PolInSAR 2017 | 23-27 January | ESA-ESRIN
Exploitation of General Polarimetric Model-based
Decomposition by Incorporating A Generalized
Volume Scattering Model
Qinghua Xie1, 2 ([email protected]), J. David Ballester-Berman2,
Juan M. Lopez-Sanchez2, Jianjun Zhu1, Changcheng Wang1
1. School of Geosciences and Info-Physics, Central South University, Changsha, China
2. Institute for Computing Research (IUII), University of Alicante, Alicante, Spain
PolInSAR 2017 | 23-27 January | ESA-ESRIN
4, Conclusion
3, Simulation And Experimental Result
1, Research Motivation
2, General Decomposition Models & Algorithm
Outline
PolInSAR 2017 | 23-27 January | ESA-ESRIN
Model-Based Decomposition Methods
* * * *data s surface d dihedral v volume c helixT f T f T f T f T (+…)
FD3: Freeman-Durden 3-Component
Decomposition (Freeman, TGRS, 1998)
Y4O: Yamaguchi 4-Component Decomposition
(Yamaguchi, TGRS, 2005)
Y4R: Y4 with Rotation (Yamaguchi , TGRS,
2011)
S4R: Y4R+ Volume Scattering by Dihedral
(Sato, GRSL, 2012)
G4U: S4R+ Additional Unitary Transformation
Which Makes T23=0 (Singh, TGRS, 2013)
……
By Exploiting key ideas in previous methods
Chen: 4 Tv Models + 2 Rotation Angles + Directly
Parameters Solving (Chen, TGRS, 2014)
Xie: Chen’s decomposition framework +modified
parameters inversion algorithm (Xie, RS, 2016)
Question : Just specific volume scattering models. Whether more generalized volume
scattering models can help improving general model-based decomposition (GMD)?
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PolInSAR 2017 | 23-27 January | ESA-ESRIN
4, Conclusion
3, Simulation And Experimental Result
2, General Decomposition Models & Algorithm
1, Research Motivation
Outline
PolInSAR 2017 | 23-27 January | ESA-ESRIN
2 0 01
= 0 1 04
0 0 1
vol random vT f
1 0 01
= 0 1 03
0 0 1
vol entropy vT f
15 5 01
= 5 7 030
0 0 8
vol horizontal vT f
15 5 01
= 5 7 030
0 0 8
vol vertical vT f
v s S d D c residualT T T T T T
*
2
1 0
= 0
0 0 0
s sT f
General Decomposition Models
Chen et.al, TGRS, 2014
0 0 01
= 0 12
0 1
c cT f j
j
2
*
d
0
= 1 0
0 0 0
dT f
* *
2 22
3 3
2 2 2
1 cos sin 2
1= cos cos sin 4
2
1sin 2 sin 4 sin
2
S S
H
s S S s S S S S S
S S S
T R T R f
Volume
Scattering
Surface
Scattering
Dihedral
Scattering
Helix
Scattering
Page 5/26
2
* 2
3 3
* 2
cos2 sin 2
1cos2 cos 2 sin 4
2
1sin 2 sin 4 sin 2
2
D D
H
d d d d d d D D D
D D D
T R T R f
PolInSAR 2017 | 23-27 January | ESA-ESRIN
Parameters Inversion Algorithm
v s S d D c residualT T T T T T Inversion Model
9 Real Observations 11 22 33 12 12 13 13 23 23{ , , , Re( ), Im( ), Re( ), Im( ), Re( ), Im( )}T T T T T T T T T
9 Unknown Parameters , , , , Re( ), Im( ), , ,v s d c S Df f f f
Optimization Criterion 2
2min : residualT
230 , , 0 2 Im
, , 14 4
v s d c
S D
f f f SPAN f TBoundary Conditions
Initial Values Traditional Yamaguchi-based decomposition methods, e.g.Y4O, Y4R
Nonlinear Optimization to Solve 9 Dimensional Problem
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PolInSAR 2017 | 23-27 January | ESA-ESRIN
Modified Chen Method
Quantitative Analysis of Polarimetric Model-Based Decomposition Methods
PolSAR Data
Monte Carlo
Simulation Test
Real data Test
Model-based Decomposition
Traditional Methods 1) Y4O 2) Y4R 3) S4R 4) G4U 5) Chen
Modified Chen Method 1) Chen’s Decomposition framework 2) Modification of The Inversion Algorithm Redefined boundary conditions; Variable transformation; Modification for Initial Values
1) Quantitative analysis of the whole parameter set; 2) Model parameters within physically valid ranges
Xie, Q.; Ballester-Berman, J.D.; Lopez-Sanchez, J.M.; Zhu,
J.; Wang, C. Quantitative Analysis of Polarimetric Model-
Based Decomposition Methods. Remote Sens. 2016, 8, 977.
