July 26, 2011 IGARSS 2011, Vancouver 1 INVESTIGATION ON THE ORIENTATION AND STRUCTURE PARAMETERS OF CANOPY USING POLSAR OBSERVATIONS Yanting Wang, Thomas Ainsworth and Jong-Sen Lee Remote Sensing Division Naval Research Laboratory
July 26, 2011 IGARSS 2011, Vancouver 1
INVESTIGATION ON THE ORIENTATION AND STRUCTURE PARAMETERS OF CANOPY
USING POLSAR OBSERVATIONS
Yanting Wang, Thomas Ainsworth and Jong-Sen Lee
Remote Sensing DivisionNaval Research Laboratory
July 26, 2011 IGARSS 2011, Vancouver 2
Objectives• Radar polarimetry enables better characterization of the targets with
shape and orientation parameters in addition to the conventional radiometric information.
• Model based decompositions are commonly used to interpret PolSAR observations.
• Multiple volume scattering models have been proposed:– The Freeman-Durden Model: randomly oriented dipoles– The Yamaguchi Model: anisotropic dipoles– The Freeman 2-Component Model: random oriented spheroids– Recently, Neumann augmented a model of anisotropic spheroids for
application to interferometric polarimetry data
• Is wide variation expected on the shape and orientation properties for different canopy types?
• Is it possible to estimate the shape and orientation parameters from PolSAR observations?
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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.
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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
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Circular Polarization Representation• The polarimetric system is redundant when modeling
spheroids: for example, co-polar powers RR=LL
• An underdetermined system – the correlation ρx is product of two components:
• For a known distribution type, ρ2 can be inferred from ρ4.– Uniform distribution– Cosine distribution– von Mises distribution
• Then the orientation parameters, both mean and dispersion, can be removed from the covariance matrix.
222
4
1baLLRR SSSS −==
022
βρρρ jrx e−=
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Orientation Distribution• The symmetric axis direction in 3-D: von Mises-
Fisher distribution
kkONONON
kkONON
k
k
ˆ)ˆ(
ˆ)ˆ(
ˆ
ˆ//
•−=
•=
⊥
ii θφθθθφθβ
coscossinsincos
cossintan
−=
ii θφθθθψ sincossincoscoscos +=
0
cos
)]cos(sinsincos[cos
)sinh(4
)sinh(4),(
=
−+
=
=
θθκ
φφθθθθκ
κπκ
κπκφθ
e
ef
Orientation distribution (β):
symmetric, zero mean
Incidence angle
distribution (ψ): shows same dispersion
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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.
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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
SS=ρ
2
2
b
a
S
Sr =
We get mean shape, r, and shape variation, Re(ρab).
Size
Shape
Orientation
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Forest Observations• Multi-frequency AIRSAR data from different forest regimes
TropicalRainforest[Guyana]Jun. 93
- Broad leaf- Thick foliage- Random branches
TemperateConifer[Germany]Jun. 91
- Needle leaf- Oriented branches
TemperateDeciduous[Michigan]Oct. 94
- Low biomass- Random branches- Leaf-off scenario
* Image source: Google Earth
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• The frequency contour at 50th percentile
– At C-band, we expect dominant scattering from leaves.
– The scatterer orientation is quite random, as shown in low ρ4.
– Rainforest: medium-low ρab, near-zero r broad leaf shape
– Conifer: lower ρab, elongated r thin column shape
– Deciduous: lower ρ4, very low ρab, elongated r random twigs
C-band Forest Observations
C-band
Blue: rain forest (Guyana)Black: conifer (Germany)Cyan: deciduous (Michigan)
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L-band Forest Observations• The frequency contour at 50th percentile
– Rainforest: very low ρ4, near-zero ρab, near-zero r random orientation and random shape (deeper penetration through thick foliage).
– Conifer: higher ρ4, negative ρab, elongated r thin column shape, anisotropic branches, substantial trunk response.
– Deciduous: increased ρ4, negative ρab substantial trunk response, mixed response from twigs, branches, and trunk.
– Varying mechanisms presented in the polarimetric response at different frequencies
L-band
Blue: rain forest (Guyana)Black: conifer (Germany)Cyan: deciduous (Michigan)
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Vegetation Observations• Agricultural fields may be
more homogeneous• AIRSAR Flevoland dataset
– Ground truth blocks for supervised classifications
C-band L-band
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stembranchy
dipole;random
uniformshape
sphere;broader
needle;thinner
Scatter plots @ 50th percentile, C-band
leafyAt C-band, scattering from leaves
– Reasonable separation with significant overlapping
Dipole shape: stembeans, grass, wheat;
Broad shape: forest, beet, potatoes;Thin column: lucerne (random),
rapeseed;Disk shape: peas
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Scatter plots @ 50th percentile, L-band
At L-band, scattering component from structure – good separation.
Anisotropic dipole: stembeans, lucerne;
Thin column: wheat;Broad shape: potatoes, beet, grass;Mixed structure: forest;Uniform structure: rapeseed, peas
dipole;random
uniformshape
stembranchy
sphere;broader
needle;thinner
leafy
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Potential Physical Characterization
• The contours demonstrate “orthogonal” dimensions along shape and orientation – no apparent coupling.
• Easier to define the divisions for classification.• Easier interpretation of target scattering.
