Abstract

Circular polarization memory is a well-known phenomenon indicating that the circular polarization light can persist better its polarization property during propagating through turbid media compared with the linear polarization light. Therefore, in principle, using circularly polarized light can probably improve the quality of image recovery in dense turbid media than using the linearly polarized light. In this paper, we propose a new polarimetric image recovery method in dense turbid media with the illumination light of circular polarization, and we realize the image recovery combining the circular polarization information and linearly polarization information. The real-world experiment results demonstrate that the proposed method is more effective than previous methods, including the traditional polarimetric image recovery method by Schechner’s [Appl. Opt. 42, 511 (2003)] based on linear polarization.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  24. H. Hu, L. Zhao, B. Huang, X. Li, H. Wang, and T. Liu, “Enhancing Visibility of Polarimetric Underwater Image by Transmittance Correction,” IEEE Photonics J. 9(3), 1–10 (2017).
  25. Q. Xu, Z. Guo, Q. Tao, W. Jiao, X. Wang, S. Qu, and J. Gao, “Transmitting characteristics of polarization information under seawater,” Appl. Opt. 54(21), 6584–6588 (2015).
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    [Crossref]
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2017 (4)

M. R. Elsayed, Y. Zhao, and J. C. W. Chan, “Polarization Guided Auto-Regressive Model for Depth Recovery,” IEEE Photonics J. 9(3), 1–16 (2017).
[Crossref]

M. Yu, H. Huang, H. Hu, L. Wu, H. Zhai, and T. Liu, “Colorimetric discrimination for Stokes polarimetric imaging,” Opt. Express 25(4), 3765–3773 (2017).
[Crossref] [PubMed]

X. Li, H. Hu, L. Wu, and T. Liu, “Optimization of instrument matrix for Mueller matrix ellipsometry based on partial elements analysis of the Mueller matrix,” Opt. Express 25(16), 18872–18884 (2017).
[Crossref] [PubMed]

H. Hu, L. Zhao, B. Huang, X. Li, H. Wang, and T. Liu, “Enhancing Visibility of Polarimetric Underwater Image by Transmittance Correction,” IEEE Photonics J. 9(3), 1–10 (2017).

2016 (2)

B. Huang, T. Liu, H. Hu, J. Han, and M. Yu, “Underwater image recovery considering polarization effects of objects,” Opt. Express 24(9), 9826–9838 (2016).
[Crossref] [PubMed]

M. Yu, T. Liu, H. Huang, H. Hu, and B. Huang, “Multispectral Stokes Imaging Polarimetry Based on Color CCD,” IEEE Photonics J. 8(5), 1–10 (2016).

2015 (6)

2014 (4)

2013 (1)

2012 (4)

M. Ozaki, K. Kakimuma, M. Hashimoto, and K. Takahashi, “Laser-based pedestrian tracking in outdoor environments by multiple mobile robots,” Sensors (Basel) 12(11), 14489–14507 (2012).
[Crossref] [PubMed]

N. Liu, Y. M. Cheng, and Y. Q. Zhao, “An Image Dehazing Method Based on Weighted Dark Channel Prior,” Guangzi Xuebao 41(3), 320–325 (2012).
[Crossref]

W. Hou, S. Woods, E. Jarosz, W. Goode, and A. Weidemann, “Optical turbulence on underwater image degradation in natural environments,” Appl. Opt. 51(14), 2678–2686 (2012).
[PubMed]

S. Tao, H. Feng, Z. Xu, and Q. Li, “Image degradation and recovery based on multiple scattering in remote sensing and bad weather condition,” Opt. Express 20(15), 16584–16595 (2012).
[Crossref]

2011 (1)

K. He, J. Sun, and X. Tang, “Single image haze removal using dark channel prior,” IEEE Trans. Pattern Anal. Mach. Intell. 33(12), 2341–2353 (2011).
[Crossref] [PubMed]

2009 (1)

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
[Crossref] [PubMed]

2008 (1)

G. N. Bailey and N. C. Flemming, “Archaeology of the continental shelf: marine resources, submerged landscapes and underwater archaeology,” Quat. Sci. Rev. 27(23), 2153–2165 (2008).
[Crossref]

2005 (1)

S. Sabbah, A. Lerner, C. Erlick, and N. Shashar, “Under water polarization vision—a physical examination,” Recent Res. Dev. Exp. Theor. Biol. 1, 123–176 (2005).