1
1=
nH
simC uun
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PolInSAR 2017 | 23-27 January | ESA-ESRIN
Volume Scattering Model: GVSM
0 / 3
1 10 / 3 0
23 / 2(1 ) / 3
/ 3 0 1
VC
2 2
hh vvS S
According to the expression of GVSM in case of setting the value of shape parameter as 1/3
(i.e., dipoles) for the covariance matrix
Unitary transformation
1 10
2 3 2
1 1 10
2 2 33(1 )
2 3 10 0
2 3
GVSM
vT
GVSM (Antropov et al. TGRS, 2011)
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PolInSAR 2017 | 23-27 January | ESA-ESRIN
Show the Generality of GVSM
Radar vegetation index ( Kim & Van zyl)
1 2 3
1 2 3
4min , ,RVI
11
logN
i
i N i i Ni
ij
H P P P
Polarimetric scattering entropy (Cloude & Pottier)
-10 -5 0 5 100.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
(dB)
RV
I an
d H
RVI
H
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PolInSAR 2017 | 23-27 January | ESA-ESRIN
Volume Scattering Model: SAVSM
SAVSM (Huang et al. TGRS, 2016) ),
1
sin2
vp
1
cos2
hp
1
2rp
2 0 01
= 0 1 04
0 0 1
vol randomT
15 5 01
= 5 7 030
0 0 8
vol horizontalT
15 5 01
= 5 7 030
0 0 8
vol verticalT
1 0
0 0h dipoleS
1 0
0 0h dipoleS
Freeman&Yamaguchi models
V SAVSM
VT n
H SAVSM
VT n
n H-SAVSM V-SAVSM
0
1
Freeman&Yamaguchi VS SAVSM models
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PolInSAR 2017 | 23-27 January | ESA-ESRIN
Generality of SAVSM
0 5 10 15 20 25-25
-20
-15
-10
-5
0
5
10
15
20
25
n
(d
B)
H-SAVSM
V-SAVSM
0 5 10 15 20 250
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
nR
VI
an
d H
RVI
H
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PolInSAR 2017 | 23-27 January | ESA-ESRIN
2 0 01
= 0 1 04
0 0 1
vol random vT f
1 0 01
= 0 1 03
0 0 1
vol entropy vT f
15 5 01
= 5 7 030
0 0 8
vol horizontal vT f
15 5 01
= 5 7 030
0 0 8
vol vertical vT f
v s S d D c residualT T T T T T
GMD with Generalized Volume Models
Chen et.al, TGRS, 2014
Volume
Scattering
G
v v s s S d d D c c residualT f T f T f T f T T
G
vT
Original
vT
Proposed
Parameter Inversion Same as Modified Chen method(Xie et.al, Remote Sensing, 2016)
GVSM
vT
SAVSM
vT n“continuous” volume models
“discrete” volume models
(Huang et al. TGRS, 2016).
