Abstract

Structured light is a prevailing and reliable active approach of 3D object reconstruction. But complex ambience is undesirable in the measurement because it could cause severe noise and increase computing overhead. In this paper, we propose a structured light coded by spatially-distributed polarization state of the illuminating patterns. The proposed structured light has the advantage of enhancing target in 3D reconstruction by polarization cues. Specifically, this method can estimate the degree of linear polarization (DOLP) in the scene, distinguish target by DOLP and selectively reconstruct it. The coding strategy and the corresponding polarimetric principle are presented and verified by experimental results. As our approach takes advantage of the intrinsic properties of liquid crystal display (LCD) projector and requires no rotation of polarizer, it is effective and efficient for practical applications.

© 2017 Optical Society of America

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References

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2016 (1)

T. M. Jordan, D. Wilby, T. H. Chiou, K. D. Feller, R. L. Caldwell, T. W. Cronin, and N. W. Roberts, “A shape-anisotropic reflective polarizer in a stomatopod crustacean,” Sci. Rep. 6, 21744 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (3)

2013 (1)

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “A practical approach to 3D scanning in the presence of interreflections, subsurface scattering and defocus,” Int. J. Comput. Vis. 102(1–3), 33–55 (2013).
[Crossref]

2011 (3)

2010 (3)

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
[Crossref]

A. Ghosh, T. Chen, P. Peers, C.A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Trans. Graph. 30(6), 162 (2010).

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

2009 (1)

2006 (1)

2002 (1)

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7(3), 329–340 (2002).
[Crossref] [PubMed]

2000 (1)

1998 (1)

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. 20(5), 470–480 (1998).
[Crossref]

1997 (1)

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15(2), 81–93 (1997).
[Crossref]

1995 (1)

1987 (1)

K. L. Boyer and A. C. Kak, “Color-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. 1, 14–28 (1987).

1982 (1)

J. L. Posdamer and M. D. Altschuler, “Surface measurement by space-encoded projected beam systems,” Comput. Graph. Image Process. 18(1), 1–17 (1982).
[Crossref]

Agrawal, A.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “A practical approach to 3D scanning in the presence of interreflections, subsurface scattering and defocus,” Int. J. Comput. Vis. 102(1–3), 33–55 (2013).
[Crossref]

Altschuler, M. D.

J. L. Posdamer and M. D. Altschuler, “Surface measurement by space-encoded projected beam systems,” Comput. Graph. Image Process. 18(1), 1–17 (1982).
[Crossref]

Anna, G.

Boffety, M.

Boyer, K. L.

K. L. Boyer and A. C. Kak, “Color-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. 1, 14–28 (1987).

Busch, J.

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Trans. Graph. 30(6), 129 (2011).
[Crossref]

Caldwell, R. L.

T. M. Jordan, D. Wilby, T. H. Chiou, K. D. Feller, R. L. Caldwell, T. W. Cronin, and N. W. Roberts, “A shape-anisotropic reflective polarizer in a stomatopod crustacean,” Sci. Rep. 6, 21744 (2016).
[Crossref] [PubMed]

Caspi, D.

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. 20(5), 470–480 (1998).
[Crossref]

Chen, T.

A. Ghosh, T. Chen, P. Peers, C.A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Trans. Graph. 30(6), 162 (2010).

T. Chen, H. P. Lensch, C. Fuchs, and H. Seidel, “Polarization and phase-shifting for 3D scanning of translucent objects,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.
[Crossref]

Chen, Z.

Chenault, D. B.

Cheng, P. W.

Chiou, T. H.

T. M. Jordan, D. Wilby, T. H. Chiou, K. D. Feller, R. L. Caldwell, T. W. Cronin, and N. W. Roberts, “A shape-anisotropic reflective polarizer in a stomatopod crustacean,” Sci. Rep. 6, 21744 (2016).
[Crossref] [PubMed]

Cronin, T. W.

T. M. Jordan, D. Wilby, T. H. Chiou, K. D. Feller, R. L. Caldwell, T. W. Cronin, and N. W. Roberts, “A shape-anisotropic reflective polarizer in a stomatopod crustacean,” Sci. Rep. 6, 21744 (2016).
[Crossref] [PubMed]

Dai, J.

Debevec, P.

