Hierarchical%20Segmentation%20of%20Polarimetric%20SAR%20Images

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Hierarchical Segmentation of Polarimetric SAR
Images

• Jean-Marie Beaulieu
• Computer Science Department
• Laval University
• Ridha Touzi
• Canada Centre for Remote Sensing
• Natural Resources Canada

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Hierarchical Segmentation of Polarimetric SAR
Images

• Hierarchical Image Segmentation
• As a maximum likelihood estimation problem
• Segmentation of polarimetric images
• Segment sizes shape constraints
• Results

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Image Segmentation is the division of the image
plane into regions
Two basic questions 1- What kind of regions do
we want ? 2- How can we obtain them ?

• Homogeneous regions
• Segment similarity

• Algorithm design

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HIERARCHICAL SEGMENTATION BY STEP-WISE
OPTIMISATION

A hierarchical segmentation begins with an
initial partition P0 (with N segments) and then
sequentially merges these segments.
level n1
level n
level n-1
Segment tree
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(No Transcript)
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Sequence of segment merges.
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SEGMENTATION AS MAXIMUM LIKELIHOOD ESTIMATION
1) need a partition of the image
2) need statistical parameters
3) need an image probability model
xi are conditionally independent
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Given an image
the likelihood of
is
The segmentation problem is to find the partition
that maximizes the likelihood.Global search
too many possible partitions. is derived
from statistics calculated over a segment s.
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The maximum likelihood increases with the number
of segments
number of segments
Can't find the optimum partition with k segments,
PkToo many, except for P1 and Pnxn.
Hierarchical segmentation ? get Pk from Pk1
by merging 2 segments.
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• Stepwise optimization
• examine each adjacent segment pair
• merge the pair that minimizes the criterion

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Merging criterion merge the 2 segments
producing the smallest decrease of the maximum
likelihood (stepwise optimization)
number of segments
Sub-optimum within hierarchical merging
framework.
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Log likelihood form
Summation inside region
Criterion ? cost of merging 2 segments
minimize
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POLARIMETRIC SAR IMAGE
Multi-channel image 3 complex elements
each element has a zero mean circular gaussian
distribution
Complex gaussian pdf (? is the covariance
matrix)
x is the complex conjugate transpose of x
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The best maximum likelihood estimate of ? is
the covariance calculated over the region
(segment)
ns is the number of pixels in segment s
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LML for a region s is
constant term for the whole image
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The variation produced by merging 2 segments is
Hierarchical segmentation at each iteration,
merge the 2 segments that minimize the stepwise
criterion Ci,j
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SEGMENTATION BY HYPOTHESIS TESTING
Test the similarity of segment covariances Ci
Cj C - merge segment with same covariance
Use the difference of determinant logarithms as a
test statistic
With the scaling factor K, the statistic is
approximately distributed as a chi-squared
variable with 6 degrees of freedom as nsi and
nsj become large.
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Segmentation by hypothesis testing
Two hypothesisH0 segments are similarH1
segments are different
Distributions of the statistic d under H0 and H1
Two types of errorsType I not merging similar
segmentsType II merging different segments
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? Prob( Type I errors )? Prob( Type II
errors )
Select the threshold to minimise ? or ?, but not
both simultaneously
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In hierarchical segmentation, type II errors
(merging different segments) can not be
corrected,while type I errors can be corrected
later on.
The distribution of H1 and ? are unknown.Reduce
? by increasing ?.
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Sequential testing? will be reduced as segment
sizes increase. ?12 ? minimum( ?1, ?2,
)?12 ? maximum( ?1, ?2, )
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Stepwise criterionFind and merge the segment
pair (i, j) that minimizes Vi,j ( 1 - ? ).
Vi,j Prob( d ? di,j H0 ) ( 1 - ? ).
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Amplitude values
hh
hv
vv
hh / hv / vv
80 pixels / cell
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Correlation module (0 1)
hh vv
hh hv
vv hv
hh vv/ hh hv/ vv hv
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Correlation phase (-180o 180o)
hh vv
hh hv
vv hv
hh vv/ hh hv/ vv hv
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Amplitude image
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1000 segments
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500 segments
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200 segments
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100 segments
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Amplitude image
5 pixels / cell
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CRITERION FOR SMALL SEGMENTS
The determinant C is null for small segments
Reduce covariance matrix model for small segments
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Gradual transition between models
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SEGMENT SHAPE CRITERIA
High speckle noise ? first merges produce ill
formed segments

• Bonding box perimeter Cp
• Bonding box area Ca
• Contour length Cl

New criteria
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Bonding box perimeter
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Bonding box area
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Contour length
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1000 segments low resolution
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1000 segments
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500 segments
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200 segments
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100 segments
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CONCLUSION

• Hierarchical segmentation produces good results
• Criterion should be adapted to the application
• Good polarimetic criterion
• The first merges should be done correctly