Abstract

Background estimation is a crucial step in underwater image dehazing. Most of the current estimation methods assume a uniform background light in the underwater environment and select the brightest pixel in the dark channel as the candidate, which fails to explain the real interactions of light rays and particles in the water medium and causes over-saturation in dehazed images. In this paper, the relationship between the maxima of dark channel and the background light in offshore underwater images is initially illustrated, and a contradiction of the assumption related to the dark channel prior used in underwater image restoration is addressed. To the best of our knowledge, this is the first work studying the statistical facts of underwater background light. Furthermore, a machine learning based background light estimation and reconstruction method is proposed based on the learning of the maximum areas of a dark channel. The subjective and objective restoration results of the state-of-the-art algorithms with and without applying the proposed background light estimation method to the offshore images are compared. The results show that the proposed method better simulated the directional distribution of the background light in a turbid water environment, and the foggy ambiguity caused by the backscattering was removed more efficiently in comparison with existing methods.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (3)

C. O. Ancuti, C. Ancuti, C. DeVleeschouwer, and P. Bekaert, “Color balance and fusion for underwater image enhancement,” IEEE Trans. Image Process. 27(1), 379–393 (2018).
[Crossref]

J. Li, K. A. Skinner, R. M. Eustice, and et al., “WaterGAN: Unsupervised generative network to enable real-time color correction of monocular underwater images,” IEEE Robot. Autom. Lett. 3(1), 387–394 (2018).
[Crossref]

C. Li, J. Guo, and C. Guo, “Emerging from water: Underwater image color correction based on weakly supervised color transfer,” IEEE Signal Process. Lett. 25(3), 323–327 (2018).
[Crossref]

2017 (2)

Y. T. Peng and P. C. Cosman, “Underwater image restoration based on image blurriness and light absorption,” IEEE Trans. Image Process. 26(4), 1579–1594 (2017).
[Crossref]

S. Zhang, T. Wang, J. Dong, and et al., “Underwater image enhancement via extended multi-scale Retinex,” Neurocomputing 245, 1–9 (2017).
[Crossref]

2015 (4)

M. Yang and A. Sowmya, “An underwater color image quality evaluation metric,” IEEE Trans. Image Process. 24(12), 6062–6071 (2015).
[Crossref]

F. C. Cheng, C. C. Cheng, P. H. Lin, and S. C. Huang, “A hierarchical airlight estimation method for image fog removal,” Eng. Appl. Artif. Intell. 43, 27–34 (2015).
[Crossref]

A. Galdran, D. Pardo, A. Picón, and A. Alvarez-Gila, “Automatic Red-Channel underwater image restoration,” J. Vis. Commun. Image Rep. 26, 132–145 (2015).
[Crossref]

J. S. Jaffe, “Underwater optical imaging: The past, the present, and the prospects,” IEEE J. Oceanic Eng. 40(3), 683–700 (2015).
[Crossref]

2014 (1)

Y. Nie and Z. Y. He, “Underwater imaging and real-time optical image processing under illumination by light sources with different wavelengths,” Acta Opt. Sin. 34(7), 0710002 (2014).
[Crossref]

2012 (5)

R. Rai, P. Gour, and B. Singh, “Underwater Image Segmentation using CLAHE Enhancement and Thresholding,” Int. J. Emerg. Technol. Adv. Eng. 2(1), 118–123 (2012).

A. T. Çelebi and S. Ertürk, “Visual enhancement of underwater images using Empirical Mode Decomposition,” Expert Syst. Appl. 39(1), 800–805 (2012).
[Crossref]

J. Y. Chiang and Y. C. Chen, “Underwater image enhancement by wavelength compensation and dehazing,” IEEE Trans. Image Process. 21(4), 1756–1769 (2012).
[Crossref]

K. B. Gibson, D. T. Vo, and T. Q. Nguyen, “An investigation of dehazing effects on image and video coding,” IEEE Trans. Image Process. 21(2), 662–673 (2012).
[Crossref]

C. H. Yeh, L. W. Kang, C. Y. Lin, and C. Y. Lin, “Efficient image/video dehazing through haze density analysis based on pixel-based dark channel prior,” Proc. IEEE ISIC 238, 14–16 (2012).