(Antropov et al. TGRS, 2011 )
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GMD-GVSM
GMD-SAVSM
PolInSAR 2017 | 23-27 January | ESA-ESRIN
Coherency Matrix Rotated Coherency Matrix
Ratio Estimation
GVSM
v v s s S d d D c c residualT f T f T f T f T T
Modified Parameters Inversion Algorithm
Solution
, , , , , , ,v s d c S Df f f f
2 2, 1 , 1 ,v v s s d d c cP f P f P f P f
T 'T
2 2
10=10log hh vvS S
Flowchart of “GMD-GVSM” method
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PolInSAR 2017 | 23-27 January | ESA-ESRIN
Flowchart of GMD-SAVSM
Coherency Matrix
Ratio Estimation
SAVSM
v v opt s s S d d D c c residualT f T n f T f T f T T
2 2
10=10log hh vvS S
Modified Parameters Inversion Algorithm
Solution
, , , , , , ,v s d c S Df f f f
2 2, 1 , 1 ,v v s s d d c cP f P f P f P f
T
0dB H-SAVSMYesV-SAVSM No
Loop from
No
Yes
First solution ,then second loop from
1 10.9 : 0.1: 0.9st stn n n
0 :1: 20n
min T SAVSMRVI RVI n
min T SAVSMRVI RVI n
1stn
No
Optimum
Yes
optn
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PolInSAR 2017 | 23-27 January | ESA-ESRIN
4, Conclusion
3, Simulation And Experimental Result
2, General Decomposition Models & Algorithm
1, Research Motivation
Outline
PolInSAR 2017 | 23-27 January | ESA-ESRIN
Monte Carlo Simulation Tests
Parameter Quantity Value
vf volume scattering coefficient 0:2:10
sf surface scattering coefficient 0:2:10
df dihedral scattering coefficient 0:2:10
cf helix scattering coefficient 0.01
s orientation angle in surface scattering model -10°
d orientation angle in dihedral scattering model -15° ratio parameter in dihedral scattering model 0.3515 - 0.0768i ratio parameter in surface scattering model -0.3377 incidence angle 45° differential propagation phase 10°
s soil dielectric constant 10
t trunk dielectric constant 30
1
Table 1. Values for input parameters
we simulated 216 different cases. In every case, we performed 1000 realizations
and 15×15 looks were averaged for reducing speckle noise
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PolInSAR 2017 | 23-27 January | ESA-ESRIN
Monte-Carlo Simulation for PolSAR Data
(1) Eigenvalue decomposition for the given covariance matrix C and computation of its square root:
(2) Simulate a normal complex Gaussian random vector using Gaussian random number generators
(4) Compute the n-looks averaged covariance matrix
(3) Compute the simulated single look complex vector
1/2u C v
1/2
V CV=D
C V*
H
D
*
1
1C =
nT
sim uun
(5) The corresponding coherency matrix is obtained by a special unitary transformation matrix.
simT
Reference: J. S. Lee and E. Pottier, Polarimetric radar imaging: from basics to applications. Boca Raton, FL: CRC Press, 2009.
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we computed the corresponding cumulative probability distribution curves of RMSE of all parameters for all the 216 different cases. Note that the cumulative distribution function is defined as
(a)
(b)
1
0 0.5 1 1.5 2 2.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RMSE(fv)
Cu
mu
lati
ve P
rob
ab
ilit
y
Modified Chen
GMD-GVSM
GMD-SAVSM
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RMSE(fs)
Cu
mu
lati
ve P
rob
ab
ilit
y
Modified Chen
GMD-GVSM
GMD-SAVSM
,XF x P X x where X represents RMSE
Results Page 18/26
PolInSAR 2017 | 23-27 January | ESA-ESRIN
(g) (h)
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RMSE(||)
Cu
mu
lati
ve P
rob
ab
ilit
y
Modified Chen
GMD-GVSM
GMD-SAVSM
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RMSE(angle())
Cu
mu
lati
ve P
rob
ab
ilit
y
Modified Chen
GMD-GVSM
GMD-SAVSM
(e) (f)
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RMSE(S)
Cu
mu
lati
ve P
rob
ab
ilit
y
Modified Chen
GMD-GVSM
GMD-SAVSM
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RMSE(D
)C
um
ula
tive P
rob
ab
ilit
y
Modified Chen
GMD-GVSM
GMD-SAVSM
(i)
1
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.180
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RMSE()
Cu
mu
lati
ve P
rob
ab
ilit
y
Modified Chen
GMD-GVSM
GMD-SAVSM
Results Page 19/26
PolInSAR 2017 | 23-27 January | ESA-ESRIN
Real Test-San Francisco, CA, USA
Radarsat2 C-band (Quad-Pol)
Date:
April 9, 2008
Original Resolution:
4.7m×4.8m
(range×azimuth)
Incidence Range:
28.45°~ 29.38°
AIRSAR L-band (Quad-Pol)
Date:
May 11, 1999
Original Resolution:
3.3m×9.26m
(range×azimuth)
Incidence Range:
28.4°~ 62.7°
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C-band Radarsat-2 Test
Figure Decomposition results from C-band Radarsat-2 data over San Francisco area. (a) Yamaguchi decomposition with orientation compensation; (b) Modified Chen decomposition by using modified parameter inversion algorithm; (c) Proposed GMD-GVSM decomposition; (d) Proposed GMD-SAVSM decomposition. The images are colored by Pd (red), Pv (green), Ps (blue).
(a) (b) (c) (d)
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PolInSAR 2017 | 23-27 January | ESA-ESRIN
L-band AIRSAR Test
Figure Decomposition results from AIRSAR-L data over San Francisco area. (a) Yamaguchi decomposition with orientation compensation; (b) Modified Chen decomposition by using modified parameter inversion algorithm; (c) Proposed GMD-GVSM decomposition; (d) Proposed GMD-SAVSM decomposition. The images are colored by Pd (red), Pv (green), Ps (blue).