2004 (2)

X. Ni and R. R. Alfano, “Time-resolved backscattering of circularly and linearly polarized light in a turbid medium,” Opt. Lett. 29(23), 2773–2775 (2004).
[Crossref] [PubMed]

S. S. Agaian, K. Panetta, and A. M. Grigoryan, “Transform-based image enhancement algorithms with performance measure,” IEEE Trans. Image Process. 130(3), 165–242 (2004).
[PubMed]

2003 (1)

2000 (1)

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE 4133, 202–213 (2000).
[Crossref]

1999 (1)

S. Winkler, “Issues in vision modeling for perceptual video quality assessment,” Signal Process. 78(2), 231–252 (1999).
[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)

1990 (1)

J. Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE J. Oceanic Eng. 15(2), 101–111 (1990).
[Crossref]

1989 (1)

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B Condens. Matter 40(13), 9342–9345 (1989).
[Crossref] [PubMed]

Agaian, S. S.

S. S. Agaian, K. Panetta, and A. M. Grigoryan, “Transform-based image enhancement algorithms with performance measure,” IEEE Trans. Image Process. 130(3), 165–242 (2004).
[PubMed]

Alfano, R. R.

Alouini, M.

S. Panigrahi, J. Fade, and M. Alouini, “Adaptive polarimetric image representation for contrast optimization of a polarized beacon through fog,” J. Opt. 17(6), 065703 (2015).
[Crossref]

J. Fade, S. Panigrahi, A. Carré, L. Frein, C. Hamel, F. Bretenaker, H. Ramachandran, and M. Alouini, “Long-range polarimetric imaging through fog,” Appl. Opt. 53(18), 3854–3865 (2014).
[Crossref] [PubMed]

Asemani, D.

E. Kermani and D. Asemani, “A robust adaptive method of moving object detection for video surveillance,” EURASIP J. Image Video Process. 2014(1), 27 (2014).
[Crossref]

Bailey, G. N.

G. N. Bailey and N. C. Flemming, “Archaeology of the continental shelf: marine resources, submerged landscapes and underwater archaeology,” Quat. Sci. Rev. 27(23), 2153–2165 (2008).
[Crossref]

Bin, X.

Blumer, R. V.

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE 4133, 202–213 (2000).
[Crossref]

Bretenaker, F.

Cao, L.

Carré, A.

Chan, J. C. W.

M. R. Elsayed, Y. Zhao, and J. C. W. Chan, “Polarization Guided Auto-Regressive Model for Depth Recovery,” IEEE Photonics J. 9(3), 1–16 (2017).
[Crossref]

Chen, C.

Cheng, Y. M.

N. Liu, Y. M. Cheng, and Y. Q. Zhao, “An Image Dehazing Method Based on Weighted Dark Channel Prior,” Guangzi Xuebao 41(3), 320–325 (2012).
[Crossref]

Dereniak, E. L.

Elsayed, M. R.

M. R. Elsayed, Y. Zhao, and J. C. W. Chan, “Polarization Guided Auto-Regressive Model for Depth Recovery,” IEEE Photonics J. 9(3), 1–16 (2017).
[Crossref]

Engheta, N.

Erlick, C.

S. Sabbah, A. Lerner, C. Erlick, and N. Shashar, “Under water polarization vision—a physical examination,” Recent Res. Dev. Exp. Theor. Biol. 1, 123–176 (2005).

Fade, J.

S. Panigrahi, J. Fade, and M. Alouini, “Adaptive polarimetric image representation for contrast optimization of a polarized beacon through fog,” J. Opt. 17(6), 065703 (2015).
[Crossref]

J. Fade, S. Panigrahi, A. Carré, L. Frein, C. Hamel, F. Bretenaker, H. Ramachandran, and M. Alouini, “Long-range polarimetric imaging through fog,” Appl. Opt. 53(18), 3854–3865 (2014).
[Crossref] [PubMed]

Fang, S.

Feng, H.

Flemming, N. C.

G. N. Bailey and N. C. Flemming, “Archaeology of the continental shelf: marine resources, submerged landscapes and underwater archaeology,” Quat. Sci. Rev. 27(23), 2153–2165 (2008).
[Crossref]

Frein, L.

Gao, J.

