polarimetry basics - esaearth.esa.int/landtraining07/d1la3-pottier.pdf · 03/09/07 lecture d1la3...

03/09/07 Lecture D1La3 Polarimetry Basics Eric POTTIER 1

Polarimetry Basics

Eric POTTIER

Monday 3 September, Lecture D1La3


RADAR POLARIMETRYRADAR POLARIMETRY

0

$x

$y( )rE z t,

$z

Radar Polarimetry (Polar : polarisation Metry: measure)is the science of acquiring, processing and analysing

the polarization state of an electromagnetic field

Radar Polarimetry deals with the full vector nature of polarized electromagnetic waves


The POLARISATION informationContained in the waves backscattered

from a given medium is highly related to:

its geometrical structurereflectivity, shape and orientation

its geophysical properties such as humidity, roughness, …

RADAR POLARIMETRYRADAR POLARIMETRY


APPLICATIONS OF RADAR POLARIMETRYIN REMOTE SENSING (EARTH MONITORING)

FORESTRY

SECURITYHUMANITARIAN DEMINING

TOPOGRAPHYCARTOGRAPHY

SEA / ICEOCEANOGRAPHY

AGRICULTURELAND USE METEOROLOGY

HYDROLOGYGEOLOGY


TRANSMITTER: XRECEIVER: X

X

X

T

RXAX

XXS

XXS XXS XXS XXS

X X X XT

RX

SCATTERING COEFFICIENT

SCATTERING COEFFICIENTSCATTERING COEFFICIENT


( )( )( )

⎪⎩

⎪⎨

⎧

=−−=−−=

=0E

kztcosEEkztcosEE

t,zE

z

yy0y

xx0x

δωδω

r

0

$x

$y( )rE z t,

$z

REAL ELECTRIC FIELD VECTOR

POLARISATION ELLIPSEPOLARISATION ELLIPSE


z0

$y

$x

( )rE z t0 ,

( ) ( )δδ 2

2

y0

y

y0x0

yx2

x0

x sinEE

cosEEEE

2EE =⎟⎟

⎠

⎞⎜⎜⎝

⎛+−⎟

⎠

⎞⎜⎝

⎛

0

$x

$y( )rE z t,

$z

THE REAL ELECTRIC FIELD VECTOR MOVES IN TIME ALONG AN ELLIPSE

POLARISATION ELLIPSEPOLARISATION ELLIPSE

With: xy δδδ −=


A : WAVE AMPLITUDE

φ : ORIENTATION ANGLE τ : ELLIPTICITY ANGLE

0A

φα

τ

$x

$y

$,$zn

$y0

$x0

( )rE z t, = 0

φ

α : ABSOLUTE PHASE

22πφπ ≤≤−

40 πτ ≤≤


ANTI-CLOCKWISE ROTATION CLOCKWISE ROTATION

LEFT HANDED POLARISATION RIGHT HANDED POLARISATION

ELLIPTICITY ANGLE : τ < 0ELLIPTICITY ANGLE : τ > 0

44πτπ ≤≤−

POLARISATION HANDENESSPOLARISATION HANDENESSROTATION SENSE: LOOKING INTO THE DIRECTION OF THE WAVE PROPAGATION

0

$x

$y

$z

+τ

−τ


HORIZONTAL POLARISATION STATE

0

rE z t( , )

$z

$y

$x

0

rE z t( , )

$z

$y

$x

⎥⎦

⎤⎢⎣

⎡=01

H ⎥⎦

⎤⎢⎣

⎡=10

V

VERTICAL POLARISATION STATE

00

==

τφ

02

=

=

τ

πφ

JONES VECTORJONES VECTOR

0

rE z t( , )

$z

$y

$x0

rE z t( , )