2011 (3)

J. Yu, C. Xiao, and D. Li, “Physics-based fast single image fog removal,” Proc. IEEE ICSP 37(2), 1048–1052 (2011).

T. Johnsen, H. A. Bouman, S. Sathyendranath, and E. Devred, “Regional-scale changes in diatom distribution in the Humboldt upwelling system as revealed by remote sensing: implications for fisheries,” ICES J. Mar. Sci. 68(4), 729–736 (2011).
[Crossref]

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]

2008 (1)

R. Fattal, “Single image dehazing,” ACM Trans. Graphics 27(3), 1 (2008).
[Crossref]

2007 (2)

K. Iqbal, R. Abdul Salam, A. Osman, and A. Zawawi Talib, “Underwater image enhancement using an integrated colour model,” Int. J. Comp. Sci. 34, 2 (2007).

J. Åhlén, D. Sundgren, and E. Bengtsson, “Application of underwater hyper spectral data for color correction purposes,” Pattern Recognit. Image Anal. 17(1), 170–173 (2007).
[Crossref]

1999 (1)

1990 (1)

C. L. Gallegos, D. L. Correll, and J. W. Pierce, “Modeling spectral diffuse attenuation, absorption, and scattering coefficients in a turbid estuary,” Limnol. Oceanogr. 35(7), 1486–1502 (1990).
[Crossref]

1988 (1)

R. J. Davies-Colley, “Measuring water clarity with a black disk,” Limnol. Oceanogr. 33(4), 616–623 (1988).
[Crossref]

1980 (1)

B. L. McGlamery, “A computer model for underwater camera systems,” Ocean Optics 0208, 221–231 (1980).
[Crossref]

Abdul Salam, R.

K. Iqbal, R. Abdul Salam, A. Osman, and A. Zawawi Talib, “Underwater image enhancement using an integrated colour model,” Int. J. Comp. Sci. 34, 2 (2007).

K. Iqbal, M. Odetayo, A. James, and R. Abdul Salam, “Enhancing the low quality images using unsupervised colour correction method,’’ in IEEE International Conference on Systems Man and Cybernetics (SMC) (2010).

Åhlén, J.

J. Åhlén, D. Sundgren, and E. Bengtsson, “Application of underwater hyper spectral data for color correction purposes,” Pattern Recognit. Image Anal. 17(1), 170–173 (2007).
[Crossref]

Alvarez-Gila, A.

A. Galdran, D. Pardo, A. Picón, and A. Alvarez-Gila, “Automatic Red-Channel underwater image restoration,” J. Vis. Commun. Image Rep. 26, 132–145 (2015).
[Crossref]

Ancuti, C.

C. O. Ancuti, C. Ancuti, C. DeVleeschouwer, and P. Bekaert, “Color balance and fusion for underwater image enhancement,” IEEE Trans. Image Process. 27(1), 379–393 (2018).
[Crossref]

C. Ancuti, C. O. Ancuti, T. Haber, and P. Bekaert, “Enhancing underwater images and videos by fusion,” in Processing of IEEE Conference on Computer Vision and Pattern Recognition, 81–88 (2012).

C. O. Ancuti, C. Ancuti, T. Haber, and P. Bekaert, “Enhancing underwater image and videos by fusion,” In Proc. CVPR, 81–88 (2012).

Ancuti, C. O.

C. O. Ancuti, C. Ancuti, C. DeVleeschouwer, and P. Bekaert, “Color balance and fusion for underwater image enhancement,” IEEE Trans. Image Process. 27(1), 379–393 (2018).
[Crossref]

C. Ancuti, C. O. Ancuti, T. Haber, and P. Bekaert, “Enhancing underwater images and videos by fusion,” in Processing of IEEE Conference on Computer Vision and Pattern Recognition, 81–88 (2012).

C. O. Ancuti, C. Ancuti, T. Haber, and P. Bekaert, “Enhancing underwater image and videos by fusion,” In Proc. CVPR, 81–88 (2012).

Arnold-Bos, A.

A. Arnold-Bos, J. P. Malkasse, and G. Kerven, “A preprocessing framework for automatic underwater images denoising,” in Proceedings of the European Conference on Propagation and Systems, Brest, France (2005).

