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03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 1
Advanced SAR 2PolarimetryEric POTTIER
Monday 3 September, Lecture D1Lb5-2
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 2
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 3
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 4
APPLICATIONS OF RADAR POLARIMETRYIN REMOTE SENSING (EARTH MONITORING)
FORESTRY
SECURITYHUMANITARIAN DEMINING
TOPOGRAPHYCARTOGRAPHY
SEA / ICEOCEANOGRAPHY
AGRICULTURELAND USE METEOROLOGY
HYDROLOGYGEOLOGY
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 5
TRANSMITTER: XRECEIVER: X
X
X
T
RXAX
XXS
XXS XXS XXS XXS
X X X XT
RX
SCATTERING COEFFICIENT
SCATTERING COEFFICIENTSCATTERING COEFFICIENT
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 6
( )( )( )
⎪⎩
⎪⎨
⎧
=−−=−−=
=0E
kztcosEEkztcosEE
t,zE
z
yy0y
xx0x
δωδω
r
0
$x
$y( )rE z t,
$z
REAL ELECTRIC FIELD VECTOR
POLARISATION ELLIPSEPOLARISATION ELLIPSE
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 7
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 −=
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 8
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 ≤≤
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 9
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 10
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
−=
+≤≤−
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 11
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 12
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 13
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)
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 14
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)
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 15
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 16
P-Band C-BandL-Band
Deutsches Zentrum für Luft- und RaumfahrtInstitut für Hochfrequenztechnik
und Radarsysteme
ALLINGALLING
©© GoogleGoogle EarthEarth
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 17-15dB 0dB-30dB
|HH|dB |HV|dB |VV|dB
Tx Rx Tx Rx Tx Rx
ALLINGALLING
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 18
|HH| |HV| |VV|©© GoogleGoogle EarthEarth
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 19
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 20
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 21
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]
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 22
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 23
PHYSICAL INTERPRETATION
SINGLE BOUNCESCATTERING
(ROUGH SURFACE)
DOUBLE BOUNCESCATTERING
VOLUMESCATTERING
TARGET GENERATORS TARGET GENERATORS
2VVHH011 SSA2T +==
2VVHH022 SSBBT −=+=
2HV033 S2BBT =−=
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 24
-15dB 0dB-30dB
|HH+VV|dB |HV|dB |HH-VV|dB
ALLINGALLING
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 25
|HH+VV| |HV| |HH-VV|T11=2A0 T33=B0-B T22=B0+B
©© GoogleGoogle EarthEarth
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 26
( )[ ] ( ) ( )[ ] ( )[ ] ( ) ( )[ ]⊥⊥⊥⊥⊥⊥
= 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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 27
[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
ELLIPTICAL BASIS TRANSFORMATIONELLIPTICAL BASIS TRANSFORMATION
( )ατφ ,, POLARIZATION ELLIPSE PARAMETERS
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 28
ELLIPTICAL BASIS TRANSFORMATIONELLIPTICAL BASIS TRANSFORMATION
0
$x
$y
$z
Pauli Color Coding (H,V)
Pauli Color Coding (+45,-45)
Pauli Color Coding (L,R)Ernst LÜNEBURG
(PIERS95 - Pasadena)
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 29
POLARIMETRIC TARGET DIMENSIONPOLARIMETRIC TARGET DIMENSION
POLARIMETRIC GOLDEN NUMBERPOLARIMETRIC GOLDEN NUMBERPOLARIMETRIC GOLDEN NUMBER
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 30
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 31
( ) ( )
( ) ( )( )
( ) 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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 32
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)
9 - 5 = 4 TARGET EQUATIONS
( )( )
DHCGFA2DGCHEA2HGBBA2DCBBA2
0
0
2200
2200
+=−=+=−+=+
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 33
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 34
POL-SAR PROCESSINGPHENOMENOLOGIC
QUALITATIVE ANALYSIS
POLARIMETRICSPECKLE
FILTERING
POLARIMETRICTARGET
DECOMPOSITION
POLARIMETRICCLASSIFICATIONMONO/DUAL CHANNELS
YY
XYYX
XX
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 35
POL-SAR PROCESSINGPHENOMENOLOGIC
QUALITATIVE ANALYSIS
POLARIMETRICSPECKLE
FILTERING
POLARIMETRICTARGET
DECOMPOSITION
POLARIMETRICCLASSIFICATIONMONO/DUAL CHANNELS
YY
XYYX
XX
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 36
SPECKLE PHENOMENON
DISTORTION OF THE INTERPRETATION
SPECKLE FILTERING
HOMOGENEOUS AREA HETEROGENEOUS AREA
DETAILS PRESERVATION(SPATIAL RESOLUTION)
