T 13 T 13 T 13 T PolSAR H V x S HV S HV = S VH. 1 Coherency [S] Pauli k P [ ] S HH S HV [S] = S VH S VV S HH + S VV = k p = 1 S HH S VV S HV (

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1 a) On the Model-Based Scattering Power Decomposition of Fully Polarimetric SAR Data Yoshio YAMAGUCHI a), Gulab SINGH, and Hiroyoshi YAMADA (PolSAR) PolSAR Coherency 9 Coherency 6 1. (PolSAR) PolSAR [1] [4] PolSAR 3x3 Covariance Coherency 4x4 Kennaugh 9 [] [5] Faculty of Engineering, Niigata University, 050 Ikarashi, Nishi-ku, Niigata-shi, Japan CSRE, Indian Institute of Technology Bombay, Powai, Mumbai-76, India a) [email protected] DOI: /transcomj.01API0001 Entropy/α/Anisotropy [6] [4] Covariance [7], [] Coherency Coherency 3 FDD (Freeman & Durden Decomposition [7]) 4 Y40 [] 4 Y4R [9] S4R [10] 100% G4U [11] [1] [13], [14] Coherency T 13. T B Vol. J101 B No. 9 pp c 01

2 T 13 T 13 T 13 T PolSAR H V x S HV S HV = S VH. 1 Coherency [S] Pauli k P [ ] S HH S HV [S] = S VH S VV S HH + S VV = k p = 1 S HH S VV S HV (1) k P Coherency [T ] = 1 n n kp kp t = T 11 T 1 T 13 T1 T T 3 T 13 T 3 T 33 () t n T 11 = 1 SHH + SV V, T = 1 SHH SV V, T 1 = 1 (SHH + SV V)(SHH SV V), T 33 = S HV, T 13 = SHV (S HH + S VV), T 3 = SHV (S HH S VV) (3) Coherency () Covariance Kennuagh [5] 9 Fitting 9 FDD [7] 3 T 1 5 5/9 T 13, T 3 Y40 [] Reflection Symmetry S HHSHV S VVSHV 0 Helix T 3 6/9 Y4R [9] Coherency θ = 1 ( ) Re{T3} tan 1 (4) T T [R(θ)] = 0 cos θ sin θ (5) 0 sin θ cos θ [T (θ)] =[R(θ)] [T ] [R(θ)] t (6) 639

3 01/9 Vol. J101 B No. 9 T 11(θ)=T 11 (6a) T 1(θ)=T 1 cos θ +T 13 sin θ (6b) T 13(θ)=T 13 cos θ T 1 sin θ (6c) T (θ)=t cos θ +T 33 sin θ +Re{T 3} sin 4θ (6d) T 33(θ)=T 33 cos θ +T sin θ Re{T 3} sin 4θ (6e) T 3(θ)=j Im{T 3} (6f) (6f) T 3(θ) 0 T 33 T T 3 Helix T 33 Coherency 9 Y4R 6/ G4U [11] (6f) T T 13 7/7 100% T 13 T 13 ± HH VV Re{S HHS VV} > 0 (7a) HH VV Re{S HHS VV} < 0 (7b) HH HV VV HV 0 Reflection Symmetry S HHS HV S VVS HV 0 (7c) Helix Reflection Symmetry Im S HV (S HH S VV) (7d) Coherency β [T ] s = 1 1+ β 1 β 0 β β 0 () α α α 0 1 [T ] d = 1+ α α 1 0 (9) Fig Scattering models and the corresponding powers. [10] [T ] uniform v = , 640

4 [T ] cos v = 1 30 [T ] sin v = 1 30 [T ] CR v = 1 15 Helix [T ] r l helix = , , 0 1 ±j 0 j 1 (10) (11) Coherency T 13 T 13 0 T 13 T 13 ±45 Re{T 13} [T ] ±45 od = ±1 ±1 0 1 (1) ±45 Im{T 13} [T ] ± cd = ±j (13) j 0 1 d 4 [16] H V ±45 d T 13 Fig. Scattering model for T 13 component by compound oriented dipoles with spacing d. ( ) ( ) λ 3λ [S] cd 1 =[S] 1 +[S] 1P +[S] P ( ) 4λ +[S] P [ ] [ ] [ ] = j j [ ] [ ] j = 1 1 j 1 ( ) ( ) [S] cd λ 3λ =[S] 1 +[S] P +[S] 1P ( ) 4λ +[S] P [ ] [ ] [ ] = j j [ ] [ ] j = 1 1 j 1 P T

