Edge%20Preserving%20Spatially%20Varying%20Mixtures%20for%20Image%20Segmentation

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Edge Preserving Spatially Varying Mixturesfor
Image Segmentation
by
Giorgos Sfikas, Christophoros Nikou, Nikolaos
Galatsanos
(CVPR 2008)
Presented by Lihan He ECE, Duke University Feb
23, 2009
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Outline

• Introduction
• Edge preserving spatially varying GMM
• Inference using MAP-EM
• Experimental results
• Conclusion

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Introduction
Image segmentation
Clustering pixels or super pixels such that the
same group has common characteristics (same
objective, similar texture)

• Adjacent pixels most likely belong to the same
  cluster
• Edge of objectives.

GMM no prior knowledge is exploited
SVGMM (spatially variant GMM)

• Spatial smoothness is imposed in the neighborhood
  of each pixel based on the Markov random field
• Without considering the edge of textures

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Introduction
In this paper

• Hierarchical Bayesian model
• Spatially varying GMM mixing weights are
  different for different pixels
• Difference of mixing weights for two neighbored
  pixels follows a student-t distribution
• Heavy tailed student-t preserves edges of
  textures
• MAP-EM is used for model inference.

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St-SVGMM
Feature vector for each pixel
SVGMM
Each pixel has its own mixing weights
weights
Each pixel xn
indicator variables
Likelihood
Prior
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St-SVGMM
Prior for mixing weight p
d2
d neighborhood adjacency type
d1
d1 horizontald2 vertical
?d(n) the set of neighbors of pixel n, with
respect to the dth adjacency type
KD different student-t distributions are
introduced, with hyperparameters
Joint prior for p
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St-SVGMM
The student-t distribution can be modeled by
introducing the latent variable
plays an important role
neighboring pixels n, k belong to the same
cluster
n, k are at the edge of two clusters
n edge location k (d) adjacency type
(horizontal or vertical) j cluster index (edges
of which cluster)
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St-SVGMM
Model summary
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Inference
MAP-EM algorithm for model inference.
Model parameters
Complete log-likelihood
E-step (update Z, U)
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Inference
M-step ( update )

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Results
U-variable maps
n edge location k (d) adjacency type j
cluster index
j1 sky
K3 clusters
Brighter regions represent lower values edges.
j2 roof shadows
j3 building
d2 vertical
d1 horizontal
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Results
Comparison on 300 images of the Berkeley image
database
Statistics on the Rand Index (RI) (measuring the
consistency between the ground truth and the
segmentation map) higher is better.
Statistics on the boundary displacement error
(BDE) (measuring error of boundary displacement
with respect to the ground truth) lower is
better.
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Results
Segmentation examples
K5
K10
K15
original image
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Results
K5
K10
K15
original image
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Conclusion

• Proposed a GMM-based clustering algorithm for
  image segmentation
• Used smoothness prior to consider the adjacent
  pixels belonging to the same cluster
• Also captured the image edge structure (no
  smoothness enforced across segment boundaries)
• All required parameters are estimated from the
  data (no requirement of empirical parameter
  selection).
• Next automatically estimating the number of
  components K.

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