Arnone, R.

Bazeille, S.

S. Bazeille, I. Quidu, L. Jaulin, and J. P. Malkasse, “Automatic underwater image pre-processing,” in Proceedings of the Characterizations du Milieu Marin (CMM ‘06), 16–19 (2006).

Bekaert, P.

C. O. Ancuti, C. Ancuti, C. DeVleeschouwer, and P. Bekaert, “Color balance and fusion for underwater image enhancement,” IEEE Trans. Image Process. 27(1), 379–393 (2018).
[Crossref]

C. Ancuti, C. O. Ancuti, T. Haber, and P. Bekaert, “Enhancing underwater images and videos by fusion,” in Processing of IEEE Conference on Computer Vision and Pattern Recognition, 81–88 (2012).

C. O. Ancuti, C. Ancuti, T. Haber, and P. Bekaert, “Enhancing underwater image and videos by fusion,” In Proc. CVPR, 81–88 (2012).

Bengtsson, E.

J. Åhlén, D. Sundgren, and E. Bengtsson, “Application of underwater hyper spectral data for color correction purposes,” Pattern Recognit. Image Anal. 17(1), 170–173 (2007).
[Crossref]

Bouman, H. A.

T. Johnsen, H. A. Bouman, S. Sathyendranath, and E. Devred, “Regional-scale changes in diatom distribution in the Humboldt upwelling system as revealed by remote sensing: implications for fisheries,” ICES J. Mar. Sci. 68(4), 729–736 (2011).
[Crossref]

Capelle-Laize, A.-S.

F. Petit, A.-S. Capelle-Laize, and P. Carre, “Underwater image enhancement by attenuation inversion with quaternions,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP ‘09), 1177–1180, (2009).

Carlevaris-Bianco, N.

N. Carlevaris-Bianco, A. Mohan, and R. M. Eustice, “Initial results in underwater single image dehazing,” in Proc. of IEEE OCEANS (2010).

Carre, P.

F. Petit, A.-S. Capelle-Laize, and P. Carre, “Underwater image enhancement by attenuation inversion with quaternions,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP ‘09), 1177–1180, (2009).

Cavallaro, A.

S. Emberton, L. Chittka, and A. Cavallaro, “Hierarchical rank-based veiling light estimation for underwater dehazing,” BMVC, 125.1-125.12 (2015).

Çelebi, A. T.

A. T. Çelebi and S. Ertürk, “Visual enhancement of underwater images using Empirical Mode Decomposition,” Expert Syst. Appl. 39(1), 800–805 (2012).
[Crossref]

Chambah, M.

M. Chambah, D. Semani, A. Renouf, P. Courtellemont, and A. Rizzi, “Underwater color constancy: enhancement of automatic live fish recognition,” in Color Imaging IX: Processing, Hardcopy, and Applications, Proceedings of SPIE, 5293, 157–168 (2003).

Chen, S.

C. Li, J. Guo, S. Chen, Y. Tang, Y. Pang, and J. Wang, “Underwater image restoration based on minimum information loss principle and optical properties of underwater imaging,” IEEE International Conference on Image Processing , ICIP, 1993–1997 (2016).

Chen, Y. C.

J. Y. Chiang and Y. C. Chen, “Underwater image enhancement by wavelength compensation and dehazing,” IEEE Trans. Image Process. 21(4), 1756–1769 (2012).
[Crossref]

Cheng, C. C.

F. C. Cheng, C. C. Cheng, P. H. Lin, and S. C. Huang, “A hierarchical airlight estimation method for image fog removal,” Eng. Appl. Artif. Intell. 43, 27–34 (2015).
[Crossref]

Cheng, F. C.

F. C. Cheng, C. C. Cheng, P. H. Lin, and S. C. Huang, “A hierarchical airlight estimation method for image fog removal,” Eng. Appl. Artif. Intell. 43, 27–34 (2015).
[Crossref]

Chiang, J. Y.

J. Y. Chiang and Y. C. Chen, “Underwater image enhancement by wavelength compensation and dehazing,” IEEE Trans. Image Process. 21(4), 1756–1769 (2012).
[Crossref]

Chittka, L.