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Trans. Graph. 30(6), 129 (2011).
[Crossref]

A. Ghosh, T. Chen, P. Peers, C.A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Trans. Graph. 30(6), 162 (2010).

Dolfi, D.

Du, E.

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19(7), 076013 (2014).
[Crossref] [PubMed]

Ekstrand, L.

Engheta, N.

Feller, K. D.

T. M. Jordan, D. Wilby, T. H. Chiou, K. D. Feller, R. L. Caldwell, T. W. Cronin, and N. W. Roberts, “A shape-anisotropic reflective polarizer in a stomatopod crustacean,” Sci. Rep. 6, 21744 (2016).
[Crossref] [PubMed]

Fernandez, S.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Fuchs, C.

T. Chen, H. P. Lensch, C. Fuchs, and H. Seidel, “Polarization and phase-shifting for 3D scanning of translucent objects,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.
[Crossref]

Fyffe, G.

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Trans. Graph. 30(6), 129 (2011).
[Crossref]

Ghosh, A.

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Trans. Graph. 30(6), 129 (2011).
[Crossref]

A. Ghosh, T. Chen, P. Peers, C.A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Trans. Graph. 30(6), 162 (2010).

Goldstein, D. L.

Goudail, F.

Gu, P. F.

Guo, Y.

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19(7), 076013 (2014).
[Crossref] [PubMed]

Gupta, M.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “A practical approach to 3D scanning in the presence of interreflections, subsurface scattering and defocus,” Int. J. Comput. Vis. 102(1–3), 33–55 (2013).
[Crossref]

Han, J.

He, H.

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19(7), 076013 (2014).
[Crossref] [PubMed]

Hu, H.

Huang, B.

Huang, H. C.

Inokuchi, S.

S. Inokuchi, K. Sato, and F. Matsuda, “Range imaging system for 3-D object recognition,” in Proceedings of the International Conference on Pattern Recognition, pp. 806–808 (1984).

Jacques, S. L.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7(3), 329–340 (2002).
[Crossref] [PubMed]

Jordan, T. M.

T. M. Jordan, D. Wilby, T. H. Chiou, K. D. Feller, R. L. Caldwell, T. W. Cronin, and N. W. Roberts, “A shape-anisotropic reflective polarizer in a stomatopod crustacean,” Sci. Rep. 6, 21744 (2016).
[Crossref] [PubMed]

Kadambi, A.

A. Kadambi, V. Taamazyan, B. Shi, and R. Raskar, “Polarized 3d: High-quality depth sensing with polarization cues,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE, 2015), pp. 3370–3378.
[Crossref]

Kak, A. C.

K. L. Boyer and A. C. Kak, “Color-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. 1, 14–28 (1987).

Karpel, N.

Y. Y. Schechner and N. Karpel, “Clear underwater vision,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2004), pp. I-536–I-546.

Kiryati, N.

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. 20(5), 470–480 (1998).
[Crossref]

Kwok, H. S.

Lee, K.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7(3), 329–340 (2002).
[Crossref] [PubMed]

Lensch, H. P.

T. Chen, H. P. Lensch, C. Fuchs, and H. Seidel, “Polarization and phase-shifting for 3D scanning of translucent objects,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.
[Crossref]

Li, H. F.

Liang, R.

Liu, S.

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19(7), 076013 (2014).
[Crossref] [PubMed]

Liu, T.

Liu, X.

Llado, X.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Ma, H.

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19(7), 076013 (2014).
[Crossref] [PubMed]

Matsuda, F.

S. Inokuchi, K. Sato, and F. Matsuda, “Range imaging system for 3-D object recognition,” in Proceedings of the International Conference on Pattern Recognition, pp. 806–808 (1984).

Namer, E.

Narasimhan, S. G.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “A practical approach to 3D scanning in the presence of interreflections, subsurface scattering and defocus,” Int. J. Comput. Vis. 102(1–3), 33–55 (2013).
[Crossref]

Peers, P.

A. Ghosh, T. Chen, P. Peers, C.A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Trans. Graph. 30(6), 162 (2010).

Posdamer, J. L.

J. L. Posdamer and M. D. Altschuler, “Surface measurement by space-encoded projected beam systems,” Comput. Graph. Image Process. 18(1), 1–17 (1982).
[Crossref]

Pribanic, T.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Pugh, E. N.

