National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.1
Measuring Orientation and Randomness of Vegetation using
Polarimetric SAR DataMotofumi Arii
Mitsubishi Space Software Co., Ltd.,
792 Kami-machiya, Kamakura,
Kanagawa, Japan
Jakob J. van Zyl and Yunjin Kim
Jet Propulsion Laboratory,
California Institute of Technology,
Pasadena, California, USA
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.2
We have modeled vegetation as a distribution of scattering elements with several parameters.
Characterization of Volume Scattering Component
0
bc
ca
SS
SSS
vvvh
hvhh
Mean orientation angle :
Type of elementally scatterer :
a, b, c: complex number
Randomness :
H
VModel
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.3
[1] A. Freeman and S. L. Durden, “A three-component scattering model for polarimetric SAR data,” IEEE Trans. Geosci. Remote Sens., vol. 36, no. 3, pp. 964–973, May 1998.
[2] Y. Yamaguchi, T. Moriyama, M. Ishido, and H. Yamada, “Fourcomponent scattering model for polarimetric SAR image decomposition,” IEEE Trans. Geosci. Remote Sens., vol. 43, no. 8, pp. 1699–1706, Aug. 2005.
[3] M. Neumann, “Remote sensing of vegetation using multi-baseline polarimetric SAR interferometry: Theoretical modeling and physical parameter retrieval,” Ph.D. dissertation, Univ. Rennes, Rennes, France, 2009.
[4] M. Arii, J. J. van Zyl, and Y. Kim, “A general characterization for polarimetric scattering from vegetation canopies,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 9, pp. 3349–3357, Sep. 2010.
Evolution of Volume Scattering Expression
Type of elementally scatterer : S
Randomness :
Mean orientation angle :
Freeman et al.[1]
10
00
Uniform
None
Yamaguchi et al. [2]
10
00
Uniform or
medium
0 or 90
Neumann et al. [3]
b
a
0
0
any
any
Arii et al. [4]
bc
ca
any
any
Flexibilitya, b, c: complex number
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.4
(*1) The order here is determined among volume, double-bounce and surface scattering from [1][2][4]. Other element such as helix in [2] is not taken into account.
Volume Component in the Polarimetric Decomposition
Volume
Double-bounce
Surface
Order of the estimation*1
First Second/Third Second/Third
Degree of Freedom
High Low Low
possibly dominant error source
In this presentation, we shall study the contribution of these vegetation parameters to the model-based polarimetric decomposition based on physical interpretation using Arii et al.’s general volume component and Non-negative eigenvalue decomposition (NNED)[5].
[5] J. J. van Zyl, M. Arii, and Y. Kim, “Model-based decomposition of polarimetric SAR covariance matrices constrained for nonnegative eigenvalues,” IEEE Trans. Geosci. Remote Sens., to be published.
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.5
Definition of Randomness and Orientation
2
21
2
2
1
2
A
1
Small=0
21
uniformp
02
_ cos1 A
p sqcos
1,02
10
m
mpdelta
A : Normalization factor
Uniform dist.
Cosine squared dist.
Delta function dist.
Ran
dom
ness
,
Large=0.91
1800 0 91.00
0
0
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.6
Arii et al.’sGeneralized Volume Component[4]
bc
caS
222*222
*22*
222*222
2Im222
Im222Im22
2Im222
8
1
CBABCjCBA
BCjCBBCj
CBABCjCBA
C
000 42,, CqCpCSCv
000000
0*
0*
0*
0*
000000
0
2sinRe2cosRe22cos2sin22sinIm2cosIm2
2cos2sin202cos2sin2
2sinIm2cosIm22cos2sin22sinRe2cosRe2
8
12
QPQPQPj
QPQP
QPjQPQP
C
000000
000000
000000
0
4sin4cos4cos4sin24sin4cos
4cos4sin24sin4cos24cos4sin2
4sin4cos4cos4sin24sin4cos
8
14
SRSRSR
SRSRSR
SRSRSR
C
*22** Re2,,,
2,,
BCSCBRACQABP
cCbaBbaA
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.7
Adaptive Model-Based Decomposition[6]
reminder0 ,, CCfCfSCfC ssddvv
ssddvv CfCfSCfCC ,, 0reminder
Our observation can be decomposed as
The form is slightly changed by simple transposition of terms.
