1.
FACULTY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF PHYSICS AND TECHNOLOGY
SEGMENTATION OF POLARIMETRIC SAR
DATA WITH A MULTI-TEXTURE PRODUCT
MODEL
Anthony P. Doulgeris,
S. N. Anfinsen, and T. Eltoft
IGARSS 2012

2.
Background: IGARSS 2011
Presented a multi-texture model for PolSAR data
• Probability Density Function for Scalar and Dual-texture
models
• Log-cumulant expressions for all multi-texture models
• Hypothesis tests to determine most appropriate multi-texture
model
Showed evidence for multi-texture from manually chosen box-
window estimates
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3.
Objective 2012
Place multi-texture models into an advanced segmentation
algorithm
• Hypothesis tests to choose between Scalar or Dual-texture
models
• 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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4.
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)
c
speckle variable x ∼ Nd (0, Σ)
1. Scalar t modulates all channels equally.
2. Speculation: scattering mechanisms impact specific channels and
may lead to different textural characteristics per channel.
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5.
Multi-texture
Scattering vector:
s = [shh; shv ; svh; svv ]t
Multi-texture product model:
s = T1/2x
where
T = 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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6.
Multi-texture PDF
Given
s = T1/2x
L
1
C = sisH = T1/2CxT1/2
i
L
i=1
LLd|C|L−d etr(−LΣ−1T−1/2CT−1/2)
x
fC|T(C|T; L, Σx) =
Γd(L)|T|L|Σx|L
Then
fC(C; L, Σx) = fC|T(C|T; L, Σx)fT(T)dT
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7.
Dual-texture Case
- Reciprocal and reflection symmetric assumptions
L3L |C|L−3
fC(C; L, Σx) = Γ3(L) |Σx|L
1 q11c11+q14c41+q41c14+q44c44
× t2L exp −L tco ftco (tco) dtco
co
1 q22c22+q23c32+q32c23+q33c33
× t2L exp −L tcross ftcross (tcross)dtcross
cross
where
qij denotes the ij th elements of Σ−1
s
ftco (tco) and ftcross (tcross) denotes the PDFs of tco and tcross,
respectively.
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8.
Multi-texture Log-Cumulants
Scalar: κν {C} = κν {W} + dν κν {T }
Dual: κν {C} = κν {W} + dν κν {Tco} + dν κν {Tcross}
co cross
(Scaled) Wishart-distribution (L, Σ)
(0)
ψd (L) + ln |Σ| − d ln(L) , ν = 1
κν {W} = (ν−1)
ψd (L) ,ν > 1
F -distribution (α, λ)
ψ (0)(α) − ψ (0)(λ) + ln( λ−1 ) , ν = 1
α
κν {T } =
ψ (ν−1)(α) + (−1)ν ψ (ν−1)(λ) , ν > 1
Texture Parameters:
Scalar (α, λ) Dual (αco, λco) & (αcross, λcross)
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9.
Multi-texture Hypothesis Test
Scalar: κν {C} = κν {W} + dν κν {T }
Dual: κν {C} = κν {W} + dν κν {Tco} + dν κν {Tcross}
co cross
Estimate texture parameters for T , Tco and Tcross
Choose from smallest of Dscalar or Ddual
10
o
9
8
Dscalar
7
X
6
Kappa 2
Ddual
5 o
4
3
2
1
W
0
−5 −4 −3 −2 −1 0 1 2 3 4 5
Kappa 3
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10.
Segmentation Algorithm
Iterative expectation maximisation algorithm with a few
modifications, scalar-texture version detailed in
Doulgeris et al. TGRS-EUSAR (2011) and
Doulgeris 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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11.
Segmentation Algorithm → Multi-texture
Iterative expectation maximisation algorithm with a few
modifications, scalar-texture version detailed in
Doulgeris et al. TGRS-EUSAR (2011) and
Doulgeris 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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12.
Simulated 8-look Data
K-Wishart U-distribution
Class 1
α = 15 α = 16.5, λ = 4220
Co-pol
K-Wishart α = 10 α = 10.4, λ = 217
Class 2
Cross-pol
G 0 λ = 30 α = 4220, λ = 28.8
Lexicographic RGB
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13.
Simulated Results
(a) Lexicographic RGB (b) Class segmentation
(d) Class log-cumulants
(c) Class histograms (e)Dual-texture log-cumulants
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14.
Real Data 1: San Francisco City
Radarsat-2 sample image from 9 April, 2008, 25-looks.
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15.
Real Data 2: Amazon Rainforest
ALOS PALSAR sample data from 13 March, 2007, 32-looks.
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16.
NO MULTI-TEXTURE !
But previously ... 15
10
5
µ= 0.881
0
0 0.5 1 1.5 2 2.5 3
15
µ = 0.0246
10
5
0
0 0.5 1 1.5 2 2.5 3
15
10 µ = 0.0241
5
0
0 0.5 1 1.5 2 2.5 3
15
µ= 0.595
10
5
0
0 0.5 1 1.5 2 2.5 3
0.5
VV
HH
0.4
0.3
κ2
0.2
VH
HV
co−pol test
0.1 x−pol test
0
K G
scalar test
0
W
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
κ3
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17.
Mixtures Give Multi-texture
Example: small co-pol difference, large cross-pol difference.
Texture (skewness) of each mixture are different = Multi-texture.
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18.
Conclusions
• Developed a Multi-texture segmentation algorithm
• Tests found only the Scalar-texture case
• Previous window-estimation may have found multi-texture
due to mixtures
• This automatic segmentation algorithm will split-up such
mixtures
• Less complicated scalar-product model is generally suitable
of PolSAR analysis
Wanted: Data-sets that may display multi-texture for testing.
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