$z

$y

$x

⎥⎦

⎤⎢⎣

⎡−

=j

12

1RC

LEFT CIRCULAR POLARISATION STATE RIGHT CIRCULAR POLARISATION STATE

4

22πτ

πφπ

+=

+≤≤−

⎥⎦

⎤⎢⎣

⎡=j1

21LC

4

22πτ

πφπ

−=

+≤≤−


TRANSMITTER: XRECEIVERS: X & Y

X

X

T

RXAX

RY

AY

⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡=

YX

XXS S

SE

YXS

XXS

YXS

XXS

YXS

XXS

YXS

XXS

X X X XT

RX

RY

JONES VECTORS

WAVE POLARIMETRY


X

Y

T

RXAX

RY

AY

[ ]⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡=

YY

XY

YX

XX

SS

SS

S

YXS

XXS

YYS

XYS

YXS

XXS

YYS

XYS

X Y X YT

RX

RY

SINCLAIR MATRICES

SCATTERING POLARIMETRY

TRANSMITTER: X & YRECEIVERS: X & Y


DOSAREADS / Dornier GmbH (D)

DO 228 (89), C160 (98), G222 (00)S, C, X-Band (Quad), Ka-Band (VV)

POLARIMETRIC AIRBORNE SAR SENSORS

AIRSARNASA / JPL (USA)

DC8P, L, C-Band (Quad)

AES1InterMap Technologies (D)GulfStream Commander

X-Band (HH), P-Band (Quad)

EMISARDCRS (DK)G3 Aircraft

L, C-Band (Quad)

ESARDLR (D)DO 228

P, L, S-Band (Quad)C, X-Band (Sngl)

MEMPHIS / AER II-PAMIRFGAN (D)

Transal C160Ka, W-Band (Quad) / X-Band (Quad)

PISARNASDA / CRL (J)

GulfStreamL, X-Band (Quad)

PHARUSTNO - FEL (NL)

CESSNA – Citation IIC-Band (Quad)

RAMSESONERA (F)

Transal C160P, L, S, C, X, Ku, Ka, W-Band (Quad)

STORMUVSQ / CETP (F)

Merlin IVC-Band (Quad)

AuSAR - INGARAD.S.T.O (Aus)

DC3 (97) KingAir 350 (00) Beach 1900CX-Band (Quad)

SAR580Environnement Canada (CA)

Convair CV-580C, X-Band (Quad)


POLARIMETRIC SPACEBORNE SAR SENSORS

ENVISAT / ASARESA (EU)

2002C-Band (Sngl / Twin)

ALOS / PALSARJAXA (J)

January 2006L-Band (Sngl / Twin / Quad)

RADARSAT 2CSA / MDA (CA)

2007C-Band (Quad)

TerraSAR-XDLR / EADS-ASTRIUM / InfoTerra GmbH

June 2007X-Band (Sngl / Twin / Quad ?)

SIR-CNASA / JPL (USA)

April 1994 (10 days)October 1994 (10 days)

L, C-Band (Quad)


©© GoogleGoogle EarthEarth

SAN FRANCISCO BAYSAN FRANCISCO BAY

AIRSAR

DC8P, L, C-Band (Quad)

03/09/07 Lecture D1La3 Polarimetry Basics Eric POTTIER 16-15dB 0dB-30dB

|HH|dB |HV|dB |VV|dB

Tx Rx Tx Rx Tx Rx



|HH| |HV| |VV|

Sinclair Color Coding



TRANSMITTER: H & VRECEIVERS: H & V

H

VPOLARIMETRIC DESCRIPTORS

[S] SINCLAIR Matrix

k Target Vector

[T] 3x3 COHERENCY Matrix

[ ] ⎥⎦

⎤⎢⎣

⎡=

VV

HV

VH

HH

SS

SS

S


BACKSCATTERING MATRIX or SINCLAIR MATRIX

BSAYX

BSAXY SS =RECIPROCITY THEOREM

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡iY

iX

YYXY

XYXXjkr

sY

sX

EE

SSSS

re

EE

TOTAL SCATTERED POWER

[ ]( ) [ ][ ]( ) 2YY

2XY

2XX

*T |S||S|2|S|SSTraceSSpan ++==

DEFINED IN THE LOCAL COORDINATES SYSTEM

[S] IS INDEPENDENT OF THE POLARISATION STATE OF THE INCIDENCE WAVE

[S] IS DEPENDENT ON THE FREQUENCY AND THE GEOMETRICAL ANDELECTRICAL PROPERTIES OF THE SCATTERER


VECTORIZATION OF [S]