SPECKLE REDUCTION(RADIOMETRIC RESOLUTION)
SPECKLE FILTERINGSPECKLE FILTERING
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 37
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 38
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
9 - 5 = 4 TARGET EQUATIONS
( )( )
DHCGFA2DGCHEA2HGBBA2DCBBA2
0
0
2200
2200
+=−=+=−+=+
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 39
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]>
TARGET DECOMPOSITIONSTARGET DECOMPOSITIONS
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 40
[ ]
[ ]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
TARGET DECOMPOSITIONSTARGET DECOMPOSITIONS
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 41
POL-SAR PROCESSINGPHENOMENOLOGIC
QUALITATIVE ANALYSIS
POLARIMETRICSPECKLE
FILTERING
POLARIMETRICTARGET
DECOMPOSITION
POLARIMETRICCLASSIFICATIONMONO/DUAL CHANNELS
YY
XYYX
XX
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 42
[ 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)
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 43
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)
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 44
[ ] [ ][ ][ ]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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 45
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)
H / A /H / A / αα DECOMPOSITION DECOMPOSITION
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 46
[ ] [ ][ ][ ]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
[ ]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
TARGET 1 TARGET 2 TARGET 3
REAL EIGENVALUESλ1 > λ2 > λ3
PARAMETERISATION OF THE SU(3) UNITARY MATRIX
H / A /H / A / αα DECOMPOSITION DECOMPOSITION
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 47
EIGENVECTORS / EIGENVALUES ANALYSIS
( )[ ] ( )[ ] [ ] ( )[ ]T U T UR Rθ θ θ=−1
( )[ ] ( )[ ][ ] ( )[ ]T U Uθ θ θ=−
3 31
Σ
ORIENTED (θ ) COHERENCY MATRIX SU(3) UNITARY ROTATION MATRIX (θ )
[ ]UR( ) cos sinsin cos
θ θ θθ θ
=−
⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
1 0 00 2 20 2 2
EIGENVALUES λ1 λ2 λ3 : ROLL INVARIANT
PROBABILITIES P1 P2 P3 : ROLL INVARIANT
ROLL INVARIANCE PROPERTY
H / A /H / A / αα DECOMPOSITION DECOMPOSITION
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 48
EIGENVECTORS UNITARY MATRIX
: ROLL INVARIANT
PHYSICAL INTERPRETATION
( )[ ] ( )[ ][ ]U U UR3 3θ θ=
[ ]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
α α α α= + +P P P1 1 2 2 3 3
PARAMETERIZATION OF THE UNITARY MATRIX
H / A /H / A / αα DECOMPOSITION DECOMPOSITION
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 49
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
H / A /H / A / αα DECOMPOSITION DECOMPOSITION
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 50
0 45° 90°
α PARAMETER
|HH+VV| |HV| |HH-VV|T11=2A0 T33=B0-B T22=B0+B
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 51
ENTROPY(DEGREE OF RANDOMNESS
STATISTICAL DISORDER)
H P Pi ii
=−=∑ log ( )3
1
3
DISTRIBUTED TARGETλ1 = λ2 = λ3= SPAN / 3
H = 1
PURE TARGETλ1=SPAN λ2=0 λ3=0
H = 0
EIGENVALUES λ1 λ2 λ3 : ROLL INVARIANT
PROBABILITIES P1 P2 P3 : ROLL INVARIANT
H / A /H / A / αα DECOMPOSITION DECOMPOSITION
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 52
ENTROPY (H)
0.5 1.00|HH+VV| |HV| |HH-VV|T11=2A0 T33=B0-B T22=B0+B
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 53
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 54
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
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 55
H - α classification
|HH+VV| |HV| |HH-VV|T11=2A0 T33=B0-B T22=B0+B
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 56
DIFFICULT MECHANISM DISCRIMINATION WHEN : H > 0.7
ANISOTROPY(EIGENVALUES SPECTRUM)
λ1 λ2 λ332
32Aλλλλ
+−
=
COMPLEMENTARY TO ENTROPY
DISCRIMINATION WHEN H > 0.7
ROLL INVARIANT
H / A /H / A / αα DECOMPOSITION DECOMPOSITION
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 57
0.2
0.3
0.4
0.5
0.60.7
0.1
H = 0.9
0.2
0.
1.0
0.4
0.6
0.8
0.2 0.4 0.6 0.8 1.0λλ
2
1
λ λλ λ
3 1
2 1
0.8
1.0
0.4 0.4 A = 0
1.0 1.0
0.3
A = 0.54
H / A /H / A / αα DECOMPOSITION DECOMPOSITION
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 58
ANISOTROPY (A)
0.5 1.00|HH+VV| |HV| |HH-VV|T11=2A0 T33=B0-B T22=B0+B
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 59
H(1-A)
3 MECHANISMS
A(1-H)
2 MECHANISMS
(1-H)(1-A)
1 MECHANISM
HA
2 MECHANISMS
0.50.250
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 60
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
H / A /H / A / αα DECOMPOSITION DECOMPOSITION
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 61
POL-SAR PROCESSINGPHENOMENOLOGIC
QUALITATIVE ANALYSIS
POLARIMETRICSPECKLE
FILTERING
POLARIMETRICTARGET
DECOMPOSITION
POLARIMETRICCLASSIFICATIONMONO/DUAL CHANNELS
YY
XYYX
XX
03/09/07 Lecture D1Lb5-2 Advanced SAR 2 - Polarimetry Eric POTTIER 62
Questions ?Questions ?