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# Multitexture_TE_V3.pdf

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### Multitexture_TE_V3.pdf

1. 1. A Multitexture Model for Multilook Polarimetric Radar Data by Torbjørn Eltoft, Stian Anfinsen, and Anthony Doulgeris
2. 2. Outline•  Background and motivation•  Multitexture model•  Mellin type statistics and the log-cumulant diagram•  Experimental studies•  Conclusions2 7/25/11
3. 3. The scalar product modelThe product model has been proposed as a generic model forgeneration of non-Gaussian distributions for polarimetric radarsignals.The scalar product model: is a multivariate Gaussian speckle variable is a scalar texture variable 3 7/25/11
4. 4. Scattering mechanisms Figure from Pottier et al. (2003) Question: Can the different polarization components be represented by the same texture variable?4 7/25/11
5. 5. Multitexture modelScattering vector:Multilook sample covariance matrix:where5 7/25/11
6. 6. Conditional pdf of sample covariance matrix:Pdf of sample covariance matrix:6 7/25/11
7. 7. Reciprocity Reflection symmetry where7 7/25/11
8. 8. Multitexture pdf of CAssume the texture components thh = tvvLet qi,j denote entry (i,j) ofLet ci,j denote entry (i,j) of 8 7/25/11
9. 9. 2-D log-cumulant diagram 5 4 3 2 Xκ2 1 K G0 0 W 95%, N=1000 −1 95%, N=100 −2 −6 −4 −2 0 2 κ3 9 7/25/11
10. 10. Mellin kind statisticsSample covariance matrix in the multitexture modelMellin type characteristic function:Statistical independence implies:10 7/25/11
11. 11. W is Wishart distributed: T is diagonal:11 7/25/11
12. 12. Log-moments: Log-cumulants:12 7/25/11
13. 13. Sample matrix log-moments:Relation between log-cumulants & log-moments: 13 7/25/11
14. 14. Asymptotic distribution of sample matrix log-cumulants:14 7/25/11
15. 15. Multi -, dual- or scalar texture models 0.6 0.5 0.5 HH VV HH VV 0.4 VH 0.4 VH HV HV 0.3 0.3 κ2κ2 0.2 0.2 HH test 0.1 HV test 0.1 co−pol test VH test K G0 VV test x−pol test 0 K G0 0 W W −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 −0.2 −0.15 −0.1 −0.05 0 0.05 κ3 κ3 0.5 HH VV 0.4 VH HV 0.3 κ2 0.2 0.1 scalar test K G0 0 W −0.14 −0.12 −0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 κ3 15 7/25/11
16. 16. Study case 1: Amazon Rainforest 550 4 500 1 450 400 350 Spaceborne: Amazon rainforest; 300 ALOS L-band, 2 No. of looks = 8 250 200 150 100 3 5016 7/25/11 50 100 150 200 250 300 350
17. 17. Amazon: Box 1 (water) 20 10 µ = 0.000129 0.5 0 HH VV 0 0.5 1 1.5 2 2.5 3 20 0.4 VH HV 10 µ = 1.48e−05 0.3 0 0 0.5 1 1.5 2 2.5 3κ2 20 0.2 10 µ = 2.05e−05 co−pol test 0 0.1 0 0.5 1 1.5 2 2.5 3 x−pol test 0 20 scalar test K G 10 0 µ = 7.41e−05 W 0 0 0.5 1 1.5 2 2.5 3 −0.2 −0.15 −0.1 −0.05 0 0.05 κ3 Amazon: Box 2 (forest) 20 10 µ= 0.115 0.7 0 0.6 VV 0 0.5 1 1.5 2 2.5 3 HH 20 VH 0.5 HV 10 µ = 0.0117 0.4 0 0 0.5 1 1.5 2 2.5 3κ2 20 0.3 10 µ = 0.0116 0.2 co−pol test 0 0 0.5 1 1.5 2 2.5 3 0.1 x−pol test 0 20 scalar test K G 0 10 µ = 0.0946 W 0 −0.4 −0.3 −0.2 −0.1 0 0 0.5 1 1.5 2 2.5 3 κ3 17 7/25/11
