Abstract

Underwater optical image simulation is a valuable tool for oceanic science, especially for the characterization of image processing techniques such as color restoration. In this context, simulating images with a correct color rendering is crucial. This paper presents an extension of existing image simulation models to RGB imaging. The influence of the spectral discretization of the model parameters on the color rendering of the simulated images is studied. It is especially shown that, if only RGB data of the scene chosen for simulations are available, a spectral reconstruction step prior to the simulations improves the image color rendering.

© 2012 Optical Society of America

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    [CrossRef]
  13. T. Treibitz and Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Machine Intell. 31, 385–399(2009).
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    [CrossRef]
  15. J. Ahlén, E. Bengtsson, and D. Sundgren, “Evaluation of underwater spectral data for colour correction applications,” in Proceedings of the 5th WSEAS International Conference on Circuits, Systems, Electronics, Control & Signal Processing (World Scientific and Engineering Academy and Society, 2006), pp. 321–326.
  16. M. Chambah, D. Semani, A. Renouf, P. Courtellemont, and A. Rizzi, “Underwater color constancy: enhancement of automatic live fish recognition,” Proc. SPIE 5293, 157–168 (2003).
  17. K. Iqbal, R. Abdul Salam, M. Osman, and A. Talib, “Underwater image enhancement using an integrated colour model,” IAENG Int. J. Comput. Sci. 34, 239–244 (2007).
  18. F. Petit, A.-S. Capelle-Laize, and P. Carre, “Underwater image enhancement by attenuation inversion with quaternions,” in IEEE International Conference on Acoustics Speech and Signal Processing (IEEE, 2009), pp. 1177–1180.
  19. L. Torres-Méndez and G. Dudek, “Color correction of underwater images for aquatic robot inspection,” in Energy Minimization Methods in Computer Vision and Pattern Recognition (Springer, 2005), pp. 60–73.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  29. E. Valero, J. Nieves, S. Nascimento, K. Amano, and D. Foster, “Recovering spectral data from natural scenes with an RGB digital camera and colored filters,” Color Res. Appl. 32, 352–360 (2007).
    [CrossRef]
  30. R. Clark, G. Swayze, R. Wise, E. Livo, T. Hoefen, R. Kokaly, and S. Sutley, “USGS digital spectral library splib06a; U.S. Geological Survey, Digital Data Series 231, http://speclab.cr.usgs.gov/spectral.lib06 ” (2007).
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    [CrossRef]
  35. Y. C. Agrawal, “The optical volume scattering function: temporal and vertical variability in the water column off the New Jersey coast,” Liminology and Oceanography 50, 1787–1794 (2005).

2010 (1)

R. Schettini and S. Corchs, “Underwater image processing: state of the art of restoration and image enhancement methods,” EURASIP J. Adv. Sig. Proc. 2010 (2010).

2009 (1)

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

2008 (2)

W. Hou, D. Gray, A. Weidemann, and R. Arnone, “Comparison and validation of point spread models for imaging in natural waters,” Opt. Express 16, 9958–9965 (2008).
[CrossRef]

D. Kocak, F. Dalgleish, and F. Caimi, “A focus on recent developments and trends in underwater imaging,” Marine Technology 42, 52–67 (2008).
[CrossRef]

2007 (3)

K. Iqbal, R. Abdul Salam, M. Osman, and A. Talib, “Underwater image enhancement using an integrated colour model,” IAENG Int. J. Comput. Sci. 34, 239–244 (2007).

J. Ahlén, D. Sundgren, and E. Bengtsson, “Application of underwater hyperspectral data for color correction purposes,” Pattern Recog. Image Anal. 17, 170–173 (2007).
[CrossRef]

E. Valero, J. Nieves, S. Nascimento, K. Amano, and D. Foster, “Recovering spectral data from natural scenes with an RGB digital camera and colored filters,” Color Res. Appl. 32, 352–360 (2007).
[CrossRef]

2006 (1)

E. Trucco and A. Olmos-Antillon, “Self-tuning underwater image restoration,” IEEE J. Ocean. Eng. 31, 511–519 (2006).
[CrossRef]

2005 (2)

Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Ocean. Eng. 30, 570–587 (2005).
[CrossRef]

Y. C. Agrawal, “The optical volume scattering function: temporal and vertical variability in the water column off the New Jersey coast,” Liminology and Oceanography 50, 1787–1794 (2005).

