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

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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

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Outline

• Motivation
• Related Work
• Proposed Method
• Results
• Discussion

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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)

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Motivation

• Computational complexity remains a major weakness
  of the MRF/MAP scheme
• How to determine the number of clusters (i.e.,
  self-validation)

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Related Work

• Interactive segmentation Boykov, ICCV01
• Lazy snapping Li, SIGGRAPH03
• Mean shift Comaniciu and Meer, 02
• TS-MRF DElia, 03
• Graph based segmentation Felzenszwalb, 04
• Spatial coherence clustering Zabih, 04

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Solving Binary MRF with Graph Mincut

• For a binary MRF ,
  the optimal labeling can be achieved by graph
  mincut

Coherence energy
Likelihood energy
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Feature Samples Representation

• Non-parametric representation

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Energy Assignment

• Based on the two components C0 and C1 and their
  corresponding subcomponents M0k and M1k , we can
  define likelihood energy and coherence energy in
  a nonparametric form.

Modified Potts Model
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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

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Energy Assignment for NS-MRF

• Cluster Remaining Energy
• Cluster Merging Energy
• Cluster Splitting Energy
• Cluster Coherence Energy

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Optimal Cluster Evolution
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Cluster Evolution
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Image Segmentation via NS-MRF

• The preservation of soft edges

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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.
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Image Segmentation via NS-MRF

• The robustness to noise

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2
1
1 C. DElia 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.
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More Results
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More Results
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More Results
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More Results
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More Results
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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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• Thanks!