![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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![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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SEGMENTATION OF POLARIMETRIC SAR DATA WITH A MULTI-TEXTURE PRODUCT MODEL
- 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 2 / 17
- 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. 3 / 17
- 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. 4 / 17
- 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 5 / 17
- 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 6 / 17
- 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. 7 / 17
- 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) 8 / 17
- 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 9 / 17
- 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 10 / 17
- 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 10 / 17
- 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 11 / 17
- 13. Simulated Results (a) Lexicographic RGB (b) Class segmentation (d) Class log-cumulants (c) Class histograms (e)Dual-texture log-cumulants 12 / 17
- 14. Real Data 1: San Francisco City Radarsat-2 sample image from 9 April, 2008, 25-looks. 13 / 17
- 15. Real Data 2: Amazon Rainforest ALOS PALSAR sample data from 13 March, 2007, 32-looks. 14 / 17
- 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 15 / 17
- 17. Mixtures Give Multi-texture Example: small co-pol difference, large cross-pol difference. Texture (skewness) of each mixture are different = Multi-texture. 16 / 17
- 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. 17 / 17