[ ] [ ]( ) [ ][ ]( )ψSTraceSVkSSSS

SVVHV

HVHH

21

==⇒⎥⎦

⎤⎢⎣

⎡=

[ ]⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡−⎥

⎦

⎤⎢⎣

⎡=

0110

2,10

012,

1001

2Pψ

SET OF 2x2 COMPLEX MATRICESFROM THE PAULI MATRICES GROUP

TARGET VECTOR

[ ]k S S S S SHH VV HH VV HVT= + −

12

2

[ ]( ) [ ][ ]( )k k k span S Trace S S S S STHH HV VV

2 2 2 22= = = = + +* *FROBENIUS NORM = SPAN [S]


TARGET VECTOR k

COHERENCY MATRIX [T]

[ ]T k kA C jD H jG

C jD B B E jFH jG E jF B B

T= ⋅ =− +

+ + +− − −

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

*2 0

0

0

HERMITIAN MATRIX - RANK 1

[ ]k S S S S SHH VV HH VV HVT= + −

12

2

A0, B0+B, B0-B : HUYNEN TARGET GENERATORS

[T] is closer related to Physical and Geometrical Properties of the ScatteringProcess, and thus allows a better and direct physical interpretation


PHYSICAL INTERPRETATION

SINGLE BOUNCESCATTERING

(ROUGH SURFACE)

DOUBLE BOUNCESCATTERING

VOLUMESCATTERING

TARGET GENERATORS TARGET GENERATORS

2VVHH011 SSA2T +==

2VVHH022 SSBBT −=+=

2HV033 S2BBT =−=


-15dB 0dB-30dB

|HH+VV|dB |HV|dB |HH-VV|dB



( )[ ] ( ) ( )[ ] ( )[ ] ( ) ( )[ ]⊥⊥⊥⊥⊥⊥

= B,BA,AA,AT

B,BA,AB,B USUS aa

CON-SIMILARITY TRANSFORMATION

SINCLAIR MATRIX

( )[ ] ( ) ( )[ ] ( )[ ] ( ) ( )[ ] 1B,BA,A3A,AB,BA,A3B,B UTUT −

⊥⊥⊥⊥⊥⊥= aa

SIMILARITY TRANSFORMATION

COHERENCY MATRIX

U(3) SPECIAL UNITARY ELLIPTICALBASIS TRANSFORMATION MATRIX ( ) ( )[ ]

⊥⊥ B,BA,A3U a

ELLIPTICAL BASIS TRANSFORMATIONELLIPTICAL BASIS TRANSFORMATION

U(2) SPECIAL UNITARY ELLIPTICALBASIS TRANSFORMATION MATRIX ( ) ( )[ ]

⊥⊥ B,BA,A2U a


[U3(2φ)] [U3(2τ)] [U3(2α)]

( ) ( )( ) ( )

( ) ( )

( ) ( )

( ) ( )( ) ( )

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−

−

− ⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

10002cos2sinj02sinj2cos

2cos02sinj010

2sinj02cos

2cos2sin02sin2cos0

001αααα

ττ

ττ

φφφφ

SPECIAL UNITARY SU(3) GROUP

SPECIAL UNITARY SU(2) GROUP

[ ] ( ) ( )( ) ( )

( ) ( )( ) ( ) ⎥

⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡ −=

−

α

α

ττττ

φφφφ

j

j

e00e

cossinjsinjcos

cossinsincos

U

( )[ ]φ2U ( )[ ]τ2U ( )[ ]α2U


( )ατφ ,, POLARIZATION ELLIPSE PARAMETERS



0

$x

$y

$z

Pauli Color Coding (H,V)

Pauli Color Coding (+45,-45)

Pauli Color Coding (L,R)Ernst LÜNEBURG

(PIERS95 - Pasadena)


POLARIMETRIC TARGET DIMENSIONPOLARIMETRIC TARGET DIMENSION

POLARIMETRIC GOLDEN NUMBERPOLARIMETRIC GOLDEN NUMBERPOLARIMETRIC GOLDEN NUMBER


TARGET MONOSTATIC POLARIMETRIC « DIMENSION »

55

=

[ ] ⎥⎦

⎤⎢⎣

⎡=

YYYX

XYXX

SSSS

S

XXYYXXXY

YYXYXX

,S,S,S

−− φφ

5 DEGREES OF FREEDOMCOHERENCY MATRIX [T]

9 HUYNEN REAL PARAMETERS(A0, B0, B, C, D, E, F, G, H)

9 - 5 = 4 TARGET EQUATIONS


( ) ( )