S. Emberton, L. Chittka, and A. Cavallaro, “Hierarchical rank-based veiling light estimation for underwater dehazing,” BMVC, 125.1-125.12 (2015).

Correll, D. L.

C. L. Gallegos, D. L. Correll, and J. W. Pierce, “Modeling spectral diffuse attenuation, absorption, and scattering coefficients in a turbid estuary,” Limnol. Oceanogr. 35(7), 1486–1502 (1990).
[Crossref]

Cosman, P. C.

Y. T. Peng and P. C. Cosman, “Underwater image restoration based on image blurriness and light absorption,” IEEE Trans. Image Process. 26(4), 1579–1594 (2017).
[Crossref]

Y. T. Peng and P. C. Cosman, “Single image restoration using scene ambient light differential,” IEEE International Conference on Image Processing, ICIP, 1953–1957 (2016).

Y. T. Peng, X. Zhao, and P. C. Cosman, “Single underwater image enhancement using depth estimation based on blurriness,” Image Processing (ICIP), 2015 IEEE International Conference on, IEEE (2015).

Courtellemont, P.

M. Chambah, D. Semani, A. Renouf, P. Courtellemont, and A. Rizzi, “Underwater color constancy: enhancement of automatic live fish recognition,” in Color Imaging IX: Processing, Hardcopy, and Applications, Proceedings of SPIE, 5293, 157–168 (2003).

Davies-Colley, R. J.

R. J. Davies-Colley, “Measuring water clarity with a black disk,” Limnol. Oceanogr. 33(4), 616–623 (1988).
[Crossref]

DeVleeschouwer, C.

C. O. Ancuti, C. Ancuti, C. DeVleeschouwer, and P. Bekaert, “Color balance and fusion for underwater image enhancement,” IEEE Trans. Image Process. 27(1), 379–393 (2018).
[Crossref]

Devred, E.

T. Johnsen, H. A. Bouman, S. Sathyendranath, and E. Devred, “Regional-scale changes in diatom distribution in the Humboldt upwelling system as revealed by remote sensing: implications for fisheries,” ICES J. Mar. Sci. 68(4), 729–736 (2011).
[Crossref]

Dong, J.

S. Zhang, T. Wang, J. Dong, and et al., “Underwater image enhancement via extended multi-scale Retinex,” Neurocomputing 245, 1–9 (2017).
[Crossref]

Dudek, G.

G. Dudek, “Color correction of underwater images for aquatic robot inspection,” International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition Springer, Berlin, Heidelberg, 60–73 (2005).

Dunn, E.

K. Wang, E. Dunn, J. Tighe, and J. M. Frahm, “Combining semantic scene priors and haze removal for single image depth estimation,” in Proc. of IEEE WACV, 800–807 (2014).

Emberton, S.

S. Emberton, L. Chittka, and A. Cavallaro, “Hierarchical rank-based veiling light estimation for underwater dehazing,” BMVC, 125.1-125.12 (2015).

Ertürk, S.

A. T. Çelebi and S. Ertürk, “Visual enhancement of underwater images using Empirical Mode Decomposition,” Expert Syst. Appl. 39(1), 800–805 (2012).
[Crossref]

Eustice, R. M.

J. Li, K. A. Skinner, R. M. Eustice, and et al., “WaterGAN: Unsupervised generative network to enable real-time color correction of monocular underwater images,” IEEE Robot. Autom. Lett. 3(1), 387–394 (2018).
[Crossref]

N. Carlevaris-Bianco, A. Mohan, and R. M. Eustice, “Initial results in underwater single image dehazing,” in Proc. of IEEE OCEANS (2010).

Fattal, R.

R. Fattal, “Single image dehazing,” ACM Trans. Graphics 27(3), 1 (2008).
[Crossref]

Frahm, J. M.

K. Wang, E. Dunn, J. Tighe, and J. M. Frahm, “Combining semantic scene priors and haze removal for single image depth estimation,” in Proc. of IEEE WACV, 800–807 (2014).

Fu, X.

X. Fu, P. Zhuang, Y. Huang, and et al., “A retinex-based enhancing approach for single underwater image, “ Image Processing (ICIP), 2014 IEEE International Conference on., IEEE, 4572–4576 (2014).