2003 (2)

M. E. Lee and R. L. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571 (2003).
[CrossRef]

M. Chambah, D. Semani, A. Renouf, P. Courtellemont, and A. Rizzi, “Underwater color constancy: enhancement of automatic live fish recognition,” Proc. SPIE 5293, 157–168 (2003).

2002 (1)

J. Chowdhary, B. Cairns, and L. D. Travis, “Case studies of aerosol retrievals over the ocean from multiangle, multispectral photopolarimetric remote sensing data,” J. Atmos. Sci. 59, 383–397 (2002).
[CrossRef]

2001 (1)

J. Jaffe, J. Mclean, M. Strand, and K. Moore, “Underwater optical imaging: status and prospects,” Oceanography 14, 64–75 (2001).

2000 (1)

1993 (1)

1990 (1)

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

1987 (1)

A. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Anal. Machine Intell. 9, 523–531 (1987).
[CrossRef]

1979 (1)

B. McGlamery, “A computer model for underwater camera systems,” Proc. SPIE 0208, 221–231 (1979).

1977 (1)

1976 (1)

1973 (1)

W. Wells, “Theory of small angle scattering,” AGARD Conf. Proc. 81, 1–20 (1973).

Abdul Salam, R.

K. Iqbal, R. Abdul Salam, M. Osman, and A. Talib, “Underwater image enhancement using an integrated colour model,” IAENG Int. J. Comput. Sci. 34, 239–244 (2007).

Agrawal, Y. C.

Y. C. Agrawal, “The optical volume scattering function: temporal and vertical variability in the water column off the New Jersey coast,” Liminology and Oceanography 50, 1787–1794 (2005).

Ahlén, J.

J. Ahlén, D. Sundgren, and E. Bengtsson, “Application of underwater hyperspectral data for color correction purposes,” Pattern Recog. Image Anal. 17, 170–173 (2007).
[CrossRef]

J. Ahlén, E. Bengtsson, and D. Sundgren, “Evaluation of underwater spectral data for colour correction applications,” in Proceedings of the 5th WSEAS International Conference on Circuits, Systems, Electronics, Control & Signal Processing (World Scientific and Engineering Academy and Society, 2006), pp. 321–326.

Amano, K.

E. Valero, J. Nieves, S. Nascimento, K. Amano, and D. Foster, “Recovering spectral data from natural scenes with an RGB digital camera and colored filters,” Color Res. Appl. 32, 352–360 (2007).
[CrossRef]

Arnone, R.

Bazeille, S.

S. Bazeille, I. Quidu, L. Jaulin, and J.-P. Malkasse, “Automatic underwater image preprocessing,” presented at CMM06, Brest, France, 16–19 October 2006).

Bengtsson, E.

J. Ahlén, D. Sundgren, and E. Bengtsson, “Application of underwater hyperspectral data for color correction purposes,” Pattern Recog. Image Anal. 17, 170–173 (2007).
[CrossRef]

J. Ahlén, E. Bengtsson, and D. Sundgren, “Evaluation of underwater spectral data for colour correction applications,” in Proceedings of the 5th WSEAS International Conference on Circuits, Systems, Electronics, Control & Signal Processing (World Scientific and Engineering Academy and Society, 2006), pp. 321–326.

Caimi, F.

D. Kocak, F. Dalgleish, and F. Caimi, “A focus on recent developments and trends in underwater imaging,” Marine Technology 42, 52–67 (2008).
[CrossRef]

Cairns, B.

J. Chowdhary, B. Cairns, and L. D. Travis, “Case studies of aerosol retrievals over the ocean from multiangle, multispectral photopolarimetric remote sensing data,” J. Atmos. Sci. 59, 383–397 (2002).
[CrossRef]

Capelle-Laize, A.-S.