Ramella-Roman, J. C.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7(3), 329–340 (2002).
[Crossref] [PubMed]

Raskar, R.

A. Kadambi, V. Taamazyan, B. Shi, and R. Raskar, “Polarized 3d: High-quality depth sensing with polarization cues,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE, 2015), pp. 3370–3378.
[Crossref]

Roberts, N. W.

T. M. Jordan, D. Wilby, T. H. Chiou, K. D. Feller, R. L. Caldwell, T. W. Cronin, and N. W. Roberts, “A shape-anisotropic reflective polarizer in a stomatopod crustacean,” Sci. Rep. 6, 21744 (2016).
[Crossref] [PubMed]

Rodriguez, J. J.

Rowe, M. P.

Salahieh, B.

Salvi, J.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Sato, K.

S. Inokuchi, K. Sato, and F. Matsuda, “Range imaging system for 3-D object recognition,” in Proceedings of the International Conference on Pattern Recognition, pp. 806–808 (1984).

Schechner, Y. Y.

E. Namer, S. Shwartz, and Y. Y. Schechner, “Skyless polarimetric calibration and visibility enhancement,” Opt. Express 17(2), 472–493 (2009).
[Crossref] [PubMed]

T. Treibitz and Y. Y. Schechner, “Polarization: Beneficial for visibility enhancement?” Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2009), pp. 525–532.

Y. Y. Schechner and N. Karpel, “Clear underwater vision,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2004), pp. I-536–I-546.

Seidel, H.

T. Chen, H. P. Lensch, C. Fuchs, and H. Seidel, “Polarization and phase-shifting for 3D scanning of translucent objects,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.
[Crossref]

Shamir, J.

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. 20(5), 470–480 (1998).
[Crossref]

Shaw, J. A.

Shi, B.

A. Kadambi, V. Taamazyan, B. Shi, and R. Raskar, “Polarized 3d: High-quality depth sensing with polarization cues,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE, 2015), pp. 3370–3378.
[Crossref]

Shwartz, S.

Sun, M.

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19(7), 076013 (2014).
[Crossref] [PubMed]

Taamazyan, V.

A. Kadambi, V. Taamazyan, B. Shi, and R. Raskar, “Polarized 3d: High-quality depth sensing with polarization cues,” in Proceedings of the IEEE International Conference on Computer Vision (IEEE, 2015), pp. 3370–3378.
[Crossref]

Treibitz, T.

T. Treibitz and Y. Y. Schechner, “Polarization: Beneficial for visibility enhancement?” Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2009), pp. 525–532.

Tunwattanapong, B.

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Trans. Graph. 30(6), 129 (2011).
[Crossref]

Tyo, J. S.

Veeraraghavan, A.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “A practical approach to 3D scanning in the presence of interreflections, subsurface scattering and defocus,” Int. J. Comput. Vis. 102(1–3), 33–55 (2013).
[Crossref]

Wilby, D.

T. M. Jordan, D. Wilby, T. H. Chiou, K. D. Feller, R. L. Caldwell, T. W. Cronin, and N. W. Roberts, “A shape-anisotropic reflective polarizer in a stomatopod crustacean,” Sci. Rep. 6, 21744 (2016).
[Crossref] [PubMed]

Wilson, C.A.

A. Ghosh, T. Chen, P. Peers, C.A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Trans. Graph. 30(6), 162 (2010).

Wolff, L. B.

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15(2), 81–93 (1997).
[Crossref]

Wu, J.

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19(7), 076013 (2014).
[Crossref] [PubMed]

Xu, Y.

Yu, X.

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Trans. Graph. 30(6), 129 (2011).
[Crossref]

Zeng, N.

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19(7), 076013 (2014).
[Crossref] [PubMed]

Zhang, S.

Y. Xu, L. Ekstrand, J. Dai, and S. Zhang, “Phase error compensation for three-dimensional shape measurement with projector defocusing,” Appl. Opt. 50(17), 2572–2581 (2011).
[Crossref] [PubMed]

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
[Crossref]

Zheng, Z. R.