Galdran, A.

A. Galdran, D. Pardo, A. Picón, and A. Alvarez-Gila, “Automatic Red-Channel underwater image restoration,” J. Vis. Commun. Image Rep. 26, 132–145 (2015).
[Crossref]

Gallegos, C. L.

C. L. Gallegos, D. L. Correll, and J. W. Pierce, “Modeling spectral diffuse attenuation, absorption, and scattering coefficients in a turbid estuary,” Limnol. Oceanogr. 35(7), 1486–1502 (1990).
[Crossref]

Ge, Y.

D. Jia and Y. Ge, “Underwater Image De-Noising Algorithm Based On Nonsubsampled Contourlet Transform And Total Variation,” 2012 International Conference on Computer Science and Information Processing (CSIP), 76–80 (2012).

Ghosh, S.

S. Ghosh, R. Ray, S. R. K. Vadali, and S. N. Shome, “Light-Particle interaction in underwater: a modified PSF,” Communications and Signal Processing (ICCSP), 2014 International Conference on. IEEE (2014).

Gibson, K. B.

K. B. Gibson, D. T. Vo, and T. Q. Nguyen, “An investigation of dehazing effects on image and video coding,” IEEE Trans. Image Process. 21(2), 662–673 (2012).
[Crossref]

Gould, R.

Gour, P.

R. Rai, P. Gour, and B. Singh, “Underwater Image Segmentation using CLAHE Enhancement and Thresholding,” Int. J. Emerg. Technol. Adv. Eng. 2(1), 118–123 (2012).

Gulliver, T. A.

B. Zheng, H. Zhang, H. Zheng, and T. A. Gulliver, “Underwater Imaging Based on Inhomogeneous Illumination,” 2011 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PacRim), 873–876 (2011).

Guo, C.

C. Li, J. Guo, and C. Guo, “Emerging from water: Underwater image color correction based on weakly supervised color transfer,” IEEE Signal Process. Lett. 25(3), 323–327 (2018).
[Crossref]

Guo, J.

C. Li, J. Guo, and C. Guo, “Emerging from water: Underwater image color correction based on weakly supervised color transfer,” IEEE Signal Process. Lett. 25(3), 323–327 (2018).
[Crossref]

C. Li, J. Guo, S. Chen, Y. Tang, Y. Pang, and J. Wang, “Underwater image restoration based on minimum information loss principle and optical properties of underwater imaging,” IEEE International Conference on Image Processing , ICIP, 1993–1997 (2016).

Haber, T.

C. Ancuti, C. O. Ancuti, T. Haber, and P. Bekaert, “Enhancing underwater images and videos by fusion,” in Processing of IEEE Conference on Computer Vision and Pattern Recognition, 81–88 (2012).

C. O. Ancuti, C. Ancuti, T. Haber, and P. Bekaert, “Enhancing underwater image and videos by fusion,” In Proc. CVPR, 81–88 (2012).

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]

He, Z. Y.

Y. Nie and Z. Y. He, “Underwater imaging and real-time optical image processing under illumination by light sources with different wavelengths,” Acta Opt. Sin. 34(7), 0710002 (2014).
[Crossref]

Huang, S. C.

F. C. Cheng, C. C. Cheng, P. H. Lin, and S. C. Huang, “A hierarchical airlight estimation method for image fog removal,” Eng. Appl. Artif. Intell. 43, 27–34 (2015).
[Crossref]

Huang, Y.

X. Fu, P. Zhuang, Y. Huang, and et al., “A retinex-based enhancing approach for single underwater image, “ Image Processing (ICIP), 2014 IEEE International Conference on., IEEE, 4572–4576 (2014).

Ingrid, K.

K. Ingrid, “Underwater Imaging and the effect of inherent optical properties on image quality,” Norwegian University of Science and Technology, Master thesis (2014).

Iqbal, K.

K. Iqbal, R. Abdul Salam, A. Osman, and A. Zawawi Talib, “Underwater image enhancement using an integrated colour model,” Int. J. Comp. Sci. 34, 2 (2007).