F. Petit, A.-S. Capelle-Laize, and P. Carre, “Underwater image enhancement by attenuation inversion with quaternions,” in IEEE International Conference on Acoustics Speech and Signal Processing (IEEE, 2009), pp. 1177–1180.

Carre, P.

F. Petit, A.-S. Capelle-Laize, and P. Carre, “Underwater image enhancement by attenuation inversion with quaternions,” in IEEE International Conference on Acoustics Speech and Signal Processing (IEEE, 2009), pp. 1177–1180.

Chambah, M.

M. Chambah, D. Semani, A. Renouf, P. Courtellemont, and A. Rizzi, “Underwater color constancy: enhancement of automatic live fish recognition,” Proc. SPIE 5293, 157–168 (2003).

Chowdhary, J.

J. Chowdhary, B. Cairns, and L. D. Travis, “Case studies of aerosol retrievals over the ocean from multiangle, multispectral photopolarimetric remote sensing data,” J. Atmos. Sci. 59, 383–397 (2002).
[CrossRef]

Clark, R.

R. Clark, G. Swayze, R. Wise, E. Livo, T. Hoefen, R. Kokaly, and S. Sutley, “USGS digital spectral library splib06a; U.S. Geological Survey, Digital Data Series 231, http://speclab.cr.usgs.gov/spectral.lib06 ” (2007).

Corchs, S.

R. Schettini and S. Corchs, “Underwater image processing: state of the art of restoration and image enhancement methods,” EURASIP J. Adv. Sig. Proc. 2010 (2010).

Courtellemont, P.

M. Chambah, D. Semani, A. Renouf, P. Courtellemont, and A. Rizzi, “Underwater color constancy: enhancement of automatic live fish recognition,” Proc. SPIE 5293, 157–168 (2003).

Dalgleish, F.

D. Kocak, F. Dalgleish, and F. Caimi, “A focus on recent developments and trends in underwater imaging,” Marine Technology 42, 52–67 (2008).
[CrossRef]

Dudek, G.

L. Torres-Méndez and G. Dudek, “Color correction of underwater images for aquatic robot inspection,” in Energy Minimization Methods in Computer Vision and Pattern Recognition (Springer, 2005), pp. 60–73.

Duntley, S.

S. Duntley, “Underwater lighting by submerged lasers and incandescent sources,” Tech. Rep. (Scripps. Inst. of Oceanography, 1971).

Foster, D.

E. Valero, J. Nieves, S. Nascimento, K. Amano, and D. Foster, “Recovering spectral data from natural scenes with an RGB digital camera and colored filters,” Color Res. Appl. 32, 352–360 (2007).
[CrossRef]

Gentili, B.

Gordon, H. R.

Gray, D.

Han, X.

S. Negahdaripour, H. Zhang, and X. Han, “Investigation of photometric stereo method for 3-d shape recovery from underwater imagery,” in MTS/IEEE Oceans (Marine Technol. Soc, 2002), pp. 1010–1017.

Hoefen, T.

R. Clark, G. Swayze, R. Wise, E. Livo, T. Hoefen, R. Kokaly, and S. Sutley, “USGS digital spectral library splib06a; U.S. Geological Survey, Digital Data Series 231, http://speclab.cr.usgs.gov/spectral.lib06 ” (2007).

Holst, G. C.

G. C. Holst and T. S. Lomheim, CMOS/CCD Sensors and Camera Systems (SPIE, 2007).

Hou, W.

Iqbal, K.

K. Iqbal, R. Abdul Salam, M. Osman, and A. Talib, “Underwater image enhancement using an integrated colour model,” IAENG Int. J. Comput. Sci. 34, 239–244 (2007).

Jaffe, J.

J. Jaffe, J. Mclean, M. Strand, and K. Moore, “Underwater optical imaging: status and prospects,” Oceanography 14, 64–75 (2001).

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

Jaulin, L.

S. Bazeille, I. Quidu, L. Jaulin, and J.-P. Malkasse, “Automatic underwater image preprocessing,” presented at CMM06, Brest, France, 16–19 October 2006).

