SEGMENTATION OF POLARIMETRIC SAR DATA WITH A MULTI-TEXTURE PRODUCT MODEL

FACULTY OF SCIENCE AND TECHNOLOGY

DEPARTMENT OF PHYSICS AND TECHNOLOGY

SEGMENTATION OF POLARIMETRIC SARDATA WITH A MULTI-TEXTURE PRODUCTMODEL

Anthony P. Doulgeris,

S. N. Anfinsen, and T. Eltoft

IGARSS 2012

Background: IGARSS 2011

Presented a multi-texture model for PolSAR data

• Probability Density Function for Scalar and Dual-texturemodels

• Log-cumulant expressions for all multi-texture models

• Hypothesis tests to determine most appropriate multi-texturemodel

Showed evidence for multi-texture from manually chosen box-window estimates

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Objective 2012

Place multi-texture models into an advanced segmentationalgorithm

• Hypothesis tests to choose between Scalar or Dual-texturemodels

• U -distribution for flexible texture modelling

• Log-cumulants for parameter estimation

• Goodness-of-fit testing for number of clusters

• Markov Random Fields for contextual smoothing

Show real multi-texture segmentation results.

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Scalar-texture

Scattering vector:s = [shh; shv; svh; svv]

t

Scalar product model:s =√tx

where

texture variable t ∼ Γ(1, α), Γ−1(1, λ), or F(1, α, λ)

speckle variable x ∼ N cd (0,Σ)

1. Scalar t modulates all channels equally.

2. Speculation: scattering mechanisms impact specific channels andmay lead to different textural characteristics per channel.

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Multi-texture

Scattering vector:s = [shh; shv; svh; svv]

t

Multi-texture product model:s = T1/2x

whereT = diag{thh; thv; tvh; tvv}

Special cases:

Scalar-texture t = thh = thv = tvh = tvv

Dual-texture tco = thh = tvv and tcross = thv = tvh

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Multi-texture PDF

Given

s = T1/2x

C =1

L

L∑i=1

sisHi = T1/2CxT

1/2

fC|T(C|T;L,Σx) =LLd|C|L−d etr(−LΣ−1

x T−1/2CT−1/2)

Γd(L)|T|L|Σx|L

Then

fC(C;L,Σx) =

∫fC|T(C|T;L,Σx)fT(T)dT

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Dual-texture Case

- Reciprocal and reflection symmetric assumptions

fC(C;L,Σx) = L3L

Γ3(L)|C|L−3|Σx|L

×∫

1t2Lco

exp(−L(q11c11+q14c41+q41c14+q44c44

tco

))ftco(tco) dtco

×∫

1t2Lcross

exp(−L(q22c22+q23c32+q32c23+q33c33

tcross

))ftcross(tcross)dtcross

where

qij denotes the ij th elements of Σ−1s

ftco(tco) and ftcross(tcross) denotes the PDFs of tco and tcross,respectively.

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Multi-texture Log-CumulantsScalar: κν{C} = κν{W} + dνκν{T}Dual: κν{C} = κν{W} + dνco κν{Tco} + dνcrossκν{Tcross}

(Scaled) Wishart-distribution (L,Σ)

κν{W} =

{ψ

(0)d (L) + ln |Σ| − d ln(L) , ν = 1

ψ(ν−1)d (L) , ν > 1

F -distribution (α, λ)

κν{T} =

{ψ(0)(α)− ψ(0)(λ) + ln(λ−1

α ) , ν = 1

ψ(ν−1)(α) + (−1)νψ(ν−1)(λ) , ν > 1

Texture Parameters:Scalar (α, λ) Dual (αco, λco) & (αcross, λcross)

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Multi-texture Hypothesis TestScalar: κν{C} = κν{W} + dνκν{T}Dual: κν{C} = κν{W} + dνco κν{Tco} + dνcrossκν{Tcross}Estimate texture parameters for T , Tco and TcrossChoose from smallest of Dscalar or Ddual

−5 −4 −3 −2 −1 0 1 2 3 4 50

1

2

3

4

5

6

7

8

9

10

o

o

X

W

Dscalar

Ddual

Kappa 3

Kap

pa 2

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Segmentation Algorithm

Iterative expectation maximisation algorithm with a fewmodifications, scalar-texture version detailed in

Doulgeris et al. TGRS-EUSAR (2011) andDoulgeris et al. EUSAR (2012).

The key features are:

• U -distribution for flexible texture modelling

• Log-cumulants for parameter estimation

• Goodness-of-fit testing for number of clusters

• Markov Random Fields for contextual smoothing

Hypothesis tests to choose Scalar or Dual-texture model

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Segmentation Algorithm → Multi-texture

Iterative expectation maximisation algorithm with a fewmodifications, scalar-texture version detailed in

Doulgeris et al. TGRS-EUSAR (2011) andDoulgeris et al. EUSAR (2012).

The key features are:

• U -distribution for flexible texture modelling→ Multi-texture

• Log-cumulants for parameter estimation→ Multi-texture

• Goodness-of-fit testing for number of clusters

• Markov Random Fields for contextual smoothing

• Hypothesis tests to choose Scalar or Dual-texture model

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Simulated 8-look Data

Class 1K-Wishartα = 15

U-distributionα = 16.5, λ = 4220

Class 2

Co-pol

K-Wishart α = 10

Cross-pol

G0 λ = 30

α = 10.4, λ = 217

α = 4220, λ = 28.8

Lexicographic RGB11 / 17

Simulated Results

(a) Lexicographic RGB

(c) Class histograms

(b) Class segmentation

(d) Class log-cumulants

(e)Dual-texture log-cumulants

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Real Data 1: San Francisco CityRadarsat-2 sample image from 9 April, 2008, 25-looks.

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Real Data 2: Amazon RainforestALOS PALSAR sample data from 13 March, 2007, 32-looks.

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NO MULTI-TEXTURE !But previously ...

0 0.5 1 1.5 2 2.5 30

5

10

15

µ = 0.881

0 0.5 1 1.5 2 2.5 30

5

10

15

µ = 0.0246

0 0.5 1 1.5 2 2.5 30

5

10

15

µ = 0.0241

0 0.5 1 1.5 2 2.5 30

5

10

15

µ = 0.595

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

0

0.1

0.2

0.3

0.4

0.5

HH

HVVH

VV

co−pol test x−pol test scalar test

K G0

W

κ3

κ 2

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Mixtures Give Multi-textureExample: small co-pol difference, large cross-pol difference.Texture (skewness) of each mixture are different = Multi-texture.

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Conclusions

• Developed a Multi-texture segmentation algorithm

• Tests found only the Scalar-texture case

• Previous window-estimation may have found multi-texturedue to mixtures

• This automatic segmentation algorithm will split-up suchmixtures

• Less complicated scalar-product model is generally suitableof PolSAR analysis

Wanted: Data-sets that may display multi-texture for testing.

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