K. Iqbal, M. Odetayo, A. James, and R. Abdul Salam, “Enhancing the low quality images using unsupervised colour correction method,’’ in IEEE International Conference on Systems Man and Cybernetics (SMC) (2010).

Isola, P.

J. Y. Zhu, T. Park, and P. Isola, et al., “Unpaired image-to-image translation using cycle-consistent adversarial networks,” arXiv preprint, (2017).

Jaffe, J. S.

J. S. Jaffe, “Underwater optical imaging: The past, the present, and the prospects,” IEEE J. Oceanic Eng. 40(3), 683–700 (2015).
[Crossref]

James, A.

K. Iqbal, M. Odetayo, A. James, and R. Abdul Salam, “Enhancing the low quality images using unsupervised colour correction method,’’ in IEEE International Conference on Systems Man and Cybernetics (SMC) (2010).

Jaulin, L.

S. Bazeille, I. Quidu, L. Jaulin, and J. P. Malkasse, “Automatic underwater image pre-processing,” in Proceedings of the Characterizations du Milieu Marin (CMM ‘06), 16–19 (2006).

Jia, D.

D. Jia and Y. Ge, “Underwater Image De-Noising Algorithm Based On Nonsubsampled Contourlet Transform And Total Variation,” 2012 International Conference on Computer Science and Information Processing (CSIP), 76–80 (2012).

Johnsen, G.

G. Johnsen, Z. Volent, E. Sakshaug, F. Sigernes, and L. H. Pettersson, “Remote sensing in the Barents Sea,” in Ecosystem Barents sea, E. Sakshaug, G. Johnsen, and K. Kovacs, (eds.), (Tapir Academic Press, 2009), pp. 139–166.

G. Johnsen, Z. Volent, E. Sakshaug, F. Sigernes, and L. H. Pettersson, “Remote sensing in the Barents Sea,” in Ecosystem Barents sea, E. Sakshaug, G. Johnsen, and K. Kovacs, (eds.), (Tapir Academic Press, 2009), pp. 139–166.

Johnsen, T.

T. Johnsen, H. A. Bouman, S. Sathyendranath, and E. Devred, “Regional-scale changes in diatom distribution in the Humboldt upwelling system as revealed by remote sensing: implications for fisheries,” ICES J. Mar. Sci. 68(4), 729–736 (2011).
[Crossref]

Kang, L. W.

C. H. Yeh, L. W. Kang, C. Y. Lin, and C. Y. Lin, “Efficient image/video dehazing through haze density analysis based on pixel-based dark channel prior,” Proc. IEEE ISIC 238, 14–16 (2012).

Kerven, G.

A. Arnold-Bos, J. P. Malkasse, and G. Kerven, “A preprocessing framework for automatic underwater images denoising,” in Proceedings of the European Conference on Propagation and Systems, Brest, France (2005).

Kovacs, K.

G. Johnsen, Z. Volent, E. Sakshaug, F. Sigernes, and L. H. Pettersson, “Remote sensing in the Barents Sea,” in Ecosystem Barents sea, E. Sakshaug, G. Johnsen, and K. Kovacs, (eds.), (Tapir Academic Press, 2009), pp. 139–166.

Li, C.

C. Li, J. Guo, and C. Guo, “Emerging from water: Underwater image color correction based on weakly supervised color transfer,” IEEE Signal Process. Lett. 25(3), 323–327 (2018).
[Crossref]

C. Li, J. Guo, S. Chen, Y. Tang, Y. Pang, and J. Wang, “Underwater image restoration based on minimum information loss principle and optical properties of underwater imaging,” IEEE International Conference on Image Processing , ICIP, 1993–1997 (2016).

Li, D.

J. Yu, C. Xiao, and D. Li, “Physics-based fast single image fog removal,” Proc. IEEE ICSP 37(2), 1048–1052 (2011).

Li, J.

J. Li, K. A. Skinner, R. M. Eustice, and et al., “WaterGAN: Unsupervised generative network to enable real-time color correction of monocular underwater images,” IEEE Robot. Autom. Lett. 3(1), 387–394 (2018).
[Crossref]

Lin, C. Y.