Jin, Z.

Karpel, N.

Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Ocean. Eng. 30, 570–587 (2005).
[CrossRef]

Kattawar, G. W.

Kocak, D.

D. Kocak, F. Dalgleish, and F. Caimi, “A focus on recent developments and trends in underwater imaging,” Marine Technology 42, 52–67 (2008).
[CrossRef]

Kokaly, R.

R. Clark, G. Swayze, R. Wise, E. Livo, T. Hoefen, R. Kokaly, and S. Sutley, “USGS digital spectral library splib06a; U.S. Geological Survey, Digital Data Series 231, http://speclab.cr.usgs.gov/spectral.lib06 ” (2007).

Lee, M. E.

M. E. Lee and R. L. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571 (2003).
[CrossRef]

Lewis, R. L.

M. E. Lee and R. L. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571 (2003).
[CrossRef]

Livo, E.

R. Clark, G. Swayze, R. Wise, E. Livo, T. Hoefen, R. Kokaly, and S. Sutley, “USGS digital spectral library splib06a; U.S. Geological Survey, Digital Data Series 231, http://speclab.cr.usgs.gov/spectral.lib06 ” (2007).

Loisel, H.

Lomheim, T. S.

G. C. Holst and T. S. Lomheim, CMOS/CCD Sensors and Camera Systems (SPIE, 2007).

Luo, M. R.

L. W. MacDonald and M. R. Luo, Colour Imaging: Vision and Technology (Wiley, 1999).

MacDonald, L. W.

L. W. MacDonald and M. R. Luo, Colour Imaging: Vision and Technology (Wiley, 1999).

Malkasse, J.-P.

S. Bazeille, I. Quidu, L. Jaulin, and J.-P. Malkasse, “Automatic underwater image preprocessing,” presented at CMM06, Brest, France, 16–19 October 2006).

Mancill, C.

McGlamery, B.

B. McGlamery, “A computer model for underwater camera systems,” Proc. SPIE 0208, 221–231 (1979).

B. McGlamery, “Computer analysis and simulation of underwater camera system performance,” Tech. Rep. (Scripps. Inst. of Oceanography, 1975).

Mclean, J.

J. Jaffe, J. Mclean, M. Strand, and K. Moore, “Underwater optical imaging: status and prospects,” Oceanography 14, 64–75 (2001).

Mertens, L.

Mitre, S. K.

C. R. Rao and S. K. Mitre, “Generalized inverse of a matrix and its application,” in Proceedings of the 6th Berkeley Symposium of Mathematical Statistics and Probability (University of California, 1972), Vol. I, pp. 601–620.

Mobley, C.

C. Mobley, Light and Water (Academic, 1994).

Mobley, C. D.

Moore, K.

J. Jaffe, J. Mclean, M. Strand, and K. Moore, “Underwater optical imaging: status and prospects,” Oceanography 14, 64–75 (2001).

Nascimento, S.

E. Valero, J. Nieves, S. Nascimento, K. Amano, and D. Foster, “Recovering spectral data from natural scenes with an RGB digital camera and colored filters,” Color Res. Appl. 32, 352–360 (2007).
[CrossRef]

Negahdaripour, S.

S. Negahdaripour, H. Zhang, and X. Han, “Investigation of photometric stereo method for 3-d shape recovery from underwater imagery,” in MTS/IEEE Oceans (Marine Technol. Soc, 2002), pp. 1010–1017.

Nieves, J.

E. Valero, J. Nieves, S. Nascimento, K. Amano, and D. Foster, “Recovering spectral data from natural scenes with an RGB digital camera and colored filters,” Color Res. Appl. 32, 352–360 (2007).
[CrossRef]

Olmos-Antillon, A.

E. Trucco and A. Olmos-Antillon, “Self-tuning underwater image restoration,” IEEE J. Ocean. Eng. 31, 511–519 (2006).
[CrossRef]

Osman, M.

K. Iqbal, R. Abdul Salam, M. Osman, and A. Talib, “Underwater image enhancement using an integrated colour model,” IAENG Int. J. Comput. Sci. 34, 239–244 (2007).

