf. Pattern Recognition Intl. Conf. Pattern Recognition City University of Hong KongCity University of Hong Kong
Thanks!Thanks!