C. H. Yeh, L. W. Kang, C. Y. Lin, and C. Y. Lin, “Efficient image/video dehazing through haze density analysis based on pixel-based dark channel prior,” Proc. IEEE ISIC 238, 14–16 (2012).

C. H. Yeh, L. W. Kang, C. Y. Lin, and C. Y. Lin, “Efficient image/video dehazing through haze density analysis based on pixel-based dark channel prior,” Proc. IEEE ISIC 238, 14–16 (2012).

Lin, P. H.

F. C. Cheng, C. C. Cheng, P. H. Lin, and S. C. Huang, “A hierarchical airlight estimation method for image fog removal,” Eng. Appl. Artif. Intell. 43, 27–34 (2015).
[Crossref]

Malkasse, J. P.

A. Arnold-Bos, J. P. Malkasse, and G. Kerven, “A preprocessing framework for automatic underwater images denoising,” in Proceedings of the European Conference on Propagation and Systems, Brest, France (2005).

S. Bazeille, I. Quidu, L. Jaulin, and J. P. Malkasse, “Automatic underwater image pre-processing,” in Proceedings of the Characterizations du Milieu Marin (CMM ‘06), 16–19 (2006).

Martinolich, P.

McGlamery, B. L.

B. L. McGlamery, “A computer model for underwater camera systems,” Ocean Optics 0208, 221–231 (1980).
[Crossref]

Mohan, A.

N. Carlevaris-Bianco, A. Mohan, and R. M. Eustice, “Initial results in underwater single image dehazing,” in Proc. of IEEE OCEANS (2010).

Nguyen, T. Q.

K. B. Gibson, D. T. Vo, and T. Q. Nguyen, “An investigation of dehazing effects on image and video coding,” IEEE Trans. Image Process. 21(2), 662–673 (2012).
[Crossref]

Nie, Y.

Y. Nie and Z. Y. He, “Underwater imaging and real-time optical image processing under illumination by light sources with different wavelengths,” Acta Opt. Sin. 34(7), 0710002 (2014).
[Crossref]

Odetayo, M.

K. Iqbal, M. Odetayo, A. James, and R. Abdul Salam, “Enhancing the low quality images using unsupervised colour correction method,’’ in IEEE International Conference on Systems Man and Cybernetics (SMC) (2010).

Osman, A.

K. Iqbal, R. Abdul Salam, A. Osman, and A. Zawawi Talib, “Underwater image enhancement using an integrated colour model,” Int. J. Comp. Sci. 34, 2 (2007).

Pang, Y.

C. Li, J. Guo, S. Chen, Y. Tang, Y. Pang, and J. Wang, “Underwater image restoration based on minimum information loss principle and optical properties of underwater imaging,” IEEE International Conference on Image Processing , ICIP, 1993–1997 (2016).

Pardo, D.

A. Galdran, D. Pardo, A. Picón, and A. Alvarez-Gila, “Automatic Red-Channel underwater image restoration,” J. Vis. Commun. Image Rep. 26, 132–145 (2015).
[Crossref]

Park, T.

J. Y. Zhu, T. Park, and P. Isola, et al., “Unpaired image-to-image translation using cycle-consistent adversarial networks,” arXiv preprint, (2017).

Peng, Y. T.

Y. T. Peng and P. C. Cosman, “Underwater image restoration based on image blurriness and light absorption,” IEEE Trans. Image Process. 26(4), 1579–1594 (2017).
[Crossref]

Y. T. Peng, X. Zhao, and P. C. Cosman, “Single underwater image enhancement using depth estimation based on blurriness,” Image Processing (ICIP), 2015 IEEE International Conference on, IEEE (2015).

Y. T. Peng and P. C. Cosman, “Single image restoration using scene ambient light differential,” IEEE International Conference on Image Processing, ICIP, 1953–1957 (2016).

Petit, F.

F. Petit, A.-S. Capelle-Laize, and P. Carre, “Underwater image enhancement by attenuation inversion with quaternions,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP ‘09), 1177–1180, (2009).

Pettersson, L. H.

G. Johnsen, Z. Volent, E. Sakshaug, F. Sigernes, and L. H. Pettersson, “Remote sensing in the Barents Sea,” in Ecosystem Barents sea, E. Sakshaug, G. Johnsen, and K. Kovacs, (eds.), (Tapir Academic Press, 2009), pp. 139–166.