Pentland, A.

A. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Anal. Machine Intell. 9, 523–531 (1987).
[CrossRef]

Petit, F.

F. Petit, A.-S. Capelle-Laize, and P. Carre, “Underwater image enhancement by attenuation inversion with quaternions,” in IEEE International Conference on Acoustics Speech and Signal Processing (IEEE, 2009), pp. 1177–1180.

Petzold, T.

T. Petzold, “Volume scattering functions for selected ocean waters,” Tech. Rep. (Scripps. Inst. of Oceanography, 1972).

Pratt, W.

Quidu, I.

S. Bazeille, I. Quidu, L. Jaulin, and J.-P. Malkasse, “Automatic underwater image preprocessing,” presented at CMM06, Brest, France, 16–19 October 2006).

Rao, C. R.

C. R. Rao and S. K. Mitre, “Generalized inverse of a matrix and its application,” in Proceedings of the 6th Berkeley Symposium of Mathematical Statistics and Probability (University of California, 1972), Vol. I, pp. 601–620.

Reinersman, P.

Renouf, A.

M. Chambah, D. Semani, A. Renouf, P. Courtellemont, and A. Rizzi, “Underwater color constancy: enhancement of automatic live fish recognition,” Proc. SPIE 5293, 157–168 (2003).

Replogle, F.

Rizzi, A.

M. Chambah, D. Semani, A. Renouf, P. Courtellemont, and A. Rizzi, “Underwater color constancy: enhancement of automatic live fish recognition,” Proc. SPIE 5293, 157–168 (2003).

Schechner, Y.

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

Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Ocean. Eng. 30, 570–587 (2005).
[CrossRef]

Schettini, R.

R. Schettini and S. Corchs, “Underwater image processing: state of the art of restoration and image enhancement methods,” EURASIP J. Adv. Sig. Proc. 2010 (2010).

Semani, D.

M. Chambah, D. Semani, A. Renouf, P. Courtellemont, and A. Rizzi, “Underwater color constancy: enhancement of automatic live fish recognition,” Proc. SPIE 5293, 157–168 (2003).

Stamnes, K.

Stavn, R. H.

Stramski, D.

Strand, M.

J. Jaffe, J. Mclean, M. Strand, and K. Moore, “Underwater optical imaging: status and prospects,” Oceanography 14, 64–75 (2001).

Sundgren, D.

J. Ahlén, D. Sundgren, and E. Bengtsson, “Application of underwater hyperspectral data for color correction purposes,” Pattern Recog. Image Anal. 17, 170–173 (2007).
[CrossRef]

J. Ahlén, E. Bengtsson, and D. Sundgren, “Evaluation of underwater spectral data for colour correction applications,” in Proceedings of the 5th WSEAS International Conference on Circuits, Systems, Electronics, Control & Signal Processing (World Scientific and Engineering Academy and Society, 2006), pp. 321–326.

Sutley, S.

R. Clark, G. Swayze, R. Wise, E. Livo, T. Hoefen, R. Kokaly, and S. Sutley, “USGS digital spectral library splib06a; U.S. Geological Survey, Digital Data Series 231, http://speclab.cr.usgs.gov/spectral.lib06 ” (2007).

Swayze, G.

R. Clark, G. Swayze, R. Wise, E. Livo, T. Hoefen, R. Kokaly, and S. Sutley, “USGS digital spectral library splib06a; U.S. Geological Survey, Digital Data Series 231, http://speclab.cr.usgs.gov/spectral.lib06 ” (2007).

Talib, A.

K. Iqbal, R. Abdul Salam, M. Osman, and A. Talib, “Underwater image enhancement using an integrated colour model,” IAENG Int. J. Comput. Sci. 34, 239–244 (2007).

Torres-Méndez, L.

L. Torres-Méndez and G. Dudek, “Color correction of underwater images for aquatic robot inspection,” in Energy Minimization Methods in Computer Vision and Pattern Recognition (Springer, 2005), pp. 60–73.