Q. Xu, Z. Guo, Q. Tao, W. Jiao, X. Wang, S. Qu, and J. Gao, “Transmitting characteristics of polarization information under seawater,” Appl. Opt. 54(21), 6584–6588 (2015).
[Crossref] [PubMed]

Q. Xu, Z. Guo, Q. Tao, W. Jiao, S. Qu, and J. Gao, “A novel method of retrieving the polarization qubits after being transmitted in turbid media,” J. Opt. 17(3), 035606 (2015).
[Crossref]

Goode, W.

Grigoryan, A. M.

S. S. Agaian, K. Panetta, and A. M. Grigoryan, “Transform-based image enhancement algorithms with performance measure,” IEEE Trans. Image Process. 130(3), 165–242 (2004).
[PubMed]

Guan, J.

Guo, Z.

Q. Xu, Z. Guo, Q. Tao, W. Jiao, X. Wang, S. Qu, and J. Gao, “Transmitting characteristics of polarization information under seawater,” Appl. Opt. 54(21), 6584–6588 (2015).
[Crossref] [PubMed]

Q. Xu, Z. Guo, Q. Tao, W. Jiao, S. Qu, and J. Gao, “A novel method of retrieving the polarization qubits after being transmitted in turbid media,” J. Opt. 17(3), 035606 (2015).
[Crossref]

Hamel, C.

Han, J.

Han, P.

Hashimoto, M.

M. Ozaki, K. Kakimuma, M. Hashimoto, and K. Takahashi, “Laser-based pedestrian tracking in outdoor environments by multiple mobile robots,” Sensors (Basel) 12(11), 14489–14507 (2012).
[Crossref] [PubMed]

He, K.

K. He, J. Sun, and X. Tang, “Single image haze removal using dark channel prior,” IEEE Trans. Pattern Anal. Mach. Intell. 33(12), 2341–2353 (2011).
[Crossref] [PubMed]

Hou, W.

Howe, J. D.

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE 4133, 202–213 (2000).
[Crossref]

Hu, B.

Hu, H.

Huang, B.

H. Hu, L. Zhao, B. Huang, X. Li, H. Wang, and T. Liu, “Enhancing Visibility of Polarimetric Underwater Image by Transmittance Correction,” IEEE Photonics J. 9(3), 1–10 (2017).

M. Yu, T. Liu, H. Huang, H. Hu, and B. Huang, “Multispectral Stokes Imaging Polarimetry Based on Color CCD,” IEEE Photonics J. 8(5), 1–10 (2016).

B. Huang, T. Liu, H. Hu, J. Han, and M. Yu, “Underwater image recovery considering polarization effects of objects,” Opt. Express 24(9), 9826–9838 (2016).
[Crossref] [PubMed]

Huang, H.

M. Yu, H. Huang, H. Hu, L. Wu, H. Zhai, and T. Liu, “Colorimetric discrimination for Stokes polarimetric imaging,” Opt. Express 25(4), 3765–3773 (2017).
[Crossref] [PubMed]

M. Yu, T. Liu, H. Huang, H. Hu, and B. Huang, “Multispectral Stokes Imaging Polarimetry Based on Color CCD,” IEEE Photonics J. 8(5), 1–10 (2016).

Jaffe, J.

J. Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE J. Oceanic Eng. 15(2), 101–111 (1990).
[Crossref]

Jarosz, E.

Jiao, W.

Q. Xu, Z. Guo, Q. Tao, W. Jiao, X. Wang, S. Qu, and J. Gao, “Transmitting characteristics of polarization information under seawater,” Appl. Opt. 54(21), 6584–6588 (2015).
[Crossref] [PubMed]

Q. Xu, Z. Guo, Q. Tao, W. Jiao, S. Qu, and J. Gao, “A novel method of retrieving the polarization qubits after being transmitted in turbid media,” J. Opt. 17(3), 035606 (2015).
[Crossref]

Ju, H.

Kakimuma, K.

M. Ozaki, K. Kakimuma, M. Hashimoto, and K. Takahashi, “Laser-based pedestrian tracking in outdoor environments by multiple mobile robots,” Sensors (Basel) 12(11), 14489–14507 (2012).
[Crossref] [PubMed]

Kemme, S. A.

Kermani, E.

