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
September 19, 2018
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?
September 19, 2018
IGARSS 2011, Vancouver

3. 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
Each elementary scatterer features a body of revolution w.r.t. the symmetric axis, ON.
The projected symmetry axis on the polarization plane is oriented towards angle b;
The local incidence angle w.r.t. the symmetry axis is y;
The principal scattering components are Sa and Sb.
September 19, 2018
IGARSS 2011, Vancouver

4. 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
If b and y are separable,
Symmetric
distribution
Orientation
dispersion
Mean orientation angle
Independent of orientation
0: sphere
1: dipole
Advantage: Orientation parameters
readily separable as phase terms.
Relates to both shape variation and orientation dispersion
September 19, 2018
IGARSS 2011, Vancouver

5. Circular Polarization Representation
The polarimetric system is redundant when modeling spheroids: for example, co-polar powers RR=LL
An underdetermined system – the correlation rx is product of two components:
For a known distribution type, r2 can be inferred from r4.
Uniform distribution
Cosine distribution
von Mises distribution
Then the orientation parameters, both mean and dispersion, can be removed from the covariance matrix.
September 19, 2018
IGARSS 2011, Vancouver

6. Orientation Distribution
The symmetric axis direction in 3-D: von Mises-Fisher distribution
Mean orientation: 0 deg
Orientation dispersion: kappa = 5 deg
Incidence angle distribution (y): shows same dispersion
Orientation distribution (b): symmetric, zero mean
September 19, 2018
IGARSS 2011, Vancouver

7. Orientation Distribution
The orientation angle is close to a von Mises distribution
Dot line: the theoretical density function of assumed von Mises distribution
Established a relation between r2 and r4.
The orientation parameters, mean and dispersion, can be determined and removed, which leaves only scatterer shape information.
September 19, 2018
IGARSS 2011, Vancouver

8. 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:
We get mean shape, r, and shape variation, Re(ab).
Size
Shape
Orientation
September 19, 2018
IGARSS 2011, Vancouver

9. Forest Observations
Multi-frequency AIRSAR data from different forest regimes
Tropical
Rainforest
[Guyana]
Jun. 93
- Broad leaf
- Thick foliage
- Random branches
Temperate
Conifer
[Germany]
Jun. 91
- Needle leaf
- Oriented branches
Temperate
Deciduous
[Michigan]
Oct. 94
- Low biomass
Random branches
Leaf-off scenario
* Image source: Google Earth
September 19, 2018
IGARSS 2011, Vancouver

10. C-band Forest Observations
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 r4.
Rainforest: medium-low rab, near-zero r  broad leaf shape
Conifer: lower rab, elongated r  thin column shape
Deciduous: lower r4, very low rab, elongated r  random twigs
C-band
Blue: rain forest (Guyana)
Black: conifer (Germany)
Cyan: deciduous (Michigan)
September 19, 2018
IGARSS 2011, Vancouver

11. L-band Forest Observations
The frequency contour at 50th percentile
Rainforest: very low r4, near-zero rab, near-zero r  random orientation and random shape (deeper penetration through thick foliage).
Conifer: higher r4, negative rab, elongated r  thin column shape, anisotropic branches, substantial trunk response.
Deciduous: increased r4, negative rab  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)
September 19, 2018
IGARSS 2011, Vancouver

12. Vegetation Observations
Agricultural fields may be more homogeneous
AIRSAR Flevoland dataset
Ground truth blocks for supervised classifications
C-band
L-band
September 19, 2018
IGARSS 2011, Vancouver

13. Scatter plots @ 50th percentile, C-band
uniform
shape
dipole;
random
At 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
leafy
branchy
stem
needle;
thinner
sphere;
broader
September 19, 2018
IGARSS 2011, Vancouver

14. Scatter plots @ 50th percentile, L-band
uniform
shape
dipole;
random
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
leafy
branchy
stem
needle;
thinner
sphere;
broader
September 19, 2018
IGARSS 2011, Vancouver

15. 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
September 19, 2018
IGARSS 2011, Vancouver

16. Classification [C-band]
Supervised Wishart Classification
Experimental Wishart Classification
(with extra step of segmentation)
September 19, 2018
IGARSS 2011, Vancouver

17. Classification [L-band]
Supervised Wishart Classification
Experimental Wishart Classification
(with extra step of segmentation)
September 19, 2018
IGARSS 2011, Vancouver

18. 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
r4 at 0.15, 0.25, and 0.5
rab from -0.9 to 0.9 with 0.2 intervals
Primary divisions
100+ initial divisions
Secondary divisions: mean shape ratio, pixel intensity
September 19, 2018
IGARSS 2011, Vancouver

19. Unsupervised Classification
Merge classes during Wishart classification
Maintain subtle variations amongst crop returns
Concentrate on shape variation and orientation angle dispersion
Class centers: Cm, Cn, …
From sample X to Cm:
Inter-class:
Merge the secondary divisions based on inter-class Wishart distance.
Secondary divisions: Merge if the classes are close, leaving 38
classes 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 (ab, 4) space
Final result: 20 classes for the AIRSAR Flevoland dataset
September 19, 2018
IGARSS 2011, Vancouver

20. Unsupervised Classification
C-band L-band
Supervised Wishart Classification
Map
Re-colored
Unsupervised
Wishart Classification
Map
Iterations not necessary, Wishart classification converges fast (pixel change < 10%)
September 19, 2018
IGARSS 2011, Vancouver

21. Unsupervised Classification
Coniferous / Deciduous Forests
Sault Saint Marie, Lake Superior, Michigan
C-band, Pauli RGB Composition
Black: Low Backscatter, SPAN<-10 dB
Gray: Surface
Green: Deciduous Forest
Blue: Coniferous Forest
Yellow: Mixed Type
September 19, 2018
IGARSS 2011, Vancouver

22. 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.
September 19, 2018
IGARSS 2011, Vancouver