Travis, L. D.

J. Chowdhary, B. Cairns, and L. D. Travis, “Case studies of aerosol retrievals over the ocean from multiangle, multispectral photopolarimetric remote sensing data,” J. Atmos. Sci. 59, 383–397 (2002).
[CrossRef]

Treibitz, T.

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

Trucco, E.

E. Trucco and A. Olmos-Antillon, “Self-tuning underwater image restoration,” IEEE J. Ocean. Eng. 31, 511–519 (2006).
[CrossRef]

Valero, E.

E. Valero, J. Nieves, S. Nascimento, K. Amano, and D. Foster, “Recovering spectral data from natural scenes with an RGB digital camera and colored filters,” Color Res. Appl. 32, 352–360 (2007).
[CrossRef]

Weidemann, A.

Wells, W.

W. Wells, “Theory of small angle scattering,” AGARD Conf. Proc. 81, 1–20 (1973).

Wise, R.

R. Clark, G. Swayze, R. Wise, E. Livo, T. Hoefen, R. Kokaly, and S. Sutley, “USGS digital spectral library splib06a; U.S. Geological Survey, Digital Data Series 231, http://speclab.cr.usgs.gov/spectral.lib06 ” (2007).

Zhang, H.

S. Negahdaripour, H. Zhang, and X. Han, “Investigation of photometric stereo method for 3-d shape recovery from underwater imagery,” in MTS/IEEE Oceans (Marine Technol. Soc, 2002), pp. 1010–1017.

AGARD Conf. Proc. (1)

W. Wells, “Theory of small angle scattering,” AGARD Conf. Proc. 81, 1–20 (1973).

Appl. Opt. (3)

Color Res. Appl. (1)

E. Valero, J. Nieves, S. Nascimento, K. Amano, and D. Foster, “Recovering spectral data from natural scenes with an RGB digital camera and colored filters,” Color Res. Appl. 32, 352–360 (2007).
[CrossRef]

EURASIP J. Adv. Sig. Proc. (1)

R. Schettini and S. Corchs, “Underwater image processing: state of the art of restoration and image enhancement methods,” EURASIP J. Adv. Sig. Proc. 2010 (2010).

IAENG Int. J. Comput. Sci. (1)

K. Iqbal, R. Abdul Salam, M. Osman, and A. Talib, “Underwater image enhancement using an integrated colour model,” IAENG Int. J. Comput. Sci. 34, 239–244 (2007).

IEEE J. Ocean. Eng. (3)

Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Ocean. Eng. 30, 570–587 (2005).
[CrossRef]

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

E. Trucco and A. Olmos-Antillon, “Self-tuning underwater image restoration,” IEEE J. Ocean. Eng. 31, 511–519 (2006).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell. (2)

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

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Figures (11)

Fig. 1.
Fig. 1.

Geometry and coordinate system of the model used for this study. The scene is assumed to be parallel to the detector plane. (a) For general calculation, (b) for the backscattering contribution calculation.

Fig. 2.
Fig. 2.

(a) Inherent optical properties for type 1 water (clear water) used in the study: Beam absorption coefficient aλ, scattering coefficient bλ, and total attenuation coefficient cλ. (b) Idem for type 2 water (turbid water). (c) Values of p(φ) used to calculated the VSF (data taken from [4]).

Fig. 3.
Fig. 3.

Spectral responses of the cameras used for the study. They were adapted (a) from [28] for camera I and (b) from [29] for camera II.

Fig. 4.
Fig. 4.

RGB representation of the reference scene with a known spectral reflectance. The reflection coefficient for each patch is perfectly known and taken from [30]. The scene was imaged in air with camera I (a) and camera II (b). Image size is 46×37 pixels.

Fig. 5.
Fig. 5.

Visual aspect of scene of Fig. 4 in subsea environments for Zo=7m. Upper row: the scene was imaged using camera I. Bottom row: idem with camera II. Left column: results of simulation for type 1 water. Right column: Idem for type 2 water.

Fig. 6.
Fig. 6.

