Deutsches Zentrum für Luft und Raumfahrt e.V. Institut für Hochfrequenztechnik und Radarsysteme ©...

Deutsches Zentrum für Luft und Raumfahrt e.V.Institut für Hochfrequenztechnik und Radarsysteme

©K.P.Papathanassiou

Polarimetric SAR Applications

K. P. Papathanassiou, E. Pottier, I. Hajnsek

German Aerospace Center

University Rennes I, France

([.])V … Matrix Vectorisation Operator … Complete Set of 2x2 Basis Matrices

Scattering Matrix & Scattering Vector

S][Scattering Matrix:

Scattering Vector: 4T

43214 CkkkkSTrace21SVk ][)]([])([:

2P ,,,

TVHHVVHHVVVHHVVHH4 SSiSSSSSS

21k ])([

Pauli Scattering Vector:

Pauli Matrices Set:

Backscattering from Reciprocal Scatterers: XXVHHV SSS Reciprocity Theorem

Distributed Scatterers & Coherency Matrix

Coherency Matrix:

Scattering Vector:

is by definition a 3x3 hermitian positive semi-definite matrix][ 3T

TVHHVVVHHVVHHP3 SSSSSS

21k ][

and contains in general 16 independent parameters (6 real and 6 complex elements)

It describes completely the polarimetric properties of distributed scatterers

2HVVVHHHVVVHHHV

HVVVHH2

VVHHVVHHVVHH

HVVVHHVVHHVVHH2

S4SSS2SSS2SSS2SSSSSSSSS2SSSSSS

kkT||)()()(|)(|))(()())((|)(|

Eigenvector Decomposition

Coherence Matrix: P3P33 kkT

Diagonalisation: 1333 UUT ]][][[][

333231

232221

131211

eeeeeeeee

000000

332313

322212

312111

eeeeeeeee

UU ][][

][][][)()()()(][ 33

13333222111

1iiii3 TTTeeeeeeeeT

where:

3 real positive eigenvalues 3 orthonormal eigenvectors][][][ 321 SSS

Advantage: Invariance of the Eigenvalue Problem under Unitary Transformations:

( by definition 3x3 hermitian PSD matrix )

Scattering Entropy / Anisotropy

Coherency Matrix Diagonalisation:

][][][)()()()(][ 33

13333222111

1iiii3 TTTeeeeeeeeT

1ii PPH log:

where:Scattering Entropy:

Scattering Anisotropy:

Totally Polarised ScattererTotally Unpolarised Scatterer

1A1A0 2 Equal Secondary Scattering Processes

Only 1 Secondary Scattering Process

Power Images

L-band

SIR-C / Test Site: Kudara,Russia

Scattering Entropy Images

C-band

L-band

Scattering Anisotropy ImagesSIR-C / Test Site: Kudara,Russia

C-band

L-band

Eigenvector Decomposition: Scattering Mechanisms

|||][ 3213 eeeU

)exp()sin()sin()exp()sin()sin()exp()sin()sin()exp()cos()sin()exp()cos()sin()exp()cos()sin(

)cos()cos()cos(][

333222111

iiiiiiU

][][][)()()(][][][][ 33

13333222111

1333 TTTeeeeeeUUT

)exp()sin()sin()exp()cos()sin(

)exp()cos(

1st Scattering Mechanism

2nd Scattering Mechanism

3rd Scattering Mechanism

Parameterisation of ein terms of five angles: ,,,,

Interpretation of Scattering Mechanisms

Isotropic Surface Scatterer Isotropic Dihedral ScattererDipol Scatterer

Anisotropic Surfaces Anisotropic Dihedrals

Mean Scattering Parameters

Coherency Matrix Diagonalisation:

Mean α-Angle:

Mean β-Angle:

Mean γ-Angle:

Mean δ-Angle:

332211 PPP

)()()(][ 3332221113 eeeeeeT

)exp()sin()sin()exp()cos()sin(

Eigenvectors: Appearance Probabilities:

