A joint classification technique based on multivariate ... · PDF fileMicrosoft PowerPoint -...

P. Lombardo, T. Macrì Pellizzeri, A. Tomasuolo

INFOCOM Dpt.

Sydney, July 9-13 IGARSS2001 1

A joint classification technique based on multivariateannealing segmentation and “H/A/α” decomposition for

fully polarimetric SAR images of suburban areas

A joint classification technique based on multivariateannealing segmentation and “H/A/α” decomposition for

fully polarimetric SAR images of suburban areas


INFOCOM Dpt. - University of Rome “La Sapienza”


INFOCOM Dpt.


Introduction & motivationIntroduction & motivation

••H / A / H / A / αα polarimetricpolarimetric decomposition decomposition ••Annealed segmentationAnnealed segmentation

Two techniques for land cover classification using polarimetric SAR images

Joint annealed segmentation technique applied over (H,A,α) images

Full exploitation of the information available in the noisy anisotropy parameter

Improved classification capability and accuracy

• Especially suited to suburban and urban areas


INFOCOM Dpt.


The “H/A/α” decomposition (I)The “H/A/α” decomposition (I)

characteristics of polarimetric SAR images expressed in terms of coherency matrix

( )( ) ( )( )

−−

+−++

=24**

*22*

*2*2

hvSvvShhShvSvvShhSvvShhShvSvvShhSvvShhSvvShhS

T

polarimetric back-scattering properties of a generictarget described by coherent scattering matrix S

=vvvh

hvhhSSSS

S

Shh, Svv: co-linear polarizationscattering coefficients

Shv, Svh: cross-linear polarizationscattering coefficients


INFOCOM Dpt.


decomposition theorem applied to fully exploit the algebraic structure of T

[ ] [ ] ∑=

⋅=−⋅⋅=−=

3

1*1

3300020001

31]3].[].[3[

iT

iii eeUUUΛUT λλ

λλ ΛΛΛΛ: eigenvalues matrix

U3=[e1 e2 e3]: unitary matrix

T

sinsincossincos

= ij

eiiij

eiiiiγ

βαδ

βααe

polarimetric properties described by

•• EntropyEntropy (H) (H)

∑ =−= 31 3logi ii PPH 332211 αααα PPP ++=

•• AngleAngle ( (αα)) •• AnisotropyAnisotropy (A) (A)

)/()( 3232 λλλλ +−=A

i-th normalized eigenvalue

The “H/A/α” decomposition (II)The “H/A/α” decomposition (II)

)321( λλλλ

++= iPi


INFOCOM Dpt.


The “H/A/α” decomposition (III)The “H/A/α” decomposition (III)

∑ =−= 31 3logi ii PPH•• EntropyEntropy

measure ofstatistical disorder

low H weakly depolarizing target

high H depolarizing target

332211 αααα PPP ++=•• AngleAngle ( (αα))

related to scatteringmechanism

low α (α ≅0°) superficial reflection

dipole scattering

multiple scattering

α ≅45°

high α (α ≅90°)


INFOCOM Dpt.


The “H/A/α” decomposition (IV)The “H/A/α” decomposition (IV)

•• AnisotropyAnisotropy (A) (A) )/()( 3232 λλλλ +−=A

• Gives extra insights on the eigenvalues distribution

• For high H, indicates whether the second highest eigenvalue is closer to thefirst one or to the third one

Statistically unstable difficult direct classification

processing scheme to jointlysegment the H/A/α parameterimages aiming at

•• obtaining the full benefits fromobtaining the full benefits fromthe anisotropy parameterthe anisotropy parameter

•• operating at the highestoperating at the highestpossible resolutionpossible resolution

Averaging T loss of resolution


INFOCOM Dpt.


The H/A/α joint segmentation (I)The H/A/α joint segmentation (I)

Simplified statisticalmodel for H, A, α

• Independent

• Gamma-distributed

• Mean values µH, µA and µα unknown a-priori (information to be extracted)

• Shape factors νH, νA, and να known a-priori(dependent on the variance of the three estimates)

Joint Probability Density Function (PDF)

( ) ( )( )

( )( )

( )( ) α

µν

νν

α

α

α

µν

νν

µν

νν

αα

α

αα

αµν

νµν

νµν

να

−−

−−

−−

Γ

⋅

Γ

⋅

Γ

= eeAeHAHpA

A

A

A

H

H

H

HAH

A

A

AA

H

H

HH

111,,

111,,


INFOCOM Dpt.


The H/A/α joint segmentation (II)The H/A/α joint segmentation (II)

• Shape factors νH, νA, and να constant over thecorresponding image

• Mean values µH, µA and µα constant over each segment

• Each image can be split into a disjoint set of segments

• Same segments for the three images H, A, α

Global jointlikelihood function

for the H, A, αimages

replacing the values of µH, µA and µα with their Maximum Likelihood estimates yields

Joint Generalized Likelihood (JGL) function

( ) ( ) ( )∑ ∑∑ ∑∑ ∑=

==

==

=

−

−

−=

Q

q

Nn

qn

qq

Q

q

Nn

qn

qAq

Q

q

Nn

qn

qHq

qqq

NNA

NNH

NNConstJGL

11

11

11

1ln1ln1ln αννν α

Q: global number of segments

Nq: number of pixels in the q-thsegment (q=1,…,Q)

Hn(q), An

(q), αn(q): values of H, A, α for the n-th

pixel of region q


INFOCOM Dpt.


The H/A/α joint segmentation (III)The H/A/α joint segmentation (III)

Maximization of JGL functionthrough simulated annealing

Identification of

• number of segments

• segment borders

H and α more stable• drive the annealing

process

• define region structure

unless A gives aunless A gives amajor contributionmajor contribution

After segmentation A is averagedover the whole segment more stable can be effectively

used for classification


INFOCOM Dpt.


Application to real data (I)Application to real data (I)

Total power L-band AIRSARimage of a urban andagricultural area in NorthernItaly (Oltrepo Pavese)

From the NASA/JPL AIRSARdatabase (June 1991)


INFOCOM Dpt.


• original anisotropy image

• anisotropy histogram

• extremely flat shape

Application to real data (II)Application to real data (II)

• total absence of features⇒ not useful segmentation


INFOCOM Dpt.


Application to real data (III)Application to real data (III)

• anisotropy image obtained byaveraging the coherency matrixover a 4×4 window

• more stable, but direct classificationstill difficult


• convergence to the truedistribution


INFOCOM Dpt.


Application to real data (IV)Application to real data (IV)

• anisotropy image after segmentation

• identification of different regions


• convergence to a bimodaldistribution


INFOCOM Dpt.


Application to real data (V)Application to real data (V)

Pixels distribution in the (H,A,α) space

• averaged images

• segmented images

• significant reduction ofanisotropy variance onboth (H,A) and (H,α) plane


INFOCOM Dpt.


Classification (I)Classification (I)

Classification schemeon the (H,α) plane

Anisotropy gives moreinformation for highvalues of entropy H


INFOCOM Dpt.


Classification (II)Classification (II)

H<0.5H>0.5, α<52, H>A

H>0.5, α<52, H<A

H>0.5, α>52, H>A

H>0.5, α>52, H<A

• Smooth region borders

• Stable regions

• High resolution maintained

• Comparison with ground truthshows good discriminationcapability


INFOCOM Dpt.


ConclusionsConclusions

Proposed a classification technique for fully polarimetric SARimages based on the joint use of H/A/α decomposition and

multivariate annealed segmentation

segmentation process driven bystable parameters H and α

identification of homogenousregions

anisotropy averagedover the whole segment

significant variancereduction

useful for classificationpurposes

application to real data shows good classification capability

A joint classification technique based on multivariate ... · PDF fileMicrosoft PowerPoint -...

Documents

Transcript of A joint classification technique based on multivariate ... · PDF fileMicrosoft PowerPoint -...