( ) ( )( )

( ) 0DFCEBBH0EDFCBBG0DHCGFA20GEFHBBD0GFEHBBC

0FEBB0DGCHEA20HGBBA20DCBBA2

0

00

00

222200

2200

2200

=−−+=−++−=−−=−+−−=−−−

=−−−=−+−=−−−=−−+

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−−++++−

=⋅=BBjFEjGH

jFEBBjDCjGHjDCA2

kkT

0

0

0T*

3x3 HERMITIAN MATRIX - RANK 1

9 PRINCIPAL MINORS = 0

PURE TARGET – MONOSTATIC CASE


TARGET MONOSTATIC POLARIMETRIC « DIMENSION »

55

=

[ ] ⎥⎦

⎤⎢⎣

⎡=

YYYX

XYXX

SSSS

S

XXYYXXXY

YYXYXX

,S,S,S

−− φφ

5 DEGREES OF FREEDOM COHERENCY MATRIX [T]9 HUYNEN REAL PARAMETERS

(A0, B0, B, C, D, E, F, G, H)


( )( )

DHCGFA2DGCHEA2HGBBA2DCBBA2

0

0

2200

2200

+=−=+=−+=+


POLSAR - POLINSARDATA

PROCESSING

POLSAR - POLINSARDATA

PROCESSING

MODEL-BASEDPHYSICAL PARAMETER

INVERSION

MODEL-BASEDPHYSICAL PARAMETER

INVERSION

POLARIMETRIC DESCRIPTORSEXTRACTION

POLARIMETRIC DESCRIPTORSEXTRACTION

BIO and GEO PHYSICALPARAMETERS

TWO-STEP INVERSION PROCEDURE

POLARIMETRICSAR DATA SET(S) QUALITATIVE ANALYSIS

QUANTITATIVE ANALYSIS

POLARIMETRIC REMOTE SENSINGPOLARIMETRIC REMOTE SENSING


POL-SAR PROCESSINGPHENOMENOLOGIC

QUALITATIVE ANALYSIS

POLARIMETRICSPECKLE

FILTERING

POLARIMETRICTARGET

DECOMPOSITION

POLARIMETRICCLASSIFICATIONMONO/DUAL CHANNELS

YY

XYYX

XX




POLARIMETRICSPECKLE

FILTERING

POLARIMETRICTARGET

DECOMPOSITION


YY

XYYX

XX


SPECKLE PHENOMENON

DISTORTION OF THE INTERPRETATION

SPECKLE FILTERING

HOMOGENEOUS AREA HETEROGENEOUS AREA

DETAILS PRESERVATION(SPATIAL RESOLUTION)

SPECKLE REDUCTION(RADIOMETRIC RESOLUTION)

SPECKLE FILTERINGSPECKLE FILTERING


SPECKLEFILTER

[ ] ∑=

=N

1i

T*ii kk

N1T[ ] T*kkT =

CONCEPT OF THE DISTRIBUTED TARGETDISTRIBUTED TARGET

AVERAGING DATA

SECOND ORDERSTATISTICS

COHERENCY MATRICES

SMOOTHING AVERAGING

SPECKLE FILTERINGSPECKLE FILTERING


PURE TARGET

POLARIMETRIC DISTRIBUTEDTARGET « DIMENSION » = 5

COHERENCY MATRIX [T]

9 REAL DEPENDANTHUYNEN PARAMETERS

(A0,B0,B,C,D,E,F,G,H)

TARGET DECOMPOSITIONSTARGET DECOMPOSITIONS


( )( )

DHCGFA2DGCHEA2HGBBA2DCBBA2

0

0

2200

2200

+=−=+=−+=+


DISTRIBUTED TARGET

POLARIMETRIC DISTRIBUTEDTARGET « DIMENSION » = 9

9 REAL INDEPENDANTHUYNEN PARAMETERS

(<A0>,<B0>,<B>,<C>,<D>,<E>,<F>,<G>,<H>)

9 TARGET INEQUATIONS

( ) ( )( ) ( )

( )( )

