1. Hierarchical Segmentation of Polarimetric SAR Images
Jean-Marie Beaulieu
Computer Science Department
Laval University
Ridha Touzi
Canada Centre for Remote Sensing
Natural Resources Canada

2. Hierarchical Segmentation of Polarimetric SAR Images
Hierarchical Image Segmentation
As a maximum likelihood estimation problem
Segmentation of polarimetric images
Segment sizes – shape constraints
Results

3. 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

4. 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 n+1
level n
level n-1
Segment tree

6. Sequence of segment merges.

7. 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

8. 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.

9. The maximum likelihood increases with the number of segments
Can't find the optimum partition with k segments, Pk Too many, except for P1 and Pnxn.
Hierarchical segmentation  get Pk from Pk+1 by merging 2 segments.

10. Stepwise optimization
examine each adjacent segment pair
merge the pair that minimizes the criterion

11. Sub-optimum within hierarchical merging framework.
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.

12. Log likelihood form
Summation inside region
Criterion  cost of merging 2 segments
minimize

13. 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

14. The best maximum likelihood estimate of  is the covariance calculated over the region (segment)
ns is the number of pixels in segment s

15. LML for a region s is
constant term for the whole image

16. The variation produced by merging 2 segments is
Hierarchical segmentation: at each iteration, merge the 2 segments that minimize the stepwise criterion Ci,j

17. 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.

18. Segmentation by hypothesis testing
Two hypothesis H0: segments are similar H1: segments are different
Distributions of the statistic d under H0 and H1
Two types of errors Type I: not merging similar segments Type II: merging different segments

19.  = Prob( Type I errors )  = Prob( Type II errors )
Select the threshold to minimise  or , but not both simultaneously

20. 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 .

21. Sequential testing:  will be reduced as segment sizes increase
Sequential testing:  will be reduced as segment sizes increase. 1+2+…  minimum( 1, 2, … ) 1+2+…  maximum( 1, 2, … )

22. Stepwise criterion Find and merge the segment pair (i, j) that minimizes Vi,j (= 1 -  ).
Vi,j = Prob( d  di,j ; H0 ) (= 1 -  ).

23. Amplitude values
|hh|
|hv|
|vv|
|hh| / |hv| / |vv|
80 pixels / cell

24. Correlation – module (0 – 1)
hh vv*
hh hv*
vv hv*
hh vv*/ hh hv*/ vv hv*

25. Correlation – phase (-180o – 180o)
hh vv*
hh hv*
vv hv*
hh vv*/ hh hv*/ vv hv*

26. Amplitude image

27. 1000 segments

28. 500 segments

29. 200 segments

30. 100 segments

31. Amplitude image
5 pixels / cell

32. CRITERION FOR SMALL SEGMENTS
The determinant |C| is null for small segments
Reduce covariance matrix model for small segments

33. Gradual transition between models

34. 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

35. Bonding box – perimeter

36. Bonding box – area

37. Contour length

38. 1000 segments – low resolution

39. 1000 segments

40. 500 segments

41. 200 segments

42. 100 segments

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