E. Kermani and D. Asemani, “A robust adaptive method of moving object detection for video surveillance,” EURASIP J. Image Video Process. 2014(1), 27 (2014).
[Crossref]

Lerner, A.

S. Sabbah, A. Lerner, C. Erlick, and N. Shashar, “Under water polarization vision—a physical examination,” Recent Res. Dev. Exp. Theor. Biol. 1, 123–176 (2005).

Li, Q.

Li, X.

X. Li, H. Hu, L. Wu, and T. Liu, “Optimization of instrument matrix for Mueller matrix ellipsometry based on partial elements analysis of the Mueller matrix,” Opt. Express 25(16), 18872–18884 (2017).
[Crossref] [PubMed]

H. Hu, L. Zhao, B. Huang, X. Li, H. Wang, and T. Liu, “Enhancing Visibility of Polarimetric Underwater Image by Transmittance Correction,” IEEE Photonics J. 9(3), 1–10 (2017).

Liang, J.

Liu, F.

Liu, N.

N. Liu, Y. M. Cheng, and Y. Q. Zhao, “An Image Dehazing Method Based on Weighted Dark Channel Prior,” Guangzi Xuebao 41(3), 320–325 (2012).
[Crossref]

Liu, T.

MacKintosh, F. C.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B Condens. Matter 40(13), 9342–9345 (1989).
[Crossref] [PubMed]

Miller, M. A.

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE 4133, 202–213 (2000).
[Crossref]

Narasimhan, S. G.

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Polarization-based vision through haze,” Appl. Opt. 42(3), 511–525 (2003).
[Crossref] [PubMed]

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Instant Dehazing of Images Using Polarization,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition1, 325–332 (2001).

Nayar, S. K.

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Polarization-based vision through haze,” Appl. Opt. 42(3), 511–525 (2003).
[Crossref] [PubMed]

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Instant Dehazing of Images Using Polarization,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition1, 325–332 (2001).

Ni, X.

Ozaki, M.

M. Ozaki, K. Kakimuma, M. Hashimoto, and K. Takahashi, “Laser-based pedestrian tracking in outdoor environments by multiple mobile robots,” Sensors (Basel) 12(11), 14489–14507 (2012).
[Crossref] [PubMed]

Panetta, K.

S. S. Agaian, K. Panetta, and A. M. Grigoryan, “Transform-based image enhancement algorithms with performance measure,” IEEE Trans. Image Process. 130(3), 165–242 (2004).
[PubMed]

Panigrahi, S.

S. Panigrahi, J. Fade, and M. Alouini, “Adaptive polarimetric image representation for contrast optimization of a polarized beacon through fog,” J. Opt. 17(6), 065703 (2015).
[Crossref]

J. Fade, S. Panigrahi, A. Carré, L. Frein, C. Hamel, F. Bretenaker, H. Ramachandran, and M. Alouini, “Long-range polarimetric imaging through fog,” Appl. Opt. 53(18), 3854–3865 (2014).
[Crossref] [PubMed]

Petty, T. E.

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE 4133, 202–213 (2000).
[Crossref]

Pine, D. J.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B Condens. Matter 40(13), 9342–9345 (1989).
[Crossref] [PubMed]

Pugh, E. N.

Qu, E.

Qu, S.

Q. Xu, Z. Guo, Q. Tao, W. Jiao, X. Wang, S. Qu, and J. Gao, “Transmitting characteristics of polarization information under seawater,” Appl. Opt. 54(21), 6584–6588 (2015).
[Crossref] [PubMed]

Q. Xu, Z. Guo, Q. Tao, W. Jiao, S. Qu, and J. Gao, “A novel method of retrieving the polarization qubits after being transmitted in turbid media,” J. Opt. 17(3), 035606 (2015).
[Crossref]

Ramachandran, H.

Ren, L.

Rowe, M. P.

Sabbah, S.

S. Sabbah, A. Lerner, C. Erlick, and N. Shashar, “Under water polarization vision—a physical examination,” Recent Res. Dev. Exp. Theor. Biol. 1, 123–176 (2005).

Schechner, Y. Y.

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
[Crossref] [PubMed]

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Polarization-based vision through haze,” Appl. Opt. 42(3), 511–525 (2003).
[Crossref] [PubMed]

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Instant Dehazing of Images Using Polarization,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition1, 325–332 (2001).