22

22

0 0

2 2

0

0 0

2 2

0

0 0

0 0

0

2 2 2 2

A B B C D H B B C E D FA B B G H G B B C F D E

A E C H D G C B B H E F GA F C G D H D B B F H G EB B E F

+ ≥ + + ≥ +− ≥ + + ≥ −≥ − − ≥ +≥ + − ≥ −

≥ + +

COHERENCY MATRIX <[T]>



[ ]

[ ]1

1

T

S⇓

DISTRIBUTEDTARGET

orAVERAGED

TARGET

[ ] [ ]∑=

=

=Ni

1iiT

N1T

DECOMPOSITIONTHEOREM

[ ]

[ ]2

2

T

S⇓

[ ]

[ ]3

3

T

S⇓

[ ]

[ ]N

N

T

S⇓

[ ]0T MEAN TARGET





POLARIMETRICSPECKLE

FILTERING

POLARIMETRICTARGET

DECOMPOSITION


YY

XYYX

XX


[ S ]COHERENT

DECOMPOSITION

E. KROGAGER(1990)

W.L. CAMERON(1990)

[ K ]

[ T ] [ C ]

TARGETDICHOTOMY

EIGENVECTORS BASEDDECOMPOSITION

MODEL BASEDDECOMPOSITION

EIGENVECTORS / EIGENVALUES ANALYSIS&

MODEL BASED DECOMPOSITION

EIGENVECTORS / EIGENVALUES ANALYSISENTROPY / ANISOTROPY / ALPHA

S.R. CLOUDE - E. POTTIER(1996-1997)

W.A. HOLM(1988)

S.R. CLOUDE(1985)

J.J. VAN ZYL(1992)

AZIMUTHAL SYMMETRY

J.R. HUYNEN(1970)

R.M. BARNES(1988)

A.J. FREEMAN – S.L. DURDEN (1992)Y. YAMAGUSHI (2005)


THE H / A / THE H / A / αα POLARIMETRICPOLARIMETRICTARGET DECOMPOSITION THEOREMTARGET DECOMPOSITION THEOREM

S.R. CLOUDE S.R. CLOUDE -- E. POTTIER (1995 E. POTTIER (1995 -- 1996)1996)


[ ] [ ][ ][ ]T U U u u u u u u

T

= =⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

−3 3

11 2 3

1

2

3

1 2 3

0 00 00 0

Σλ

λλ

*

ORTHOGONALEIGENVECTORS

REAL EIGENVALUESλ1 > λ2 > λ3

Pii

kk

=

=∑

λ

λ1

3

[ ]k S S S S SXX YY XX YY XYT= + −1

22

[ ] [ ]TN

k kN

Ti iT

i

N

ii

N

= ⋅ == =∑ ∑1 1

1 1

*

TARGET VECTOR

LOCAL ESTIMATE OFTHE COHERENCY MATRIX

EIGENVECTORS / EIGENVALUES ANALYSIS

H / A /H / A / αα DECOMPOSITION DECOMPOSITION


3 ROLL INVARIANT PARAMETERS

332211 PPP αααα ++=

ENTROPY

H P Pi ii

= −=∑ log ( )3

1

3

ANISOTROPY

32

32Aλλλλ

+−

=

α PARAMETER

[ ]U3 =⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

cos cos cossin sin sinsin( sin( sin(

( ) ( ) ( )( )cos( )e ( )cos( )e ( )cos( )e

)sin ( )e ) sin ( )e )sin( )e

1 2 3

1 1j 1

2 2j 2

3 3j 3

1 1j 1

2 2j 2

3 3j 3

α α αα β α β α βα β α β α β

δ δ δ

γ γ γ

PARAMETERISATION OF THE SU(3) UNITARY MATRIX

S.R. CLOUDE - E. POTTIER (1995 - 1996)



PHYSICAL INTERPRETATION

SINGLE BOUNCESCATTERING

(ROUGH SURFACE)

DOUBLE BOUNCESCATTERING

VOLUMESCATTERING

a ba a

a

⇒⇓ν

α

0

0

a ba a

a

− ⇒⇓

ε

α π

0

2

a b>> ⇒ ≈⇓

ε ν

α πa

4

α α α α= + +P P P1 1 2 2 3 3 : ROLL INVARIANT



0A2 BB0 + BB0 − 0 45° 90°

α PARAMETER


0A2 BB0 + BB0 −

ENTROPY (H)

