igarss11_mw_v2.ppt

July 29, 2011 IGARSS 2011, Vancouver 1

A SIMULATION STUDY OF TOPOGRAPHIC EFFECTS ON POLSAR CLASSIFICATION OF

FORESTS AND CROPS

M. L. Williams1 and T. L. Ainsworth2

1Cooperative Research Centre for Spatial Information2Remote Sensing Division, Naval Research Laboratory


Methodology• Assess the Effects of Underlying Topography on

Polarimetric Forest Backscatter Using Simulated Data• Estimate the Polarimetric Returns not Corrected by

Orientation Angle Compensations– Compare orientation-angle corrected data against forest returns

simulated over flat terrain

• Simulated Imagery Allows One to Tease Apart Forest Scattering Mechanisms – Direct canopy backscatter, ground-trunk interaction, canopy

attenuation, etc.

• Goal: Use the Analysis of Simulated Data to Develop Better Forest Scattering Models for PolSAR Imagery


Forest Simulations Start With a Tree

Bare Vertical Trunk

Dead Primary Branches

Upper Crown

Model of a Scots Pine, ~18m in heightBased on Detailed Measurements

Lower Crown

Detail of the Crown

Primary and Secondary Branch Structures


To Make a Forest

• Tree Branches Grow to Edge of Canopy Envelop – Upper Crown – Live Branches– Lower Crown – Dry Branches– Add Needles / Leaves

• Generate a Set of Unique Trees• Semi-Randomly Plant the Forest:


Scene Generation

View from Radar Platform at Mid-track

• A realization of a random, sloped ground surface generated according to surface roughness, soil moisture and slope parameters.

• Ground surface covered by layer of random vegetation.

• A forest stand realized as a circular area populated by trees.

• Trees have a distribution of heights around the supplied mean value.

• Tree positions are determined by shuffling from an initially uniform grid, with a crown-overlap cost function.

• Red envelopes mark “living” pine crown, grey layer is “dry” timber.

• Each tree is unique and realized in detail for SAR simulation.


SAR Simulator – PolSARproSim• Basic Simulations Performed with Stand-alone Version

of the PolSARproSIM Software– Coherent, polarimetric SAR simulator – Methodology documented within PolSARpro

• Five Basic Scattering Components – Signal attenuated by all vegetation layers

Direct Ground

Direct Short Vegetation

Direct Forest

Ground-Forest Backscatter

Ground / Short- Vegetation Return


Scene Summary• Primary Characteristics

– Scots Pine forest - ~2600 trees• Relatively sparse canopy with large trunk structure

• Mean tree height: 18m

• Mean canopy radius: 2.6m

• Canopy attenuates radar signals

– Low vegetation ground cover• Weak scatterer, weak signal attenuation

– Moderately rough, moist ground surface

• Range and/or Azimuth Ground Slopes– Independent variables in this initial study

• Coupled Radar Scattering Components – Attenuation, Ground Slopes & Multiple Scattering


Polarimetric Analysis• A Select Set of Polarimetric Descriptors:

• Orientation Angle: θ– Related to range(γ) and azimuth(ω) slopes– The complex phase of the RR-LL correlation (circular basis)

∀ α-angle: Average scattering mechanism – Surface: 0°, Dipole: 45°, Dihedral: 90°

• Double Bounce Scattering Strength– Dominant scattering mechanism in our (current) simulated forest– Arises primarily from ground-trunk interactions

• Circular Basis Correlations – |ρ4|: Reciprocal of orientation angle variance

• Magnitude of the RR-LL correlation • Independent of the underlying scattering mechanism

– |ρr|: Reciprocal of the shape variation • Relates to the variance of the effective scatterer shape• Depends explicitly on the scattering mechanism

( ) ( )( ) ( ) ( )φφγ

ωθsincostan

tantan

+−−=


A SAR Image Realization L-band, 5 Meter Resolution

RGB Image: HH, HV, VV

• Forest covered central region• Low vegetation area surrounds forest• Range increases from left to right

HH HV VH VV


α-angle Histograms

Range Slope: 0°, 1°, 2° & 4°

Rapid decrease of high α components between 0° & 2°

Azimuth Slope: 0°, 6°, 8° & 10°

No change until ~6° slope then a shift to lower α values


With azimuth slope set to zero, the orientation angle does not depend on range slope.

0 0.2 0.4 0.6 0.8 10

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Ort Dispersion (ρ4)

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\s_cov_m006_p000

\s_cov_m004_p000

\s_cov_m002_p000\s_cov_p002_p000

\s_cov_p004_p000

\s_cov_p006_p000

-40 -20 0 20 400

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Orientation (deg)

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\s_cov_m006_p000

\s_cov_m004_p000

\s_cov_m002_p000\s_cov_p002_p000

\s_cov_p004_p000

\s_cov_p006_p000

Range Slopes in Grassy RegionsOrientation Angle & Correlation |ρ4|

Low orientation angle correlations without a strong dependence on range slope. Slightly lower for positive slopes.