5 01/9 Vol. J101 B No. 9 (1) (13) T Total Power: TP = P s + P d + P v + P h + P od + P cd (14) P s P d P v P h Helix P od 45 P cd Compound (6SD: 6-component Scattering Power Decomposition) () (13) P i (i = s, d, v, h, od, cd) (14) Coherency (6) [T (θ)] = P s[t ] s + P d [T ] d + P v[t ] v + P h [T ] h + P od [T ] od + P cd [T ] cd (15) T 11(θ) T 1(θ) T 13(θ) T 1(θ) T (θ) T 3(θ) T 31(θ) T 3(θ) T 33(θ) 1 β 0 = Ps 1+ β β β 0 + P α α 0 d 1+ α α Pv P h 0 1 ±j j 1 + P od + P cd 1 0 ±1 ± ±j j 0 1 T 3(θ) =j Im{T 3} = ±j P h T 13(θ) =± P od ± j P cd T 33(θ) = Pv 4 + P h + P od + P cd (16) P h P od P cd P v P h = Im{T 3(θ)}, P od = Re{T 13(θ)}, P cd = Im{T 13(θ)}, P v =[T 33(θ) P h P od P cd ] (17) P s P d α β P s 1+ β + P d α 1+ α = S P s β 1+ β + P d 1+ α = D (1) P sβ 1+ β + P dα 1+ α = C S = T 11(θ) Pv P od P cd D = T (θ) Pv 4 P h C = T 1(θ) (19) [7] [11] α =0 β =0 C 0 =T 11 + P h TP (0) [9] P s P d C 0 > 0 α =0 P s = S + C S, P d = D C S (1) 64

6 Fig Flow-chart for 6-component scattering power decomposition. 643

01/9 Vol. J101 B No. 9 C 0 < 0 β =0 P s = S C D, P d = D + C D () (15) (16) 3 [7] 4 [] [11] 6 (6SD) 3. Coherency Re{T 3} =0 3 P h P od P cd 5 (16) P v P s P d 0 3 3.

7 01/9 Vol. J101 B No. 9 C 0 < 0 β =0 P s = S C D, P d = D + C D () (15) (16) 3 [7] 4 [] [11] 6 (6SD) 3. Coherency Re{T 3} =0 3 P h P od P cd 5 (16) P v P s P d RGB 3 RGB R P d G P v B P s Helix P h 45 P od Compound P cd ALOS Off nadir FDD 3 [7] 5/9 4 Fig. 4 Scattering power decomposition image of San Francisco. Fully polarimetric data: ALOS c JAXA. 45 FDD Reflection Symmetry Y40 [] Helix 4 FDD 644

8 G4U [13] 6SD Google Earth 4 5 G4U 6SD Web [17] 5. PiSAR- PiSAR- NICT X 30cm PolSAR Fig. 5 5 Comparison of decomposition result. 6 PiSAR-X Fig. 6 Time series fully polarimetric radar image near Minami-Aso, before and after Kumamoto earthquake. Observation by PiSAR-X on 015/1/05(up) and 016/04/17(low). 645

01/9 Vol. J101 B No. 9 7 Fig. 7 6 Close-up image of landslide at Minami-Aso village of Fig. 6. 016 4 17 4 16 G4U 6 P s P d P v 6 7 5x 5 imaging window 7 1 6 7 Web [17] 6.

9 01/9 Vol. J101 B No. 9 7 Fig. 7 6 Close-up image of landslide at Minami-Aso village of Fig G4U 6 P s P d P v 6 7 5x 5 imaging window Web [17] 6. Coherency T % ALOS JAXA, NICT [1] ESA, [] S.R. Cloude and E. Pottier, A review of target decomposition theorems in radar polarimetry, IEEE Trans. Geosci. Remote Sens., vol.34, no., pp.49 51, March DOI: / [3] 007. [4] J.S. Lee and E. Pottier, Polarimetric Radar Imaging: from basics to applications, CRC Press, 009. [5] B vol.j9-b, no.9, pp , Sept [6] S.R. Cloude and E. Pottier, An entropy based classification scheme for land applications of polarimetric SAR, IEEE Trans. Geosci. Remote Sens., vol.35, no.1, pp.6 7, Jan DOI: / [7] A. Freeman and S. Durden, A three-component scattering model for polarimetric SAR data, IEEE Trans. Geosci. Remote Sens., vol.36, no.3, pp , May 199. DOI: / [] Y. Yamaguchi, T. Moriyama, M. Ishido, and H. Yamada, Four-component scattering model for polarimetric SAR image decomposition, IEEE Trans. Geosci. Remote Sens., vol.43, no., pp , Aug DOI: /TGRS [9] Y. Yamaguchi, A. Sato, W.-M. Boerner, R. Sato, and H. Yamada, Four-component scattering power decomposition with rotation of coherency matrix, IEEE Trans. Geosci. Remote Sens., vol.49, no.6, pp.51 5, June 011. DOI: /TGRS