Mean Scattering Mechanism

α-Angle Images

C-band

L-band

a=90°

a=45°

Polarimetric Segmentation and Classification

Scattering Entropy / a-Angle Plane Segmentation

Low Entropy Multiple Scattering

Medium Entropy Multiple

Scattering

Low Entropy Surface Scattering

Medium Entropy Dominant Surface Scattering

Medium Entropy Dipol Scattering

Low Entropy Dipol Scattering

0 0.2 0.4 0.6 0.8 10

Entropy

High Entropy Multiple Scattering

Please Note: Slides Are Under Construction !!!

H / H / Segmentation Segmentation

C1 C2 C3 C4 C5 C6 C7 C8H / Segmentation divided into 8 basic zones

TTTrLpLLp

mT1pLL

eTLTTP

.../ )(

COMPLEX WISHART DISTRIBUTIONCOMPLEX WISHART DISTRIBUTION

Coherency Matrix

L: Number of Look p: Polarimetric Dimension

WISHART Segmentation WISHART Segmentation

SUPERVISED WISHART CLASSIFIER (Lee 1994)SUPERVISED WISHART CLASSIFIER (Lee 1994)

BAYES MAXIMUM LIKELIHOOD CLASSIFICATION PROCEDURE

mjTdTdifTT jmm

KTPTLTTTrLTd mm1

mm lnlnwith

[Tm] : Cluster Center of the class m

PROVIDE INITIAL [Tm](0)

FOR EACH CLASS

Cluster Center of the class m(Lee 1998)

CLASSIFY THE WHOLE IMAGEWITH THE DISTANCE PROCEDURE

mjTdTdifTT jmm

COMPUTE [Tm](k+1) FOR EACH CLASSUSING THE CLASSIFIED PIXELS OF STEP 2

TERMINAISONCRITERION ?

0 0.2 0.4 0.6 0.8 10102030405060708090

Entropy (H)

H / H / WISHART Segmentation WISHART Segmentation

C1 C2 C3 C4 C5 C6 C7 C8

4th ITERATIONWEIHERBACHTAL DLR - ESAR L-band 1988

8 Training sets

16 New Training sets

Introduction of the Anisotropy (A)information once the first classification

procedure has met its termination criterion

H / H / / A - WISHART Segmentation / A - WISHART Segmentation

C1 C2 C3 C4 C5 C6 C7 C8

C9 C10 C11 C12 C13 C14 C15 C16

4th ITERATIONWEIHERBACHTAL DLR - ESAR L-band 1988

C1 C2 C3 C4 C5 C6 C7 C8

C9 C10 C11 C12 C13 C14 C15 C16

C1 C2 C3 C4 C5 C6 C7 C8

C9 C10 C11 C12 C13 C14 C15 C16

TSUKUBA SCIENCE CITYTSUKUBA SCIENCE CITYNASDA / CRL / PI-SAR L-band and X-band (1997/30/09)NASDA / CRL / PI-SAR L-band and X-band (1997/30/09)

DUAL-FREQ CLASSIFICATION DUAL-FREQ CLASSIFICATION

L. Ferro-Famil, E. Pottier, J.S. Lee (1999 - 2000)

TSUKUBA L-Band

C1 C2 C3 C4 C5 C6 C7 C8

C9 C10 C11 C12 C13 C14 C15 C16

4th ITERATION

H / H / WISHART Segmentation WISHART Segmentation

H / H / WISHART Segmentation WISHART Segmentation TSUKUBA X-Band 4th ITERATION

C1 C2 C3 C4 C5 C6 C7 C8

C9 C10 C11 C12 C13 C14 C15 C16

Single Image Unsupervise

d H/ Wishart

Classification

ClassCombinatio

Unsupervised Wishart

(66) Classificatio

ClassNumber

Reduction

Image L

Image X 8 classes

64 classes

ClassifiedImage

N classes

Initialization

Unsupervised Segmentation of Dual Frequency Polarimetric Data

(L. Ferro-Famil et al., 1999)(L. Ferro-Famil et al., 1999)