Grass Region Forest

Small range tilt reduces double bounce power in forest, but not in the grassy regions.

Range Slopes in Forest AreaDouble Bounce Power & Ground-Forest Component

Ground-Forest Component

The ground-forest multiple scattering accounts for the rapid drop of the double bounce backscatter.

-30 -25 -20 -15 -10 -5 0 50

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Double Bounce Power (dB)

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\s_cov_m004_p000

\s_cov_m002_p000

\s_cov_p002_p000

\s_cov_p004_p000\s_cov_p006_p000

-30 -25 -20 -15 -10 -5 0 50

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\gfs_cov_p000_p000\gfs_cov_m006_p000

\gfs_cov_m004_p000

\gfs_cov_m002_p000

\gfs_cov_p002_p000

\gfs_cov_p004_p000\gfs_cov_p006_p000

All tree trunks are perfectly vertical – not a good approximation.


The orientation angle basically matches changes in azimuth slopes.

Azimuth Slopes in Grassy RegionsOrientation Angle & Correlation |ρ4|

Low correlation values imply poor estimates of orientation angles.

0 0.2 0.4 0.6 0.8 10

200

400

600

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1200


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\s_cov_p000_p002

\s_cov_p000_p004\s_cov_p000_p006

\s_cov_p000_p008

\s_cov_p000_p010

-40 -20 0 20 400

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Orientation (deg)

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\s_cov_p000_p002

\s_cov_p000_p004\s_cov_p000_p006

\s_cov_p000_p008

\s_cov_p000_p010


-30 -25 -20 -15 -10 -5 0 50

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\s_cov_p000_p002

\s_cov_p000_p004\s_cov_p000_p006

\s_cov_p000_p008

\s_cov_p000_p010

Grass Region Forest

Small azimuth tilts allow ground-trunk scattering, only larger slopes reduce double bounce power in forest.

Azimuth Slopes in Forest AreaDouble Bounce Power


The ground-forest multiple scattering component accounts for double bounce changes with azimuth slope.

Tree trunk forward scattering is not limited to specular directions.

-30 -25 -20 -15 -10 -5 0 50

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\gfs_cov_p000_p006



The orientation angle basically matches changes in azimuth slopes.

Azimuth Slopes in Forest AreaOrientation Angle & Correlation |ρ4|

Higher correlation values in forest area imply good estimates of the orientation angles.

0 0.2 0.4 0.6 0.8 10

500

1000

1500

2000


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\s_cov_p000_p004

\s_cov_p000_p006

\s_cov_p000_p008\s_cov_p000_p010

-20 -15 -10 -5 0 50

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Orientation (deg)

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\s_cov_p000_p004

\s_cov_p000_p006

\s_cov_p000_p008\s_cov_p000_p010


Full SAR Simulation

Azimuth Slopes in Forest AreaOrientation Angle

Orientation angle estimates from full SAR simulation closely matches the orientation angles of the strong ground-forest scattering component.

The ground-forest induced orientation angle shows low variance (high correlations) independent of azimuth slope.

The orientation angle variance from the full simulation increases with increases in the azimuth slope.

-20 -15 -10 -5 0 50

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Orientation (deg)

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\s_cov_p000_p004

\s_cov_p000_p006

\s_cov_p000_p008\s_cov_p000_p010

-20 -15 -10 -5 0 50

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Orientation (deg)


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\gfs_cov_p000_p006




Full SAR Simulation

Azimuth Slopes in Forest AreaScatter Shape Variation

The Shape Variation reflects inherent changes to the polarimetric scattering.

Even after orientation angle compensation, once the azimuth slopes exceed ~6°, the ground-forest scattering component changes character.

The double bounce scattering, probably generated from ground-trunk interactions, is greatly reduced.

This change in Shape Variation is consistent with the α-angle changes due to azimuth slopes shown earlier.


-1 -0.8 -0.6 -0.40

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Shape Variation (ρab)

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\gfs_cov_p000_p002


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\gfs_cov_p000_p010

-1 -0.5 0 0.5 10

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\s_cov_p000_p002

\s_cov_p000_p004\s_cov_p000_p006

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Grassy Region

Major Forest Scattering Components

Forest scattering, at least for our simulated Scots Pine forest, is almost completely specified by the Direct Forest (blue) and the Ground-Forest (green) scattering components.