0.5 1.00


0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

60

70

80

90

Entropy (H)

Alp

ha(α

)

9

3

LOWENTROPY

MEDIUMENTROPY

HIGHENTROPY

SURFACESCATTERING

VOLUMESCATTERING

MULTIPLESCATTERING

DIPOLE

DIHEDRAL SCATTERER FORESTRY DBLE BOUNCE

BRANCH / CROWNSTRUCTURE

CLOUD OF ANISOTROPICNEEDLES

NO FEASIBLEREGION

PERTURBATION OF 1st ORDERSCATTERING THEORIES DUE

TO 2nd ORDER EVENTS

DEGREE OF ARBITRARINESS(SCATTERING PROCESSES

RANDOM NOISE

1

47

2

65VEGETATION

8

SEGMENTATION OF THE H /α SPACE

BRAGG SURFACE SURFACE ROUGHNESSPROPAGATION EFFECTS


10n

0

1

2

H0.5 1.00

α0 45° 90°

Alp

ha( α

)

0 0.2 0.4 0.6 0.8 10

102030405060708090

Entropy (H)

POLSAR DATA POLSAR DATA DISTRIBUTIONDISTRIBUTION

IN THEIN THEH /H / αα PLANEPLANE


0A2 BB0 + BB0 −

H - α classification


0A2 BB0 + BB0 −

ANISOTROPY (A)

0.5 1.00


H(1-A)

3 MECHANISMS

A(1-H)

2 MECHANISMS

(1-H)(1-A)

1 MECHANISM

HA

2 MECHANISMS

0.50.250


332211 PPP αααα ++=

ENTROPY

)P(logPH3

1ii3i∑

=

−=

3 ROLL INVARIANT PARAMETERS

ANISOTROPY

32

32Aλλλλ

+−

=

α PARAMETER

( )( )

( )( )⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

−−−−=

AHAH

AHAH

I

111

1

α PHYSICAL SCATTERING MECHANISM

TYPE OF SCATTERING PROCESS

SEGMENTATION / CLASSIFICATION





POLARIMETRICSPECKLE

FILTERING

POLARIMETRICTARGET

DECOMPOSITION


YY

XYYX

XX


[ ]TVVHVHH SSSX 2= ( ) [ ][ ] XCX

C

T

eXP1*

31

−−=π

[ ]THVVVHHVVHH SSSSSk 22

1 −+= ( ) [ ][ ] kTk

T

T

ekP1*

31

−−=π

[ ] [ ]∑∑==

=⋅=N

ii

N

i

Tii T

Nkk

NT

11

* 11

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

( ) ( )[ ]Lm

TTTrLpLLp

mTpLL

eTLTTP pp

m

1.../

2)1(

1

+−ΓΓ= −

−−−

π

Target Vector

COMPLEX WISHART DISTRIBUTIONCOMPLEX WISHART DISTRIBUTION

Coherency Matrix

L: Number of Look p: Polarimetric Dimension


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

( ) ( )[ ]Lm

TTTrLpLLp

mTpLL

eTLTTP pp

m

1.../

2)1(

1

+−ΓΓ= −

−−−

π

WISHART CLASSIFIER (Lee 1994)

BAYES MAXIMUM LIKELIHOOD CLASSIFICATION PROCEDURE

[ ] [ ] [ ]( ) [ ]( ) mjTdTdifTT jmm ≠∀<∈

[ ]( ) [ ] [ ]( ) [ ]( ) [ ]( )( ) KTPTLTTTrLTd mmmm +−+= − lnln1

with

[Tm] : Cluster Center of the class m


UNSUPERVISEDPOLSAR

CLASSIFICATIONE.POTTIER, J.S LEE (2000)

VV

HVVH

HH

WISHART PDF [ ] [ ]( ) [ ] [ ] [ ]( )

( ) ( )[ ]Lm

TTTrLpLLp

mTpLL

eTLTTP pp

m

1.../

2)1(

1

+−ΓΓ= −

−−−

π

H / A / α DECOMPOSITION THEOREM

a

0

30

60

90

0 00.5

11

HA

0.5H A α


1994 LEE et al. PROPOSED A SUPERVISEDALGORITHM BASED ON THE COMPLEXWISHART DISTRIBUTION FOR THECOMPLEX COVARIANCE / COHERENCY MATRIX.

