igarss11_wang_v2.ppt

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


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?


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


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−=


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


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

SS=ρ

2

2

b

a

S

Sr =

We get mean shape, r, and shape variation, Re(ρab).

Size

Shape

Orientation


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


• 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)


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)


Vegetation Observations• Agricultural fields may be

more homogeneous• AIRSAR Flevoland dataset

– Ground truth blocks for supervised classifications

C-band L-band


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


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


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


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)


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)


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


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, …


Unsupervised Classification

Re-colored UnsupervisedWishart ClassificationMap

Supervised Wishart ClassificationMap

Iterations not necessary, Wishart classification converges fast (pixel change < 10%)

C-band L-band


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


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.

igarss11_wang_v2.ppt

Technology

orientation parameters

orientation properties

size shape orientation

orientation compensated

mean shape

mises distribution

shape variation

independent parameters