Scrymgeour, D. A.

Shao, X.

Shashar, N.

S. Sabbah, A. Lerner, C. Erlick, and N. Shashar, “Under water polarization vision—a physical examination,” Recent Res. Dev. Exp. Theor. Biol. 1, 123–176 (2005).

Smith, M. H.

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE 4133, 202–213 (2000).
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Stevens, M. A.

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE 4133, 202–213 (2000).
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Takahashi, K.

M. Ozaki, K. Kakimuma, M. Hashimoto, and K. Takahashi, “Laser-based pedestrian tracking in outdoor environments by multiple mobile robots,” Sensors (Basel) 12(11), 14489–14507 (2012).
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K. He, J. Sun, and X. Tang, “Single image haze removal using dark channel prior,” IEEE Trans. Pattern Anal. Mach. Intell. 33(12), 2341–2353 (2011).
[Crossref] [PubMed]

Tao, Q.

Q. Xu, Z. Guo, Q. Tao, W. Jiao, S. Qu, and J. Gao, “A novel method of retrieving the polarization qubits after being transmitted in turbid media,” J. Opt. 17(3), 035606 (2015).
[Crossref]

Q. Xu, Z. Guo, Q. Tao, W. Jiao, X. Wang, S. Qu, and J. Gao, “Transmitting characteristics of polarization information under seawater,” Appl. Opt. 54(21), 6584–6588 (2015).
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Tao, S.

Teale, D. M.

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE 4133, 202–213 (2000).
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T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
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van der Laan, J. D.

Wang, H.

H. Hu, L. Zhao, B. Huang, X. Li, H. Wang, and T. Liu, “Enhancing Visibility of Polarimetric Underwater Image by Transmittance Correction,” IEEE Photonics J. 9(3), 1–10 (2017).

Wang, X.

Wang, Y.

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S. Winkler, “Issues in vision modeling for perceptual video quality assessment,” Signal Process. 78(2), 231–252 (1999).
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L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vis. Comput. 15(2), 81–93 (1997).
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Q. Xu, Z. Guo, Q. Tao, W. Jiao, S. Qu, and J. Gao, “A novel method of retrieving the polarization qubits after being transmitted in turbid media,” J. Opt. 17(3), 035606 (2015).
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Xu, Z.

Yu, M.

Zhai, H.

Zhang, W.

Zhao, L.

H. Hu, L. Zhao, B. Huang, X. Li, H. Wang, and T. Liu, “Enhancing Visibility of Polarimetric Underwater Image by Transmittance Correction,” IEEE Photonics J. 9(3), 1–10 (2017).

Zhao, Y.

M. R. Elsayed, Y. Zhao, and J. C. W. Chan, “Polarization Guided Auto-Regressive Model for Depth Recovery,” IEEE Photonics J. 9(3), 1–16 (2017).
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T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
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Photon. Res. (1)

Phys. Rev. B Condens. Matter (1)

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B Condens. Matter 40(13), 9342–9345 (1989).
[Crossref] [PubMed]

Proc. SPIE (1)

J. D. Howe, M. A. Miller, R. V. Blumer, T. E. Petty, M. A. Stevens, D. M. Teale, and M. H. Smith, “Polarization sensing for target acquisition and mine detection,” Proc. SPIE 4133, 202–213 (2000).
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S. Sabbah, A. Lerner, C. Erlick, and N. Shashar, “Under water polarization vision—a physical examination,” Recent Res. Dev. Exp. Theor. Biol. 1, 123–176 (2005).

Sensors (Basel) (1)

M. Ozaki, K. Kakimuma, M. Hashimoto, and K. Takahashi, “Laser-based pedestrian tracking in outdoor environments by multiple mobile robots,” Sensors (Basel) 12(11), 14489–14507 (2012).
[Crossref] [PubMed]

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Figures (8)

Fig. 1
Fig. 1 The flowchart of the polarimetric image recovery method in turbid media combining circularly polarized light and linearly polarized light.

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Fig. 2
Fig. 2 (a) Experimental setup for underwater imaging. (b) Intensity image in clear water.

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Fig. 3
Fig. 3 (a)-(d) are the images taken with the specific orientations of the linear polarizer and the quarter-wave retarder.