We estimate unknown parameters (S, 0, and ) by minimizing the reminder term. To achieve this, we firstly determine volume component, and then do the eigen value decomposition.
[6] M. Arii, J. J. van Zyl, and Y. Kim, “Adaptive model-based decomposition of polarimetric SAR covariance matrices,” IEEE Trans. Geosci. Remote Sens., vol. 49, no. 3, pp. 1104–1113, Mar. 2011.
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.8
Black Forest
Forest A (38)
Forest C (57)
Forest B (47)
Forest D (63)
Cropland (53)
Urban (59)L-band image of the Black Forest in Germany obtained by NASA/JPL AIRSAR system in the summer of 1991. The dotted arrows specify the direction of topographic change. Incidence angle for each area surrounded by solid rectangular is shown in the parentheses in degree.
Snapshot
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.9
delta
P-bandC-band L-band
uniform
cos_sq
Randomness and Entropy
0
1
(,S)
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.10
Definition of || and
10
0
0
0 b
b
aS
By letting c=0 in the scattering matrix, scattering matrix for cylinder can be defined as
,10
0
cylS
where the can be generally expressed as
.exp/ jba
|| and are independent parameters.
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.11
|| - Zone Map
|| - zone map implicitly tells that the dipole can be a best candidate to represent volume scattering in the model-based decomposition because it is the furthermost from two other distinctive scatterers; isotropic and double-bounce.
.)(deg0 180
1
90
10
01
10
0j
45 135
5.0
10
00
10
01
Isotropic zone Double-bounce zone
Dipole zone
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.12
Forest A Forest B Forest C Forest D Urban
C
L
P
0 maxcos
Cropland
By varying || and , we can derive and 0 as shown below.
Quick Look : Randomness
Double-bounce zone in urban area is significantly wider than that in the other areas as expected.
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.13
C
L
P
Urban Cropland
Vertical Horizontal
Quick Look : Mean Orientation Angle
VVHH VVHH
Double-bounce scattering Surface scattering
Reddish pixels are recognized at L- and P-bands. These forested areas are more or less affected by double-bounce scattering at longer wavelengths due to the permeability of tree.
Forest A Forest B Forest C Forest D
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.14
Review of Surface and Double-Bounce Scattering
To conduct further analysis, co-polarization ratio (HH/VV) of covariance matrix, Cv, derived from estimated and shall be used, where an effect of the order of decomposition should be significant. The is fixed to zero (dipole) for simplicity.
Before moving into the next step, following four facts will be quickly reviewed.
Fact A1 : HH < VV for surface scattering
Fact A2 : Co-pol ratio for surface scattering decreases in terms of incidence angle
Fact B1 : HH > VV for double-bounce scattering
Fact B2 : Co-pol ratio for double-bounce scattering increases in terms of incidence angle
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.15
Fact A
.0,sin2cos8
0,sin2cos82424
2424
kWhk
kWhk
VVVV
hhHH
SPM [7] gives expressions for backscattering cross sections from rough surface as
Then the ratio can be expressed as
,2
2
vv
hh
VV
HH
where
22
22
22 sincos
sin1sin1,
sincos
1
vvhh
Note that the ratio is a function of incidence angle and dielectric property.
[7] S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math., vol. 4, pp. 351-378, 1951.
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.16
Simulated co-polarization ratio from rough surface in terms of incidence angle is shown in the figure. It can be easily recognized that the ratio is always less than one, i.e. HH<VV, and shows decreasing tendency in terms of incidence angle.
Fact AC
o-po
lariz
atio
n ra
tio o
f gro
und
scat
terin
g
Incidence Angle (deg.)