(a) (b) (c) (d)
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PolInSAR 2017 | 23-27 January | ESA-ESRIN
Table Statistics of power of scattering components in selected areas with different land cover classes.
Statistics of power of scattering components
Area Methods Ps(%) Pd(%) Pv(%) Pc(%)
Forest
Y4R 35.98 13.72 45.21 5.09
Modified Chen 34.71 22.48 37.73 5.08
GMD–GVSM 32.48 21.02 41.40 5.10
GMD–SAVSM 33.81 21.76 39.30 5.12
Park
Y4R 29.31 11.51 53.21 5.97
Modified Chen 29.88 20.09 44.06 5.97
GMD–GVSM 26.47 18.75 48.79 5.99
GMD–SAVSM 28.77 19.80 45.40 6.03
Build-up A
Y4R 20.51 35.34 37.53 6.62
Modified Chen 20.10 40.57 32.74 6.59
GMD–GVSM 19.73 40.95 32.66 6.66
GMD–SAVSM 20.31 42.04 30.94 6.71
Build-up B
Y4R 33.48 48.35 14.15 4.01
Modified Chen 25.27 56.83 13.89 4.00
GMD–GVSM 26.54 55.15 14.29 4.01
GMD–SAVSM 27.75 53.53 14.68 4.04
Ocean
Y4R 95.12 1.86 2.60 0.41
Modified Chen 93.39 4.52 1.68 0.41
GMD–GVSM 93.33 4.52 1.74 0.41
GMD–SAVSM 93.01 4.43 2.15 0.41
1
C-band RadarSat-2 L-band AIRSAR
Page 23/26
Area Methods Ps(%) Pd(%) Pv(%) Pc(%)
Forest
Y4R 27.81 18.59 44.92 8.68
Modified Chen 27.36 29.30 34.66 8.68
GMD–GVSM 26.20 28.67 36.43 8.70
GMD–SAVSM 26.17 28.55 36.57 8.71
Park
Y4R 29.43 29.20 34.71 6.66
Modified Chen 24.93 40.21 28.21 6.65
GMD–GVSM 24.67 39.50 29.16 6.67
GMD–SAVSM 25.15 37.83 30.34 6.68
Build-up A
Y4R 30.99 37.60 24.74 6.67
Modified Chen 27.22 49.62 16.59 6.57
GMD–GVSM 27.34 49.11 16.96 6.59
GMD–SAVSM 26.03 47.18 20.20 6.59
Build-up B
Y4R 21.41 59.42 16.10 3.07
Modified Chen 15.53 68.22 13.19 3.06
GMD–GVSM 16.25 66.32 14.37 3.06
GMD–SAVSM 16.18 62.05 18.70 3.07
Ocean
Y4R 93.85 1.86 3.52 0.77
Modified Chen 91.82 5.35 2.06 0.77
GMD–GVSM 91.71 5.31 2.21 0.77
GMD–SAVSM 91.18 5.31 2.75 0.76
1
PolInSAR 2017 | 23-27 January | ESA-ESRIN
4, Conclusion
3, Simulation And Experimental Result
1, Research Motivation
2, General Decomposition Models & Algorithm
Outline
PolInSAR 2017 | 23-27 January | ESA-ESRIN
Conclusion
A number of Monte Carlo simulations shown the proposed ‘GMD-GVSM’ method
outperforms ‘GMD-SAVSM’ method and the previous existing strategies for PolSAR model-
based parameter inversion.
Both proposed methods provide a wide range of volume scattering models, which are
directly estimated by data themselves. In addition, they just need one non-linear optimization
calculation, which can significantly reduce both numerical issues and the computation cost.
As an overall conclusion we can state that the ‘GMD-GVSM’ method is a promising
methodology for quantitative target decompositions. More validations and applications need
be investigated in future.
The real test results indicate that radar frequency is an issue on affecting decomposition
results and developing more general decomposition methods is helpful for avoiding scattering
interpretation ambiguities.
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PolInSAR 2017 | 23-27 January | ESA-ESRIN
Thanks For Your Kind Attention!
Qinghua Xie1, 2 ([email protected]), J. David Ballester-Berman2,
Juan M. Lopez-Sanchez2, Jianjun Zhu1, Changcheng Wang1
1. School of Geosciences and Info-Physics, Central South University, Changsha, China
2. Institute for Computing Research (IUII), University of Alicante, Alicante, Spain