• Feasibility of using simple, gridded divisions to initiate classification:– Demonstrated through supervised classification
experiments
Size
Shape
Orientation
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Classification [C-band]Supervised
Target Type Orientation Randomness
Shape Variation
Mean Shape
Ratio (dB)
Total Span (dB)
Bare Soil 0.25 ~ 0.50 0.7 ~ 0.8 -2 ~ -1 -26 ~ -22 Forest 0.05 ~ 0.15 0.1 ~ 0.2 -1 ~ 1 -20 ~ -16 Grass 0.15 ~ 0.25 0.0 ~ 0.1 1 ~ 3 -24 ~ -20 Wheat 0.25 ~ 0.50 0.7 ~ 0.8 1 ~ 3 -20 ~ -16 Lucerne 0.15 ~ 0.25 0.1 ~ 0.3 1 ~ 3 -22 ~ -18 Stem Beans 0.05 ~ 0.15 -0.1 ~ 0.1 1 ~ 3 -20 ~ -16 Beets 0.05 ~ 0.15 0.3 ~ 0.4 -1 ~ 1 -18 ~ -14 Potatoes 0.05 ~ 0.15 0.2 ~ 0.3 -1 ~ 1 -18 ~ -14 Rapeseed 0.15 ~ 0.25 0.5 ~ 0.6 1 ~ 3 -20 ~ -16 Peas 0.15 ~ 0.25 0.5 ~ 0.6 -1 ~ 1 -20 ~ -16
Supervised Wishart Classification Experimental Wishart Classification(with extra step of segmentation)
July 26, 2011 IGARSS 2011, Vancouver 17
Classification [L-band]Supervised
Target Type Orientation Randomness
Shape Variation
Mean Shape
Ratio (dB)
Total Span (dB)
Bare Soil 0.50 ~ 0.70 0.8 ~ 0.9 -5 ~ -3 -28 ~ -22 Forest 0.05 ~ 0.20 -0.2 ~ 0.0 -3 ~ -1 -16 ~ -12 Grass 0.50 ~ 0.70 0.2 ~ 0.4 0 ~ 1 -26 ~ -22 Wheat 0.50 ~ 0.70 0.2 ~ 0.4 -5 ~ -3 -24 ~ -20 Lucerne 0.50 ~ 0.70 -0.2 ~ 0.0 1 ~ 3 -24 ~ -20 Stem Beans 0.50 ~ 0.70 -0.2 ~ 0.0 1 ~ 3 -18 ~ -14 Beets 0.05 ~ 0.20 0.3 ~ 0.5 -1 ~ 2 -22 ~ -16 Potatoes 0.05 ~ 0.20 0.1 ~ 0.3 -1 ~ 2 -18 ~ -14 Rapeseed 0.20 ~ 0.40 0.7 ~ 0.8 -3 ~ -1 -22 ~ -16 Peas 0.20 ~ 0.40 0.5 ~ 0.7 -3 ~ -1 -18 ~ -14
Supervised Wishart Classification Experimental Wishart Classification(with extra step of segmentation)
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Unsupervised Classification• Initial segmentation with discrete boundaries is
feasible for agricultural crops. – Establish a database of the discrete boundaries; or– Build an unsupervised classification process.
Initial Segmentation: start with dense, discrete, gridded
divisions
ρ4 at 0.15, 0.25, and 0.5
ρab from -0.9 to 0.9 with 0.2 intervals
Primary divisions
Secondary divisions: mean shape ratio, pixel intensity
100+ initial divisions
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Unsupervised Classification• Merge classes during Wishart classification
– Maintain subtle variations amongst crop returns– Concentrate on shape variation and orientation
angle dispersion
Merge the secondary divisions based on inter-class Wishart
distance.
)(lnln XCXC 1mm−+−≈ trnnd
[ ])()(21
m1
nn1
m CCCC −− +≈ trtrdmn
From sample X to Cm:
Inter-class:
Secondary divisions: Merge if the classes are close, leaving 38classes for the AIRSAR Flevoland dataset
Primary divisions: merge only if• one of the classes has a small population; • the classes have comparable compactness; and • the classes are direct neighbors in (ρab, ρ4) space
Final result: 20 classes for the AIRSAR Flevoland dataset
Class centers: Cm, Cn, …
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Unsupervised Classification
Re-colored UnsupervisedWishart ClassificationMap
Supervised Wishart ClassificationMap
Iterations not necessary, Wishart classification converges fast (pixel change < 10%)
C-band L-band
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Unsupervised Classification• Coniferous / Deciduous Forests
Sault Saint Marie, Lake Superior, Michigan
C-band, Pauli RGB Composition
Black: Low Backscatter, SPAN<-10 dBGray: SurfaceGreen: Deciduous ForestBlue: Coniferous ForestYellow: Mixed Type
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Summary• An empirical retrieval of shape and orientation
parameters for volumetric scatterers– Volume scattering dominates – Orientation distribution: von Mises – Homogenous targets
• The shape and orientation parameters and size form “orthogonal” dimensions in the polarimetric space.– Application of discrete, gridded boundaries
• Different model parameters for different forest types• Different polarimetric response at C-band and L-band• The simple grid divisions were used to initiate Wishart
polarimetric classification, giving rise to an automated unsupervised PolSAR classification procedure based on scatterer shape parameters and orientation dispersion.