The document discusses using a binary partition tree (BPT) to represent polarimetric synthetic aperture radar (PolSAR) data in both the space and time domains. A BPT is a hierarchical, multi-scale data structure where each node represents a connected region obtained by merging two child nodes. The document outlines how to construct a BPT using different dissimilarity measures to evaluate region similarity during merging. It also describes how pruning a space-time BPT can be used for PolSAR speckle filtering across both space and time.

1. Binary Partition Tree as a Polarimetric
SAR Data Representation in the
Space-Time Domain
AUTHORS: ALBERTO ALONSO-GONZÁLEZ
CARLOS LÓPEZ-MARTÍNEZ
PHILIPPE SALEMBIER
UNIVERSITAT POLITÈCNICA DE CATALUNYA
ESCOLA TÈCNICA SUPERIOR D’ENGINYERIA DE TELECOMUNICACIÓ DE BARCELONA
July, 2011 DEPARTAMENT DE TEORIA DEL SENYAL I COMUNICACIONS
REMOTE SENSING LABORATORY

2. OUTLINE
Binary Partition Tree
BPT-based processing scheme
BPT pruning for PolSAR speckle filtering
Space-time BPT
BPT pruning for Space-Time PolSAR speckle
filtering
Conclusions
Remote Sensing Lab.
2 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

3. BINARY PARTITION TREE
BPT is a region-based and multi-scale data representation
● Each node of the tree represents a connected region
of the data
Region model
● Hierarchical structure: each node represents the
region generated by merging of its two son nodes
 The leaves of the tree represent single pixels
 The root node represents the whole dataset
● Between the leaves and the root there are a wide
number of nodes representing homogeneous regions
of the image at different detail levels
The BPT can be considered as a data abstraction
Motivation: Due to its multi-scale nature, the BPT contains a lot of useful
information about the image structure that may be exploited for
different applications
Remote Sensing Lab.
3 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

4. BPT CONSTRUCTION PROCESS
BPT construction: iterative algorithm in a bottom-up approach
Each iteration the two most similar neighboring regions are merged
Starting from the pixels, as the leaves of the tree, to the root node,
representing the whole dataset
Region Model: Estimated covariance matrix Z over all the pixels of the region:
N
1
H
Z =〈k k 〉=
N
∑ kikH
i
i=1
To guide the BPT construction process the similarity between regions has to
be evaluated
Dissimilarity measure: Evaluates the similarity of two regions.
Measure in the region model space.
The dissimilarity measure is the
keystone of the construction process
Remote Sensing Lab.
4 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

5. DISSIMILARITY MEASURES I
Dissimilarity measures are based in two region features:
●
Polarimetric information (3 by 3 covariance matrix)
●
Region size information (number of pixels of each region)
Revised Wishart dissimilarity: Based on the Wishart pdf
Full matrix: d sw  A , B = tr  Z −1 Z B tr  Z −1 Z A  ⋅ n An B 
A B
 
N
Z A Z B
Diagonal: d dw  A , B = ∑ ii
Z A ZB
ii
⋅n A n B 
i=1 ii ii
Geodesic dissimilarity: Adapted to the hermitian positive definite matrix cone
geometry
Full matrix: ∥
d sg  A , B = log  Z Z B 
−1
A ∥ F
ln
2 n A nB
n A nB  
    
N
ZA 2 nA nB
d dg  A , B= ∑ ln
2
Diagonal: ln ii
i=1 ZB n An B ii
 
N N N
2 H
∥A∥ =
F ∑ ∑ ∣aij∣ = tr  A
i=1 j =1
A= ∑ 2
i=1
i
Remote Sensing Lab.
5 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

6. DISSIMILARITY MEASURES II
Ward relative dissimilarity: based on the increment of the Error Sum of
Squares (ESS)
2 2
d wr  A , B =n A⋅ N H  Z A − Z AB  N AB∥ n B⋅ N H  Z B −Z AB  N AB∥
∥ AB F ∥ AB F
 Z A11

0 0
n A⋅Z A n B⋅Z B
where: N A= 0 Z A22 0 Z AB =
n An B
0 0 Z A33
Diagonal relative normalized dissimilarity: based on the normalized
difference of the matrix diagonal vector
1/ 2
 
