Measuring Orientation and Randomness of Vegetation using Polarimetric SAR Data

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





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





[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





(*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.





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

pdf

pdf

pdf

A : Normalization factor

Uniform dist.

Cosine squared dist.

Delta function dist.

Ran

dom

ness

,

Large=0.91

1800 0 91.00

0

0





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





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.





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





delta

P-bandC-band L-band

uniform

cos_sq

Randomness and Entropy

0

1

(,S)





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.





|| - 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





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.





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





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





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.





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





Fact B1

BC

S o

f dou

ble-

boun

ce s

catte

ring

[dB

]


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.





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


0

0.5

1

0 30 60 90

C-bandL-bandP-band

Attenuated depending upon incidence angle





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





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





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


0

1

2

3

4

5

6

35 45 55 65

0

3

6

35 45 55 65

CLP





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

Measuring Orientation and Randomness of Vegetation using Polarimetric SAR Data

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