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Fig. 4
Fig. 4 (a) Intensity image of the scene, and (b) the degree of linear polarization p l _ s c a t ( x , y ) , (c) the degree of circular polarization p c _ s c a t ( x , y ) .

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Fig. 5
Fig. 5 (a) The intensity image of the scene in the turbid water. (b) Recovered image by our method. (c) Recovered image by the traditional polarimetric dehazing method in [13].

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Fig. 6
Fig. 6 (a) The intensity images of the scene in turbid water with different densities of milk. (b) Recovered images by the traditional polarimetric dehazing method in [13]. (c) Recovered images by our method.

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Fig. 7
Fig. 7 Enlarged views of details with different densities of milk marked in Fig. 5(a). The images of low density correspond to Fig. 5.

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Fig. 8
Fig. 8 (a) The intensity image of the wooden board in clear water. (b) The intensity image of the wooden boards in the turbid water. (c) Recovered image by our method. (d) Recovered image by Schechner’s method. (e) Recovered image by PDI method. (f) Recovered image by Liang’s method. (g) The intensity image of the non-flat plastic toy in clear water. (h) The intensity image of the non-flat plastic toy in the turbid water. (i) Recovered image by our method. (j) Recovered image by Schechner’s method. (k) Recovered image by PDI method. (l) Recovered image by Liang’s method.

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Tables (1)

Tables Icon

Table 1 The contrast of targets in Fig. 7.

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Equations (16)

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I ( x , y ) = D ( x , y ) + B ( x , y ) = L ( x , y ) t ( x , y ) + A ∞ ( 1 − t ( x , y ) ) ,
I | | ( x , y ) = D ( x , y ) 2 + B | | ( x , y ) , I ⊥ ( x , y ) = D ( x , y ) 2 + B ⊥ ( x , y ) .
t ( x , y ) = 1 − B ( x , y ) A ∞ = 1 − I | | ( x , y ) − I ⊥ ( x , y ) p s c a t A ∞ , L ( x , y ) = I ( x , y ) − B ( x , y ) t ( x , y ) = I | | ( x , y ) + I ⊥ ( x , y ) − B ( x , y ) t ( x , y ) ,
s 0 o = L ( x , y ) t ( x , y )   ,
s 0 b = A ∞ [ 1 − t ( x , y ) ]   .
S = S o + S b = [ s 0 o s 1 o s 2 o s 3 o ] + [ s 0 b s 1 b s 2 b s 3 b ]   ,
S = S l - p o l a r i z e d + S c - p o l a r i z e d + S u n p o l a r i z e d           = [ s 1 2 + s 2 2 s 1 s 2 0 ] + [ s 3 0 0 s 3 ]   + [ s 0 − s 1 2 + s 2 2 − s 3 0 0 0 ] ,
p l = s 1 2 + s 2 2 s 0   ,       p c = s 3 s 0   .
A ∞ = 1 | Ω | ∑ ( x , y ) ∈ Ω s 0 ( x , y )   ,
p l _ s c a t = 1 | Ω | ∑ ( x , y ) ∈ Ω [ [ s 1 ( x , y ) ] 2 + [ s 2 ( x , y ) ] 2 s 0 ( x , y ) ]   ,
s 0 _ l b ( x , y ) = [ s 1 b ( x , y ) ] 2 + [ s 2 b ( x , y ) ] 2 ε l p l _ s c a t = s 1 2 ( x , y ) + s 2 2 ( x , y ) ε l p l _ s c a t   .
  t l ( x , y ) = 1 − s 1 2 ( x , y ) + s 2 2 ( x , y ) ε l p l _ s c a t A ∞ , L l ( x , y ) = s 0 ( x , y ) − A ∞ [ 1 − t l ( x , y ) ] t l ( x , y ) .
A ∞ = 1 | Ω | ∑ ( x , y ) ∈ Ω L l ( x , y )   ,
p c _ s c a t = 1 | Ω | ∑ ( x , y ) ∈ Ω [ s 3 ( x , y ) L l ( x , y ) ]   ,
s 0 _ c b ( x , y ) = s 3 b ( x , y ) ε c p c _ s c a t = s 3 ( x , y ) ε c p c _ s c a t .
t c ( x , y ) = 1 − s 3 ε c p c _ s c a t A ∞ , L c ( x , y ) = L l ( x , y ) − A ∞ [ 1 − t c ( x , y ) ] t c ( x , y ) .

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