1998 LEE et al. DEVELOPED A COMBINED UNSUPERVISEDCLASSIFICATION METHOD THAT USES THE H / a PLANEWHICH INITIALLY CLASSIFIES THE POLSAR IMAGE. THISSEGMENTED IMAGE IS THEN USED AS TRAINING SETS FORTHE INITIALIZATION OF THE SUPERVISED WISHARTCLASSIFIER.

1999 INTRODUCTION OF THE ANISOTROPY (E. POTTIER - J.S.LEE)

IMPROVEMENT OF THE CAPABILITY TO DISTINGUISHBETWEEN DIFFERENT CLASSES WHOS CENTERS END INTHE SAME ENTROPY (H) AND ALPHA (α) ZONE.

Dr J.S. LEEN.R. L US -NAVY

H / A / H / A / αα -- WISHART CLASSIFIERWISHART CLASSIFIER


Alp

ha (

α)

0 0.2 0.4 0.6 0.8 10

102030405060708090

Entropy (H)

k - mean CLASSIFICATION PROCEDURE

[ ]( ) [ ]∑=

=

=mNk

kk

mm T

NT

1

0 1

Cluster Center of the class m(Lee 1998)

PROVIDE INITIAL [Tm](0)

FOR EACH CLASS

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 ?


C1 C2 C3 C4 C5 C6 C7 C8

SAN FRANCISCO BAY JPL - AIRSAR L-band 1988

0A2 BB0 + BB0 −

4th ITERATION


2 Successive k - mean Classification procedures

21>A

8 Training sets

16 New Training sets

Introduction of the Anisotropy (A)information once the first Classification procedure

has met its termination criterion

21<A 2

1>A



0A2 BB0 + BB0 −C1 C2 C3 C4 C5 C6 C7 C8

C9 C10 C11 C12 C13 C14 C15 C16

4th ITERATION



0A2 BB0 + BB0 −


ICE AREA JPL - AIRSAR L-band

0A2 BB0 + BB0 −C1 C2 C3 C4 C5 C6 C7 C8

C9 C10 C11 C12 C13 C14 C15 C16


DEATH VALLEY JPL - AIRSAR L-band

0A2 BB0 + BB0 −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

0A2 BB0 + BB0 −

OBERPFAFFENHOFEN - ESAR L-band H / A / α and WISHART CLASSIFIER


OBERPFAFFENHOFEN - ESAR L-band H / A / α and WISHART CLASSIFIER

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

POLinSAR Project

0A2 BB0 + BB0 −

TRAUNSTEIN - ESAR L-band H / A / α and WISHART CLASSIFIER


0A2 BB0 + BB0 −C1 C2 C3 C4 C5 C6 C7 C8

C9 C10 C11 C12 C13 C14 C15 C16

ALLING - ESAR L-band H / A / α and WISHART CLASSIFIER


POL-InSARCLASSIFICATION

L. FERRO-FAMIL, E.POTTIER, J.S LEE (2002)

VV

HHVH

WISHART PDF [ ] [ ]( ) [ ] [ ] [ ]( )

( ) ( )[ ]Lm

TTTrLpLLp

mTpLL

eTLTTP pp

m

1.../

2)1(

1

+−ΓΓ= −

−−−

π

OPTIMUM INTERFEROMETRICCOHERENCES SPECTRUM

POLSARCLASSIFICATION

VV

HHVH


POLARIMETRICINTERFEROMETRIC SAR

POL-InSAR

POLARIMETRICPOLARIMETRICINTERFEROMETRIC SARINTERFEROMETRIC SAR

POLPOL--InSARInSAR


Ground range

R1R2

Target height: hP

α

θ

Baseline

YYXX

XY

XXXY

YY

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−+

=

1

11

11

XY

YYXX

YYXX

1

S2SSSS

21k

⎥⎦

⎤⎢⎣

⎡=

2

1

kk

kPOLARIMETRIC

INTERFEROMETRICTARGET VECTOR

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−+

=

2

22

22

XY

YYXX

YYXX

2

S2SSSS

21k


⎥⎦

⎤⎢⎣

⎡=2

1

kk

kPOLARIMETRIC

INTERFEROMETRICTARGET VECTOR

[ ][ ] [ ]