ACM Trans. Graph. (2)

A. Ghosh, T. Chen, P. Peers, C.A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Trans. Graph. 30(6), 162 (2010).

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Trans. Graph. 30(6), 129 (2011).
[Crossref]

Appl. Opt. (3)

Comput. Graph. Image Process. (1)

J. L. Posdamer and M. D. Altschuler, “Surface measurement by space-encoded projected beam systems,” Comput. Graph. Image Process. 18(1), 1–17 (1982).
[Crossref]

IEEE Trans. Pattern Anal. (2)

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. 20(5), 470–480 (1998).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Gray code structured light patterns.
Fig. 2
Fig. 2 Polarization-coded structured light patterns.
Fig. 3
Fig. 3 Experimental scheme. The scale of the figure has been adapted to fit the page. The true distance between the projector and objects is around 1400mm and the baseline of projector-camera pair is 181mm. The projected pattern in this figure is an illustrative example for the polarization-coded structured light patterns.
Fig. 4
Fig. 4 Pattern-illuminated experimental scene (a) without polarizer (b) with polarizer. For comparability, reasonable exposure compensation is employed in the capture of (b) as thoroughly investigated in [30].
Fig. 5
Fig. 5 DOLP analysis of the scene. (a) The estimated DOLP by our method. (b) The measured DOLP by conventional method. (c) Cross-sections of DOLP results on the Line I, II and III as labeled in (a) and (b).
Fig. 6
Fig. 6 Visualization of the 3D point cloud of (a) the enhanced targets; (b) the enhanced laptop by high-pass DOLP filter; (c) the enhanced adhesive tape by band-pass DOLP filter. (d) Visualization of the 3D point cloud retrieved by conventional Gray code structured light.
Fig. 7
Fig. 7 Depth maps retrieved by different thresholds. Figures in upper line, (a) to (c), are corresponding to the polarization-coded structured light method, where the DOLP is taken as the threshold basis. Figures in lower line, (d) to (f), are corresponding to the conventional Gray code structured light method, where the IC is taken as the threshold basis.
Fig. 8
Fig. 8 Relationship between pattern contrast threshold and the evaluation factors for the target (a) laptop and (b) tape. Data of left bar are from polarization-coded structured light and data of right bar from Gray code structured light. The value on the top of entire bar is the target-scene ratioβ. The proportion that the darker bar occupies in the entire bar indicates the integrity ratioαof target, which is not decimally marked. Value of the merit factor γis labeled in the dark bar.
Fig. 9
Fig. 9 Depth curves of the main target by the polarization-coded structured light (Blue) and the Gray code structured light (Red).

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

IC= I pat I inv I pat + I inv ,
DOLP= I || I I || + I ,
S ||, = M P||, M O S in =( 0.5 ±0.5 0 0 ±0.5 0.5 0 0 0 0 0 0 0 0 0 0 )( m 11 m 12 m 13 m 14 m 21 m 22 m 23 m 24 m 31 m 32 m 33 m 34 m 41 m 42 m 43 m 44 )( 1 1 0 0 ) =0.5( ( m 11 + m 12 )±( m 21 + m 22 ) ±( m 11 + m 12 )+( m 21 + m 22 ) 0 0 ),
I || = S 0,|| = m 11 + m 12 + m 21 +m 22 ,
I = S 0, = m 11 + m 12 m 21 m 22 ,
DOLP= m 22 + m 21 m 11 + m 12 .
M O = 1 2 ( tan θ tan θ + ) 2 ( cos 2 θ + cos 2 θ + cos 2 θ cos 2 θ + 0 0 cos 2 θ cos 2 θ + cos 2 θ + cos 2 θ + 0 0 0 0 2cos θ + cos θ 0 0 0 0 2cos θ + cos θ )
DOLP= m 22 m 11 .
S (||,) = M P M O S in =( 0.5 0.5 0 0 0.5 0.5 0 0 0 0 0 0 0 0 0 0 )( m 11 m 12 m 13 m 14 m 21 m 22 m 23 m 24 m 31 m 32 m 33 m 34 m 41 m 42 m 43 m 44 )( 1 1 1 1 0 0 0 0 ) =0.5( m 11 + m 12 + m 21 + m 22 m 11 m 12 + m 21 m 22 m 11 + m 12 + m 21 + m 22 m 11 m 12 + m 21 m 22 0 0 0 0 ),
I || = S 0,|| = m 11 + m 12 + m 21 +m 22 ,
I = S 0, = m 11 m 12 + m 21 m 22 ,
I || I I || + I = m 22 + m 12 m 11 + m 21 m 22 m 11 DOLP.

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