[10] A. Sato, Y. Yamaguchi, G. Singh, and S.-E. Park, Four-component scattering power decomposition with extended volume scattering model, IEEE Geosci. Remote Sens. Lett., vol.9, no., pp.166 170, 01.

Remote Sens., vol.51, no.5, pp.3014 30, March 013. DOI: 10.1109/TGRS. 01.1446. [1] M. Arii, J. van Zyl, and Y.

Chen, X. songwang, S. ping Xiao, and M. Sato, General polarimetric model-based decomposition for coherency matrix, IEEE Trans. Geosci. Remote Sens., vol.5, no.3, pp.143 155, March 014. DOI: 10.

10 [10] A. Sato, Y. Yamaguchi, G. Singh, and S.-E. Park, Four-component scattering power decomposition with extended volume scattering model, IEEE Geosci. Remote Sens. Lett., vol.9, no., pp , 01. DOI: /LGRS [11] G. Singh, Y. Yamaguchi, and S.-E. Park, General four-component scattering power decomposition with unitary transformation of coherency matrix, IEEE Trans. Geosci. Remote Sens., vol.51, no.5, pp , March 013. DOI: /TGRS [1] M. Arii, J. van Zyl, and Y. Kim, Adaptive modelbased decomposition of polarimetric SAR covariance matrices, IEEE Trans. Geosci. Remote Sens., vol.49, no.3, pp , March 011. DOI: / TGRS [13] S.-W. Chen, X. songwang, S. ping Xiao, and M. Sato, General polarimetric model-based decomposition for coherency matrix, IEEE Trans. Geosci. Remote Sens., vol.5, no.3, pp , March 014. DOI: /TGRS [14] Y. Cui, Y. Yamaguchi, J. Yang, H. Kobayashi, S.-E. Park, and G. Singh, On complete model-based decomposition of polarimetric SAR coherency matrix data, IEEE Trans. Geosci. Remote Sens., vol.5, no.4, pp , April 014. DOI: / TGRS [15] G. Singh and Y. Yamaguchi, Model-based and six component scattering power decomposition, Electronic Proc. of IGARSS 017, DOI: /IGARSS , July 017. [16] K. Kitayama, Y. Yamaguchi, J. Yang, and H. Yamada, Compound scattering matrix of targets aligned in the range direction, IEICE Trans. Commun., vol.e4-b, no.1, pp.1, Jan [17] ie.niigata-u.ac.jp/yamaguchi/ Gulab SINGH 199 Chaudhary Charan Singh University Meerut (India) 010 Ph.D. Degree Assistant Professor at Indian Institute of Technology Bombay India NASA MIMO SAR 3 IEEE AP-S Young Engineer Award 9 1 IEEE IEEE&IEICE Fellow 19 IEEE GRSS Education Award (00) Distinguished Achievement Award (017)

(a) (b) (c) Canny (d) 1 ( x α, y α ) 3 (x α, y α ) (a) A 2 + B 2 + C 2 + D 2 + E 2 + F 2 = 1 (3) u ξ α u (A, B, C, D, E, F ) (4) ξ α (x 2 α, 2x α y α,

(a) (b) (c) Canny (d) 1 ( x α, y α ) 3 (x α, y α ) (a) A 2 + B 2 + C 2 + D 2 + E 2 + F 2 = 1 (3) u ξ α u (A, B, C, D, E, F ) (4) ξ α (x 2 α, 2x α y α, [II] Optimization Computation for 3-D Understanding of Images [II]: Ellipse Fitting 1. (1) 2. (2) (edge detection) (edge) (zero-crossing) Canny (Canny operator) (3) 1(a) [I] [II] [III] [IV ] E-mail [email protected]