Error ϵBc on the simulation of the backscattering contribution in type 1 water as a function of the number N of wavelengths for Zo=15m. The results are plotted as a percentile ratio of maxx,yEB,truec(x,y) for (a) the red channel, (b) the green channel, and (c) the blue channel.

Fig. 7.
Fig. 7.

Error ϵUR on the simulation of the scene contribution in the red channel for type 1 water as a function of the number N of wavelengths. The result is plotted as a percentile ratio of maxx,yEU,trueR(x,y) and for Zo=15m.

Fig. 8.
Fig. 8.

Same as Fig. 7, but for type 2 water with Zo=7m.

Fig. 9.
Fig. 9.

Visual aspect of scene of Fig. 4 in subsea environments for Zo=7m. Upper row: the scene was imaged using camera I. Bottom row: idem with camera II. Left columns: results of simulation with for type 1 water. Right columns: idem for type 2 water. (a), (c), (e), (g): simulations were performed with the simple RGB approach. (b), (d), (f), (h): idem with the reconstruction approach.

Fig. 10.
Fig. 10.

Irradiance profiles of the 20 patches corresponding to the images of Fig. 4(a) simulated for Zo=7m with camera I. Row 1: irradiance profiles in air. Row 2: irradiance profiles in type 1 water. Row 3: irradiance profiles in type 2 water. Plain curves: ground truth. Dots and dashed line: simple RGB approach. Crosses: reconstruction approach. (a) Red channel; (b) blue channel.

Fig. 11.
Fig. 11.

(a) Initial RGB image (256×160 pixels) taken with a standard camera. (b) Simulated RGB image for type 1 water and a distance Zo=7m with a reconstruction step and the multispectral approach (N=25). (c) Idem using the simple RGB approach. (d), (e), (f) Red channels correspond respectively to (a), (b), and (c).

Equations (23)

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Etot,λ(x,y)=Eu,λ(x,y)+Eb,λ(x,y)
Eu,λ(x,y)=ecλRcE0,λ(x,y)+E0,λ(x,y)*hλ(x,y,Zo),
E0,λ(x,y)=πTλ4Nl2(ZoFlZo)2Lλ(x,y)cos4θ,
Es,λ(x,y,z)=ecλRsEs,0,λ(x,y,z)+Es,0,λ(x,y,z)*hλ(x,y,Zsz),
hλ(x,y,Z)=(eGλZecλZ)FT1{eBλZω}x,y,
Ek,λ(x,y,zk)=Ek,0,λ(x,y,zk)ecλRk+Ek,0,λ(x,y,zk)*hλ(x,y,Zk)
Ek,0,λ(x,y,zk)=Tλ4Nl2(ZoFlZo)2×βλ(φk)Es,λ(x,y,zk)πcos3θkΔz,
d(z)=Fl2zN(Zoz)(ZoFl).
Eb,λ(x,y)=k=1Zo/Δz[Ek,λ*Ddefocus](x,y,zk)|zk=Δz×(k1/2).
Sc(x,y)=λQc(λ)ϕc(λ)Etot,λ(x,y)dλ,
Ec(x,y)=λϕc(λ)Etot,λ(x,y)dλ.
ENc(x,y)Δλn=1Nϕc(λn)Etot,λn(x,y),
ENc(x,y)=EU,Nc(x,y)+EB,Nc(x,y)
EU,Nc(x,y)=Δλn=1Nϕc(λn)Eu,λn(x,y),
EB,Nc(x,y)=Δλn=1Nϕc(λn)Eb,λn(x,y).
βλ(φ)=p(φ)bλ,
ϵc(N)=1Px,y|E,Nc(x,y)E,truec(x,y)|,
Rλn(N)N(x,y)=1JnjΩn(N)Rλj100(x,y),
Ergbc(x,y)=Eu,λc(x,y)+Eb,λc(x,y),
r^=G1ΘT(ΘG1ΘT)1m
D=[121000121000121000121000121],
E^Nc(x,y)=E^U,N(x,y)+EB,N(x,y),
Rc(x,y)=n=1Nϕc(λn)Rλn(x,y)

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