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Binary Partition Tree as a Polarimetric SAR Data Representation in the
Space-Time DomainALBERTO ALONSO-GONZÁLEZCARLOS LÓPEZ-MARTÍNEZPHILIPPE SALEMBIER
UNIVERSITAT POLITÈCNICA DE CATALUNYAESCOLA TÈCNICA SUPERIOR D’ENGINYERIA DE TELECOMUNICACIÓ DE BARCELONA
DEPARTAMENT DE TEORIA DEL SENYAL I COMUNICACIONSREMOTE SENSING LABORATORY
July, 2011
AUTHORS:
2Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
OUTLINEOUTLINE
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
3Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
BINARY PARTITION TREEBINARY PARTITION TREE
● Each node of the tree represents a connected region of the data
● 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
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
BPT is a region-based and multi-scale data representation
Region model
● Between the leaves and the root there are a wide number of nodes representing homogeneous regions of the image at different detail levels
4Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
BPT CONSTRUCTION PROCESSBPT CONSTRUCTION PROCESS
BPT construction: iterative algorithm in a bottom-up approachEach iteration the two most similar neighboring regions are mergedStarting 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:
Dissimilarity measure: Evaluates the similarity of two regions. Measure in the region model space.
To guide the BPT construction process the similarity between regions has to be evaluated
The dissimilarity measure is the keystone of the construction process
Z=⟨k kH ⟩= 1N ∑
i=1
N
k ik iH
5Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
DISSIMILARITY MEASURES IDISSIMILARITY MEASURES I
Revised Wishart dissimilarity: Based on the Wishart pdf
Geodesic dissimilarity: Adapted to the hermitian positive definite matrix cone geometry
Dissimilarity measures are based in two region features:● Polarimetric information (3 by 3 covariance matrix)● Region size information (number of pixels of each region)
Full matrix:
Diagonal:
Full matrix:
Diagonal:
∥A∥F=∑i=1N
∑j=1
N
∣aij∣2=tr AH A=∑i=1
N
i2
d sw A ,B =tr Z A−1 Z B tr Z B
−1 Z A⋅nAnB
d dw A , B =∑i=1N Z AiiZ B iiZ AiiZ B ii ⋅nAnB
d sg A , B =∥log Z A−1Z B ∥Fln 2n AnBnAnB d dg A , B=∑i=1N ln2Z AiiZ B ii ln2 nAnBnAnB
6Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
DISSIMILARITY MEASURES IIDISSIMILARITY MEASURES IIWard relative dissimilarity: based on the increment of the Error Sum of Squares (ESS)
Diagonal relative normalized dissimilarity: based on the normalized difference of the matrix diagonal vector
Diagonal relative dissimilarity: based on the sum of the relative errors respect to both regions
d dr A , B=∑i=1N Z A ii−Z BiiZ B iiZ B ii−Z AiiZ Aii
21 /2
nAnB
Z AB=nA⋅Z AnB⋅Z B
nAnBwhere:
d wr A ,B =nA⋅∥N ABH Z A−Z AB N AB∥F
2nB⋅∥N AB
H Z B−Z AB N AB∥F2
N A=Z A11 0 00 Z A22 00 0 Z A33
d dn A ,B =∑i=1N Z Aii−Z BiiZ AiiZ Bii 21/2
nAnB
7Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
BPT-BASED PROCESSING SCHEMEBPT-BASED PROCESSING SCHEME
Data Results
BPT Construction BPT Pruning
Application independent Application dependent
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
➔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
BPT
8Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
BPT-BASED SPECKLE FILTERINGBPT-BASED SPECKLE FILTERING
Measure of the error committed when representing a region by its estimated covariance matrix
➔ A pruning threshold is defined over this error
A region homogeneity measure has to be defined for the BPT pruning
➔ Region homogeneity:
This measure can be interpreted as the relative MSE of the region X
BPT Pruning
BPT pruning for filtering: Top-down approach, selecting the first nodes that fulfill
X = 1nX∥Z X∥
2∑i=1
n X
∥X i−Z X∥2
p
X p
Alberto Alonso, Carlos López-Martínez and Philippe Salembier, “Filtering and Segmentation of PolarimetricSAR Data Based on Binary Partition Trees,” accepted IEEE TGRS
Alberto Alonso, Carlos López-Martínez and Philippe Salembier, “Filtering and Segmentation of PolarimetricSAR Data With Binary Partition Trees,” IGARSS 2010
9Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
RESULTS WITH REAL DATARESULTS WITH REAL DATA
ESAR Airborne sensor, L-band, Oberpfaffenhofen, Germany, 1999
Original image Data courtesy of DLRSpatial resolution: 1.5m x 1.5m |S
hh+S
vv| |S
hv+S
vh| |S
hh-S
vv|
10Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
RESULTS WITH REAL DATARESULTS WITH REAL DATA
Data courtesy of DLR
ESAR Airborne sensor, L-band, Oberpfaffenhofen, Germany, 1999
Region homogeneity based pruning
d sw p=−2dB
11Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
RESULTS WITH REAL DATARESULTS WITH REAL DATA
Data courtesy of DLRd sw
ESAR Airborne sensor, L-band, Oberpfaffenhofen, Germany, 1999
Region homogeneity based pruning
p=−1 dB
12Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
RESULTS WITH REAL DATARESULTS WITH REAL DATA
p=0dB Data courtesy of DLRd sw
ESAR Airborne sensor, L-band, Oberpfaffenhofen, Germany, 1999
Region homogeneity based pruning
13Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
SMALL DETAILS PRESERVATIONSMALL DETAILS PRESERVATION
Original
IDAN Boxcar 7x7
BPT: d sw , p=−2dB
BPT: d sw , p=0dBBPT: d sw , p=−1dB
|Shh
+Svv
|, |Shv
+Svh
|, |Shh
-Svv
|
14Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
SPACE-TIME BPTSPACE-TIME BPTThe BPT representation can be extended to series of co-registered images
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
|Shh
+Svv
||S
hv+S
vh|
|Shh
-Svv
|
Data courtesy of ESA
15Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
SPACE-TIME BPTSPACE-TIME BPTTo 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
16Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
SPACE-TIME BPT EXPLOITATIONSPACE-TIME BPT EXPLOITATION
PolSARimage
Results
BPT Construction
BPT Pruning
Application independent
Application dependent
BPTSpace-
timedataset
The same tree pruning strategies can be employed over the space-time BPT representation
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”
17Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
SPACE-TIME FILTERINGSPACE-TIME FILTERINGResults of space-time BPT filtering over the first acquisition:
d sg , p=−5dB d sg , p=−3dB
➔On space-time BPT filtering the region models are estimated employing samples of different acquisitions |S
hh+S
vv|, |S
hv+S
vh|, |S
hh-S
vv|
d sg , p=−5dB d sg , p=−3dB
Space-time BPT filtering Single image BPT filtering
18Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
SPACE-TIME FILTERINGSPACE-TIME FILTERINGThe average region depth in the temporal dimension in the first slice:
359371 2,067223969 2,652127957 4,06852077 6,72714660 7,7584666 7,921
Pruning factor Regions at 1st acquisition Average region depth-5 dB-4 dB-3 dB-2 dB-1 dB0 dB d sg
At 4 times more samples may be attained by the space-time BPT filtering application with respect to a single PolSAR image filtering
p=−3 dB
➔The polarimetric information temporal evolution is preserved by the 3D BPT
19Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
TEMPORAL EVOLUTIONTEMPORAL EVOLUTION
1 2 3 4 5 6 7 8Acquisition number: |S
hh+S
vv|, |S
hv+S
vh|, |S
hh-S
vv|
Temporal evolution of the filtered dataset in Pauli and H/A/Alpha parameters
d sg , p=−3dB0 1Entropy H
20Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
TEMPORAL EVOLUTIONTEMPORAL EVOLUTION
1 2 3 4 5 6 7 8Acquisition number:
Temporal evolution of the filtered dataset in Pauli and H/A/Alpha parameters
d sg , p=−3dB0º 90ºAlpha
0 1Anisotropy A
21Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
TEMPORAL CHANGE DETECTIONTEMPORAL CHANGE DETECTIONAnalyzing the temporal contours of the space-time BPT homogeneous regions, a map can be generated representing the number of changes:
p=−5 dB p=−3 dB p=−1 dB
d sg
0
7
22Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
TEMPORAL CHANGE DETECTIONTEMPORAL CHANGE DETECTIONDetail of an urban area:
d sg
|Shh
+Svv
||S
hv+S
vh|
|Shh
-Svv
|
Original Changes detected
➔Some small blue dots can be seen, corresponding to stable human-made structures within the urban areas
p=−5 dB0
7
23Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
TEMPORAL CHANGE DETECTIONTEMPORAL CHANGE DETECTION
0
7
Values for stable regions in the temporal dimensions:
d sg , p=−5dB
24Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
VESSEL DETECTIONVESSEL DETECTIONDetail of a 270 by 270 pixel sea area, original Pauli images:
1 2 3 4 5 6 7 8Acquisition number: |S
hh+S
vv|, |S
hv+S
vh|, |S
hh-S
vv|
d dw , p=−1dB➔The sea area is filtered as one region in the temporal dimension but
small details as the vessels are preserved also in this dimension
ML 3x3 has been applied over plots
25Remote Sensing Lab.Signal Theory and Communications Dept.Universitat Politècnica de Catalunya
CONCLUSIONSCONCLUSIONS
The BPT constructed with the proposed algorithm and dissimilarity measures has proven to be a useful region-based and multi-scale data representation
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 exploitation can be addressed as a tree pruning process, allowing the generalization of the application rationale
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