The cyan curve, the combination of Direct Forest and Ground-Forest scattering, almost exactly matches the Full Scattering curve (red).

Forest Returns

-30 -25 -20 -15 -10 -5 0 50

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.\dfs_cov_p000_p000.tla

.\gfs_cov_p000_p000.tla

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Mixed


Major Forest Scattering Components

The Full Orientation Angle Correlation matches the Correlation formed from the Direct Forest and Ground-Forest scattering components.

Similarly, the Full Shape Variation reflects the combination of the Direct Forest and Ground-Forest scattering.

0 0.2 0.4 0.6 0.8 10

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Mixed

-1 -0.5 0 0.5 10

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Mixed


Preliminary Conclusions (1)

• Results Based on a Single Forest Simulation

– Relatively light canopy attenuation

– Sparse forest – typical of Scots Pine

• Known Defects in the Tree Realizations

– All tree trunks aligned perfectly vertical

– One can design trees with randomly angled trunks

• Only Investigated Polarimetric Variations with Ground Slope

– Wider variety of forest parameters needed

– Adjust relative weighting of canopy attenuation, direct ground scattering, tree architecture, etc.

• Simulations May Produce Artificial Artifacts Not Seen in Scenery

– Blind use or application of software may be misleading


Preliminary Conclusions (2)• Both Range and Azimuth Slopes Reduce Double Bounce Ground-

Trunk Scattering in this Forest– Both orientation angle correlation and shape variation indicate inherent

changes in polarimetric scattering due to topographic slopes

• Orientation Angle Compensation Does Not Remove All Topographic Effects on SAR Polarimetry

• The Large Number of Forest Parameters May Limit Full Investigation – Tree architecture, relative ground / canopy scattering strength, and

canopy attenuation may be the important variables


Background


Volume of Spheroid Scatterers• Assuming a cloud of spheroids for volumetric

canopy scatterers, characterized by independent parameters: size, shape and orientation.

O

X

Y

Z

N)cos,sinsin,cos(sin θφθφθ

φ

θiθ

)cos,0,(sin ii θθ)0,1,0(

)sin,0,cos( ii θθ−

Each elementary scatterer features a body of revolution w.r.t. the symmetric axis, ON.

( )( )

−

− ββ

ββψ

ψββββ

cossin

sincos

0

0

cossin

sincos

b

a

S

S

The projected symmetry axis on the polarization plane is oriented towards angle β;

The local incidence angle w.r.t. the symmetry axis is ψ;

The principal scattering components are Sa and Sb.


Circular Polarization Representation• Oriented targets can be clearly expressed in the

circular polarization basis– Mean orientation angle from the phase of RR-LL– Similar to circularly polarized weather radar analysis

222

4

1baLLRR SSSS −==

222

4

1baLRRL SSSS +==

β42*

4

1 jbaLLRR eSSSS −−=

( ) ( ) β2**

4

1 jbabaRLRR eSSSSSS −+−=

( ) ( ) β2**

4

1 jbabaRLLL eSSSSSS +−=

If β and ψ are separable,

Advantage: Orientation parameters readily separable as phase terms.

( ) 044

44 4cos βββ ρββ jjj eee −−− ≡−=

*22

*22

2

2

Re2

Re2

baba

baba

ba

ba

SSSS

SSSS

SS

SSCDR

++

−+=

+

−=

022

2

22

*22Im2

ββ ρρρ jr

j

baba

baba

x eeSSSS

SSjSS−− ≡

+−

+−=

Symmetric distribution Orientation

dispersionMean orientation angle

Independent of orientation 0: sphere 1: dipole

Relates to both shape variation and orientation dispersion


Orientation Distribution• The orientation angle is close to a von Mises

distribution

0,0

cos

0 )(2

1)(

===

βθβκ

κπβ e

If

Established a relation between ρ2 and ρ4.The orientation parameters, mean and dispersion, can be determined and removed, which leaves only scatterer shape information.


Physical Parameters Retrieval• It is then straightforward to solve the principal

components from orientation compensated data

• Theoretically, the solution works for a single volume scattering mechanism and homogenous targets, resolving parameters:

( )*222Re2 RLRRRRRLa SSSSS ++=

( )*222Re2 RLRRRRRLb SSSSS −+=

( )*22* Im2 RLRRRRRLba SSjSSSS +−=

( )22

ba

*ba

ab

SS

SSeℜ=ρ

2

2

b

a

S

Sr =

We get mean shape and shape variation.

Size

Shape

Orientation

igarss11_mw_v2.ppt

Documents

forest stand

sloped ground surface

canopy attenuation

edge of canopy

surface roughness

layer of random vegetation

simulated dataestimate

treesrelatively sparse