Picón, A.

A. Galdran, D. Pardo, A. Picón, and A. Alvarez-Gila, “Automatic Red-Channel underwater image restoration,” J. Vis. Commun. Image Rep. 26, 132–145 (2015).
[Crossref]

Pierce, J. W.

C. L. Gallegos, D. L. Correll, and J. W. Pierce, “Modeling spectral diffuse attenuation, absorption, and scattering coefficients in a turbid estuary,” Limnol. Oceanogr. 35(7), 1486–1502 (1990).
[Crossref]

Quidu, I.

S. Bazeille, I. Quidu, L. Jaulin, and J. P. Malkasse, “Automatic underwater image pre-processing,” in Proceedings of the Characterizations du Milieu Marin (CMM ‘06), 16–19 (2006).

Rai, R.

R. Rai, P. Gour, and B. Singh, “Underwater Image Segmentation using CLAHE Enhancement and Thresholding,” Int. J. Emerg. Technol. Adv. Eng. 2(1), 118–123 (2012).

Ray, R.

S. Ghosh, R. Ray, S. R. K. Vadali, and S. N. Shome, “Light-Particle interaction in underwater: a modified PSF,” Communications and Signal Processing (ICCSP), 2014 International Conference on. IEEE (2014).

Renouf, A.

M. Chambah, D. Semani, A. Renouf, P. Courtellemont, and A. Rizzi, “Underwater color constancy: enhancement of automatic live fish recognition,” in Color Imaging IX: Processing, Hardcopy, and Applications, Proceedings of SPIE, 5293, 157–168 (2003).

Rizzi, A.

M. Chambah, D. Semani, A. Renouf, P. Courtellemont, and A. Rizzi, “Underwater color constancy: enhancement of automatic live fish recognition,” in Color Imaging IX: Processing, Hardcopy, and Applications, Proceedings of SPIE, 5293, 157–168 (2003).

Sakshaug, E.

G. Johnsen, Z. Volent, E. Sakshaug, F. Sigernes, and L. H. Pettersson, “Remote sensing in the Barents Sea,” in Ecosystem Barents sea, E. Sakshaug, G. Johnsen, and K. Kovacs, (eds.), (Tapir Academic Press, 2009), pp. 139–166.

G. Johnsen, Z. Volent, E. Sakshaug, F. Sigernes, and L. H. Pettersson, “Remote sensing in the Barents Sea,” in Ecosystem Barents sea, E. Sakshaug, G. Johnsen, and K. Kovacs, (eds.), (Tapir Academic Press, 2009), pp. 139–166.

Sathyendranath, S.

T. Johnsen, H. A. Bouman, S. Sathyendranath, and E. Devred, “Regional-scale changes in diatom distribution in the Humboldt upwelling system as revealed by remote sensing: implications for fisheries,” ICES J. Mar. Sci. 68(4), 729–736 (2011).
[Crossref]

Semani, D.

M. Chambah, D. Semani, A. Renouf, P. Courtellemont, and A. Rizzi, “Underwater color constancy: enhancement of automatic live fish recognition,” in Color Imaging IX: Processing, Hardcopy, and Applications, Proceedings of SPIE, 5293, 157–168 (2003).

Shome, S. N.

S. Ghosh, R. Ray, S. R. K. Vadali, and S. N. Shome, “Light-Particle interaction in underwater: a modified PSF,” Communications and Signal Processing (ICCSP), 2014 International Conference on. IEEE (2014).

Sigernes, F.

G. Johnsen, Z. Volent, E. Sakshaug, F. Sigernes, and L. H. Pettersson, “Remote sensing in the Barents Sea,” in Ecosystem Barents sea, E. Sakshaug, G. Johnsen, and K. Kovacs, (eds.), (Tapir Academic Press, 2009), pp. 139–166.

Singh, B.

R. Rai, P. Gour, and B. Singh, “Underwater Image Segmentation using CLAHE Enhancement and Thresholding,” Int. J. Emerg. Technol. Adv. Eng. 2(1), 118–123 (2012).

Skinner, K. A.

J. Li, K. A. