segmentation of polarimetric sar data with a multi-texture product model
TRANSCRIPT
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
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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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