N 2
Z A −Z B
d dn  A , B = ∑ ii
Z A Z B
ii
 n A n B 
i=1 ii ii
Diagonal relative dissimilarity: based on the sum of the relative errors
respect to both regions
1/2
 
N 2
ZA −ZB Z B −Z A
d dr  A , B= ∑ ii
ZB
ii
 ii
ZA
ii
 n An B 
i =1 ii ii
Remote Sensing Lab.
6 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

7. BPT-BASED PROCESSING SCHEME
The BPT data abstraction may be exploited for different applications
➔ To exploit the BPT structure a tree pruning process is proposed
➔ The most useful or interesting regions from the tree are selected
Data Results
BPT Construction BPT Pruning
BPT
Application independent Application dependent
➔ The BPT construction process can be considered application independent
since it only exploits the internal relationships within the data
➔ The BPT pruning process is application dependent since it searches for
interesting regions within the tree for a particular purpose
Remote Sensing Lab.
7 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

8. BPT-BASED SPECKLE FILTERING
A region homogeneity measure has to be defined for the BPT pruning
 Measure of the error committed when representing a region by its
estimated covariance matrix
nX
1 2
➔ Region homogeneity:  X = 2 ∑∥
X i− Z X ∥
n X ∥Z X ∥ i =1
This measure can be interpreted as the relative MSE of the
region X
➔ A pruning threshold  p is defined over this error
BPT pruning for filtering: Top-down approach, selecting the first nodes
that fulfill  X  p
Alberto Alonso, Carlos López-Martínez and Philippe
Salembier, “Filtering and Segmentation of Polarimetric
SAR Data With Binary Partition Trees,” IGARSS 2010
Alberto Alonso, Carlos López-Martínez and Philippe
Salembier, “Filtering and Segmentation of Polarimetric
BPT Pruning SAR Data Based on Binary Partition Trees,” accepted
IEEE TGRS
Remote Sensing Lab.
8 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

9. RESULTS WITH REAL DATA
ESAR Airborne sensor, L-band, Oberpfaffenhofen, Germany, 1999
Spatial resolution: Original image Data courtesy of DLR
1.5m x 1.5m
|Shh+Svv| |Shv+Svh| |Shh-Svv|
Remote Sensing Lab.
9 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

10. RESULTS WITH REAL DATA
ESAR Airborne sensor, L-band, Oberpfaffenhofen, Germany, 1999
d sw  p=−2 dB Data courtesy of DLR
Region homogeneity based pruning
Remote Sensing Lab.
10 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

11. RESULTS WITH REAL DATA
ESAR Airborne sensor, L-band, Oberpfaffenhofen, Germany, 1999
d sw  p=−1 dB Data courtesy of DLR
Region homogeneity based pruning
Remote Sensing Lab.
11 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

12. RESULTS WITH REAL DATA
ESAR Airborne sensor, L-band, Oberpfaffenhofen, Germany, 1999
d sw  p=0 dB Data courtesy of DLR
Region homogeneity based pruning
Remote Sensing Lab.
12 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

13. SMALL DETAILS PRESERVATION
Original BPT: d sw ,  p=−2 dB
BPT: d sw ,  p=−1 dB BPT: d sw ,  p=0 dB
IDAN Boxcar 7x7
|Shh+Svv|, |Shv+Svh|, |Shh-Svv|
Remote Sensing Lab.
13 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

14. SPACE-TIME BPT
The BPT representation can be extended to series of co-registered images
|Shh+Svv|
|Shv+Svh|
|Shh-Svv|
RADARSAT-2, C-band, Fine Quad-Pol, Flevoland, Netherlands, Beam FQ13
➔ The dataset contains 8 images from April 14th, 2009 to September 29th,
2009, with an acquisition every 24 days
➔ The full dataset contains 4000 x 2000 x 8 pixels
Data courtesy of ESA Remote Sensing Lab.
14 Signal Theory and Communications Dept.
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15. SPACE-TIME BPT
To generate a space-time BPT representation the following elements have to
be defined
 A new pixel connectivity in the space-time domain:
10-connectivity:
Each pixel (blue) has
10 neighbors (red)
 A region model. As for a single PolSAR image, the estimated covariance
matrix Z will be employed
 A dissimilarity measure on the region model space. Since the region model
is the same, previously defined dissimilarity measures will be employed
Assuming the same data behavior in space and time dimensions
Remote Sensing Lab.
15 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