[ ] [ ] ⎥⎦

⎤⎢⎣

⎡=

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⋅

⋅⋅=⋅=

2*T

12

121*T

22*T

12

*T21

*T11*T

6 TT

kkkk

kkkkkkT

ΩΩ

POLARIMETRIC INTERFEROMETRIC COHERENCY MATRIX (6x6)

[ ][ ][ ]12

2

1

TT

Ω

HERMITIAN POLARIMETRIC COHERENCY MATRIX (3x3)

HERMITIAN POLARIMETRIC COHERENCY MATRIX (3x3)

NON HERMITIAN POLARIMETRIC INTER-COHERENCY MATRIX (3x3)


DUAL CHANNELS POLINSAR UNSUPERVISED SEGMENTATION

[ ][ ] [ ]

[ ] [ ] ⎥⎦

⎤⎢⎣

⎡=

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⋅

⋅⋅=⋅=

2*T

12

121*T

22*T

12

*T21

*T11*T

6 TT

kkkk

kkkkkkT

ΩΩ

POLARIMETRIC INTERFEROMETRIC COHERENCY MATRIX (6x6)

[ ]6T FOLLOWS A WISHART DISTRIBUTION

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

[ ]( )mCLm

61

mpL

6m6 ,LW

p,LK

TtrexpT/TP Σ

Σ

ΣΣ =

−=

−−

( ) ( ) ( )1pL...LL

p,LK Lp

2)1p(p

+−=−

ΓΓπL: Number of Look

p: Polarimetric Dimension

[Σm] : Cluster Center of the class m

With:


With: Complex Unitary Vectors( )21 w,w

POLSAR IMAGES 1*T

11 kwI ⋅= and

[ ][ ] [ ] *T

222*T

111

*T2121

*22

*11

*21

21wTwwTw

ww

IIII

II)w,w(

Ωγ ==

( )γγarg INTERFEROMETRIC PHASE

INTERFEROMETRIC COHERENCE

2*T

22 kwI ⋅=

COMPLEX POLARIMETRIC INTERFEROMETRIC COHERENCE

polartemporalspatialSNR γγγγγ ⋅⋅⋅=


ESARDO 228

P, L, S-Band (Quad)C, X-Band (Sngl)

P-Band

L-Band C-Band

X-Band

Courtesy of

Experimental SyntheticAperture Radar SystemExperimental SyntheticAperture Radar System


DLR E-SAR L BandIn-Pol SAR (1.5m x 3m) – Baseline 15m

Arg(γ)POL-SAR INFORMATION IN-SAR INFORMATION


COMPLEMENTARY INFORMATION

DLR E-SAR L BandIn-Pol SAR (1.5m x 3m) – Baseline 5m

|γ|POL-SAR INFORMATION IN-SAR INFORMATION


HOMOGENEOUS AREA

CONSTANT INTERFEROMETRICCOHERENCE

HETEROGENEOUS AREA

DIFFERENT POLARIMETRICSCATTERING MECHANISMS


HETEROGENEOUS AREA

DIFFERENT INTERFEROMETRICCOHERENCE

HOMOGENEOUS AREA

SAME POLARIMETRICSCATTERING MECHANISMS


0A2 BB0 + BB0 −γINTERFEROMETRIC COHERENCE


C1 C2 C3 C4 C5 C6 C7 C8

C9 C10 C11 C12 C13 C14 C15 C16

Wishart H-A-α segmentation

γINTERFEROMETRIC COHERENCE


Oriented buildings segmented from vegetated areas

Optical Image POLSAR Image POLSAR Segmentation

INSAR Image POLINSAR SegmentationVOL POLINSAR Segmentation


Low density forested areas segmented from dense forest

Optical Image POLSAR Image POLSAR Segmentation

INSAR Image VOL POLINSAR Segmentation POLINSAR Segmentation


Questions ?Questions ?

polarimetry basics - esaearth.esa.int/landtraining07/d1la3-pottier.pdf · 03/09/07 lecture d1la3...

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