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

VVVH

HVHH

SSSS

S][Scattering Matrix:

Scattering Vector: 4T

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

0ii0

20110

21001

21001

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

VVHH

P3P33

S4SSS2SSS2SSS2SSSSSSSSS2SSSSSS

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

:][



Eigenvector Decomposition

Coherence Matrix: P3P33 kkT

:][

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

333231

232221

131211

2

eeeeeeeee

U ][

1

1

1

000000

][

332313

322212

312111

21

2

eeeeeeeee

UU ][][

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

23

13333222111

3

1iiii3 TTTeeeeeeeeT

0321

33

23

13

3

32

22

12

2

31

21

11

1

eee

eeee

eeee

e

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

23

13333222111

3

1iiii3 TTTeeeeeeeeT

32

32

32

32

PPPPA

:

321

iiP

:i3

3

1ii PPH log:

where:Scattering Entropy:

Scattering Anisotropy:

Totally Polarised ScattererTotally Unpolarised Scatterer

0H

1H1H0

0A

1A1A0 2 Equal Secondary Scattering Processes

Only 1 Secondary Scattering Process



Power Images

HH

L-band

SIR-C / Test Site: Kudara,Russia

VV HV

Azim

uth

Range



Scattering Entropy Images

C-band

L-band

H=0

H=1




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

C-band

L-band

A=0

A=1



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

333222111

321

3

iiiiiiU

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

23

13333222111

1333 TTTeeeeeeUUT

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

)exp()cos(

ii

ie

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

0001

][S

1001

][S

1001

][S



Mean Scattering Parameters

Coherency Matrix Diagonalisation:

321

iiP

:

Mean α-Angle:

Mean β-Angle:

Mean γ-Angle:

Mean δ-Angle:

332211 PPP

332211 PPP

332211 PPP

332211 PPP

)()()(][ 3332221113 eeeeeeT


)cos(

iie


)cos(

iii

iii

i

i

iie

Eigenvectors: Appearance Probabilities:

Mean Scattering Mechanism



α-Angle Images

C-band

L-band

a=0°

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

10

20

30

40

50

60

70

80

90

Entropy

a-An

gle

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



N

1ii

N

1i

Tii T

N1kk

N1T *

Lm

TTTrLpLLp

mT1pLL

eTLTTP

21pp

1m

.../ )(

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

mNk

1kk

m

0m T

N1T

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

mNj

jj

m

km T

NT

1

1 1

TERMINAISONCRITERION ?

Alp

ha (

)

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



21A

8 Training sets

16 New Training sets

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

procedure has met its termination criterion

21A 2

1A

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



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

ns

Unsupervised Wishart

(66) Classificatio

n

ClassNumber

Reduction

Image L

Image X 8 classes

64 classes

64 classes

ClassifiedImage

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

022

1

ii

mRRRR

SSSSS

k PS

Ps

HV

VVHH

VVHH

P

0000

02*

*2

PSPSPS

PSpSPS

PP RRRRRR

RRRRRR

kkT

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

,00,

rP

rS

VVVH

HVHH

RR

SSSS

S

22

22

)sincos(

))sin1()(sin1(

rr

rrPR

2

2

sincos

sincos

r

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

21

11

P

20 1

“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

1

P()

1

k

SensorScattering

PlaneAzimuthal Oriented Surface

+ =



))4(sinc1(00

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

13

1312

121

CCCCC

T

23 2

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)

20 1



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

ß1



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

N N N

0 1.5 km



Alpha < 43 degreeEntropy < 0.5 Anisotropy

Surface Scatterers



Soil Moisture Maps Selected for Bare Agricultural Fields

Dielectric Constant Volumetric Moisture

N N

0 500 m

Field 10

Field 13

Field 14

Field 16



0

10

20

30

40

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

estim

ated

mv [v

ol. %

]

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

0

5

10

15

20

25

0 5 10 15 20 25measured '

estim

ated

'

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

N

0 500 m

Field 14

Field 13

Field 16

Field 10



0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1measured ks

estim

ated

ks

Elbe Weiherbach0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1measured ks

estim

ated

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

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