2_IGARSS2011_BPT_v2.pdf

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


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


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


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


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


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


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


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|



Data courtesy of DLR


Region homogeneity based pruning

d sw p=−2dB



Data courtesy of DLRd sw



p=−1 dB



p=0dB Data courtesy of DLRd sw




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

|


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


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


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”


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


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


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


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


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


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


TEMPORAL CHANGE DETECTIONTEMPORAL CHANGE DETECTION

0

7

Values for stable regions in the temporal dimensions:

d sg , p=−5dB


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


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

2_IGARSS2011_BPT_v2.pdf

Technology

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log z z b

z b diagonal

z x n x z x

b iinn n

n bz b

n kikhi

n2za zb z b z ad dr