0
0.1
0.2
0.3
0 30 60 90
drymediumwet
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.17
Fact B1
BC
S o
f dou
ble-
boun
ce s
catte
ring
[dB
]
Incidence Angle (deg.)
Flat Plate B
10g
3c
-70
-40
-10
20
0 30 60 90
HH VV
Backscattering cross section of double-bounce scattering can be derived from Fresnel reflection coefficient.
Brewster’s angle of Flat Plate B
Flat Plate A
Brewster’s angle of Flat Plate A
VV is generally smaller than HH due to Brewster’s angles for both flat plates.
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.18
With roughness on the ground, attenuation coefficient of specular scattering must be considerable. The coefficient [8] becomes
222 cos2exp khCatt
Simulated attenuation coefficients at various bands are shown in the figure. For each case, increasing tendency is recognized in terms of incidence angle.
Fact B2
[8] M. Arii, “Soil moisture retrieval under vegetation using polarimetric radar,” Ph.D. dissertation California Institute of Technology, Pasadena, CA, pp. 68-101, 2009.
Atte
nuat
ion
ratio
, Cat
t
Incidence Angle (deg.)
0
0.5
1
0 30 60 90
C-bandL-bandP-band
Attenuated depending upon incidence angle
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.19
0
5
10
15
0 0.2 0.4 0.6 0.8
Forest CUrbanCropland
Wavelength (m)
Co-
pola
rizat
ion
ratio
Co-polarization Ratio in terms of Wavelength
To investigate wavelength dependency, co-polarization ratios in terms of bands are plotted.
The ratio for cropland stays around one whereas those for forest and urban are increasing. This follows our understanding, where scattering from agricultural area can be mainly contributed by surface scattering component (Fact A2), and that in urban is strongly affected by double-bounce scattering (Fact B) which should be dominant at longer wavelength due to its permeability. 1
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.20
Wavelength (m)
Co-
pola
rizat
ion
ratio
0
2
4
0 0.2 0.4 0.6 0.8
Forest AForest BForest CForest D
The ratio for each forest area is plotted. The ratios less than one are achieved for C-band, and they are increased as the wavelength increases. This is acceptable by considering attenuation effect which becomes significant with shorter wavelength. The increasing tendency at longer wavelengths would be mainly caused by horizontally oriented distributed branches or double-bounce scattering from Fact B.
Co-polarization Ratio in terms of Wavelength : Forest
1
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.21
Co-polarization Ratio in terms of Incidence Angle
By comparing the C-band result with Fact A, shorter wavelength sees canopy as a rough surface. On the other hand, increasing tendencies at longer wavelengths may be explained by double-bounce scattering mechanism, or horizontally distributed volume scattering.
Note that the P-band at higher incidence angle can penetrate volume layer more than L-band from Fact B2 so that it might be affected by another scattering mechanism such as azimuth tilt [5].
Co-
pola
rizat
ion
ratio
Incidence Angle (deg.)
0
1
2
3
4
5
6
35 45 55 65
0
3
6
35 45 55 65
CLP
National Aeronautics and Space Administration
Jet Propulsion LaboratoryCalifornia Institute of Technology
Pasadena, California
MITSUBISHI SPACE SOFTWARE Co., LTD.22
Summary and Future Work We physically and quantitatively validated the adaptive model-based
decomposition technique with fully generalized volume component for vegetation canopy.
We deepened our understanding of the behavior qualitatively based on co-polarization ratio in terms of incidence angles and frequencies. The ratio of the volume component shows significant sensitivity to the dominant scattering mechanism so that estimation error for each scattering mechanism is not negligible in some cases. For example, double-bounce scattering having HH>VV may be misinterpreted as higher amount of volume component with horizontal mean orientation angle.
Care must be paid when one applies the adaptive model-based decomposition with generalized volume component. Reasonable physical constraint based on solid understanding of scattering theory is now required.
Sensitivity Study by Elaborated Forward Model
Fully Controlled Experiment
Validation