H / WISHART Segmentation

Dual Frequency ClassificationDual Frequency Classification

TSUKUBA L-Band & X-BandDual Segmentation

C1 C2 C3 C4 C5 C6 C7 C8

C9 C10 C11 C12 C13 C14 C15 C16

Surface Parameter Inversion

Polarimetric Surface

Scattering Model

0expsinexpcos

PSPSPS

PSpSPS

PP RRRRRR

RRRRRR

Coherency Matrix for a Ideal Bragg Surface with non cross-polarisation and non depolarisation

)sincos(

))sin1()(sin1(

sincos

rSR is independent of roughness

Cloude S. R., Hajnsek I. & Papathanassiou, K. P., “Eigenvector Methods for the Extraction of Surface Parameters in Polarimetric SAR”, CEOS, SAR-Workshop,Toulouse, 1999

otherwise 0

“Configurational averaging over a uniform

distribution about zero of the Bragg surface slope in the plane perpendicular to the scattering plane.“

Rotation Symmetric Roughness TermIdeal Bragg

SurfaceReal

Surface

zero cross-polarisation

and zero depolarisation

non-zero cross-

polarisation and non-zero depolarisation

SensorScattering

PlaneAzimuthal Oriented Surface

))4(sinc1(00

0))4(sinc1( )2(sinc*0)2(sinc

1=C PS RR **2 PSPS RRRRC 2

1 PS RRC

Coherency Matrix of a Real Surfacewith Cross-Polarisation and

Depolarisation

The polarimetric coherence and the level of cross-polarised power is

controlled by a single parameter ß1

A is independent on e‘ and depends only on roughness (ß1)

Variation of cross-polarisation anddepolarisation with model

parameter ß1

Prediction of the Polarimetric Surface Scattering Model for Surface Roughness

Variation of anisotrophy with model parameter

Entropy/Alpha Diagram for 45 degrees AOI

Prediction of the Polarimetric Surface Scattering Model for Dielectric Constant

LHH Image AlphaEntropy

Eigenvector Decomposition Test Site Elbe River August 1997

0 1.5 km

Alpha < 43 degreeEntropy < 0.5 Anisotropy

Surface Scatterers

Soil Moisture Maps Selected for Bare Agricultural Fields

Dielectric Constant Volumetric Moisture

0 500 m

Field 10

Field 13

Field 14

Field 16

0 10 20 30 40measured m v [vol %]

Elbe 0-4 cmElbe 4-8 cmWeiherbach 0-4 cmWeiherbach 4-8 cm

0 5 10 15 20 25measured '

Elbe 0-4 cmElbe 4-8 cmWeiherbach 0-4 cmWeiherbach 4-8 cm

Measured versus Estimated

Dielectric Constant e‘ Volumetric Moisture mv [%]

0-4 cm 4-8 cm corr.

Elbe RMSerror 8 30.7/0.8

Weih RMSerror 7 60.2/-

0-4 cm 4-8 cm corr.

Elbe RMSerror 5 10.6/0.7

Weih RMSerror 5 40.2/-

Surface Roughness Map Derived from AnisotropySelected for Bare Agricultural Fields

0 500 m

Field 14

Field 13

Field 16

Field 10

0 0.2 0.4 0.6 0.8 1measured ks

Elbe Weiherbach0

0 0.2 0.4 0.6 0.8 1measured ks

Weiherbach

Surface Roughness ks

ks corr.

Elbe RMSerror 0.3 0.6

Weih RMSerror 0.21 0.35

ks corr.

Weih RMSerror 0.1 -

Elbe and Weiherbach Weiherbach Noise Filtered

Deutsches Zentrum für Luft und Raumfahrt e.V. Institut für Hochfrequenztechnik und Radarsysteme ©...

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