18. 18. Amazon: Box 3 (clear-cut area) 20 µ= 0.078 1 10 0 VH 0 0.5 1 1.5 2 2.5 3 0.8 HV 20 VV HH 10 µ = 0.000467 0.6 0 0 0.5 1 1.5 2 2.5 3κ2 20 0.4 µ = 0.000493 10 co−pol test 0 0.2 0 0.5 1 1.5 2 2.5 3 x−pol test 0 20 scalar test K G 10 µ= 0.075 0 W 0 0 0.5 1 1.5 2 2.5 3 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 κ3 Amazon: Box 4 (low-intensity water) 20 10 µ = 5.03e−05 0.6 0 HH 0 0.5 1 1.5 2 2.5 3 20 0.5 VV 10 µ = 6.96e−06 0.4 0 0 0.5 1 1.5 2 2.5 3 HVκ2 0.3 20 VH 10 µ = 7.42e−06 0.2 co−pol test 0 0 0.5 1 1.5 2 2.5 3 0.1 x−pol test 0 20 scalar test K G 0 10 µ = 2.84e−05 W 0 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0 0.5 1 1.5 2 2.5 3 κ3 18 7/25/11
19. 19. Study case 2: Nezer Forest 400 350 300 250 3 200 Airborne: Nezer forest; 150 AIRSAR P-band, 2 No. of looks = 16 100 4 1 50 50 100 150 200 250 300 350 400 45019 7/25/11
20. 20. Nezer: Box 1 (bare soil) 20 0.1 10 µ = 0.00013 HH 0 0.08 VV 0 0.5 1 1.5 2 2.5 3 20 VH HV 0.06 10 µ = 1.48e−05 0κ2 0 0.5 1 1.5 2 2.5 3 0.04 20 co−pol test 10 µ = 2.02e−05 0.02 0 x−pol test K G scalar test 0 0 0.5 1 1.5 2 2.5 3 0 20 W 10 µ = 7.36e−05 −0.02 −0.01 −0.005 0 0.005 0.01 0 0 0.5 1 1.5 2 2.5 3 κ3 Nezer: Box 2 (old forest) 40 0.16 µ= 0.185 20 0.14 HH 0 0 0.5 1 1.5 2 2.5 3 0.12 VHVV HV 40 0.1 20 µ = 0.0419 0.08 0 0 0.5 1 1.5 2 2.5 3κ2 40 0.06 20 µ = 0.0419 0.04 co−pol test x−pol test 0 0.02 scalar test K G0 0 0.5 1 1.5 2 2.5 3 40 0 W 20 µ = 0.0832 −0.02 0 −0.04 −0.03 −0.02 −0.01 0 0.01 0 0.5 1 1.5 2 2.5 3 κ3 20 7/25/11
21. 21. Nezer: Box 3 (young forest) 40 0.12 20 µ = 0.0572 0.1 0 VH HV 0 0.5 1 1.5 2 2.5 3 40 0.08 HH 20 µ = 0.00785 0.06 VV 0 0 0.5 1 1.5 2 2.5 3κ2 40 0.04 20 µ = 0.00785 co−pol test 0.02 x−pol test scalar test K G0 0 0 0.5 1 1.5 2 2.5 3 40 0 W 20 µ = 0.0384 −0.02 −0.015 −0.01 −0.005 0 0.005 0.01 0 0 0.5 1 1.5 2 2.5 3 κ3 Nezer: Box 4 (class mixture) 40 1.8 20 µ= 0.101 1.6 0 VH HV 0 0.5 1 1.5 2 2.5 3 1.4 50 µ= 0.029 1.2 1 0 0 0.5 1 1.5 2 2.5 3 HHκ2 50 0.8 µ= 0.029 0.6 VV co−pol test 0 0.4 0 0.5 1 1.5 2 2.5 3 x−pol test 20 0.2 scalar test K G0 µ = 0.0624 10 0 W 0 0 0.5 1 1.5 2 2.5 3 −4.5 −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 κ3 21 7/25/11
22. 22. Conclusions •  Introduced a multitexture statistical model for the multi-look polarimetric sample covariance matrix •  Shown that in the reciprocal, reflection symmetrical case the pdf can be explicitly formulated as a dual texture model •  Used Mellin kind statistics to develop experimental procedures to test the nature of the texture variables •  Preliminary experimental studies conclude: §  The scalar texture model is often valid §  When multitexture is needed, the dual-model is often sufficient §  Mixtures often appear as multitexture22 7/25/11