16. SPACE-TIME BPT EXPLOITATION
The same tree pruning strategies can be employed over the space-time BPT
representation
PolSAR
image
Results
Space- BPT Pruning
time BPT
dataset BPT Construction
Application dependent
Application independent
 In fact, since the application dependent part is based on the BPT, not in the
data itself, the BPT allows the generalization of the application rationale
 For the filtering application this rationale can be expressed as: “extract the
biggest homogeneous regions of the image”
Remote Sensing Lab.
16 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

17. SPACE-TIME FILTERING
Results of space-time BPT filtering over the first acquisition:
d sg ,  p =−5 dB d sg ,  p =−3 dB d sg ,  p =−5 dB d sg ,  p =−3 dB
Space-time BPT filtering Single image BPT filtering
➔ On space-time BPT filtering the region models are estimated employing samples of
different acquisitions
|Shh+Svv|, |Shv+Svh|, |Shh-Svv| Remote Sensing Lab.
17 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

18. SPACE-TIME FILTERING
The average region depth in the temporal dimension in the first slice:
Pruning factor Regions at 1st acquisition Average region depth
-5 dB 359371 2,067
-4 dB 223969 2,652
-3 dB 127957 4,068
-2 dB 52077 6,727
-1 dB 14660 7,758
0 dB 4666 7,921 d sg
At  p=−3 dB 4 times more samples may be attained by the space-time BPT
filtering application with respect to a single PolSAR image filtering
➔ The polarimetric information temporal evolution is preserved by the 3D BPT
Remote Sensing Lab.
18 Signal Theory and Communications Dept.
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19. TEMPORAL EVOLUTION
Temporal evolution of the filtered dataset in Pauli and H/A/Alpha parameters
Acquisition number: |Shh+Svv|, |Shv+Svh|, |Shh-Svv|
1 2 3 4 5 6 7 8
Entropy H d sg ,  p =−3 dB
0 1 Remote Sensing Lab.
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20. TEMPORAL EVOLUTION
Temporal evolution of the filtered dataset in Pauli and H/A/Alpha parameters
0 1
Acquisition number: Anisotropy A
1 2 3 4 5 6 7 8
Alpha 0º d sg ,  p =−3 dB
90º Remote Sensing Lab.
20 Signal Theory and Communications Dept.
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21. TEMPORAL CHANGE DETECTION
Analyzing the temporal contours of the space-time BPT homogeneous
regions, a map can be generated representing the number of changes:
7
0
d sg
 p=−5 dB  p=−3 dB  p=−1 dB
Remote Sensing Lab.
21 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

22. TEMPORAL CHANGE DETECTION
Detail of an urban area:
Original Changes
detected
7
|Shh+Svv|
|Shv+Svh|
|Shh-Svv|
0
 p=−5 dB
d sg
➔ Some small blue dots can be seen, corresponding to stable human-made structures
within the urban areas
Remote Sensing Lab.
22 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

23. TEMPORAL CHANGE DETECTION
Values for stable regions in the temporal dimensions:
7
0
d sg ,  p =−5 dB
Remote Sensing Lab.
23 Signal Theory and Communications Dept.
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24. VESSEL DETECTION
Detail of a 270 by 270 pixel sea area, original Pauli images:
Acquisition number: |Shh+Svv|, |Shv+Svh|, |Shh-Svv|
1 2 3 4 5 6 7 8
ML 3x3 has been applied over plots
d dw ,  p =−1 dB
➔ The sea area is filtered as one region in the temporal dimension but
small details as the vessels are preserved also in this dimension
Remote Sensing Lab.
24 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

25. CONCLUSIONS
 The BPT constructed with the proposed algorithm and dissimilarity measures
has proven to be a useful region-based and multi-scale data representation
 The BPT exploitation can be addressed as a tree pruning process, allowing
the generalization of the application rationale
 The proposed BPT-based speckle filtering technique does not introduce bias
or distortion and has a good spatial resolution preservation, being a very
promising technique for PolSAR data processing. When employing a full-
matrix dissimilarity measure the whole process is sensitive to all the
polarimetric information
 The BPT structure has been extended to the time domain. Over this domain
the same speckle filtering application can be exploited and the temporal
contours have been analyzed as a temporal change detection application
 However, it has some drawbacks: the BPT construction is more complex and
requires more computational resources than other simpler filtering strategies
Remote Sensing Lab.
25 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya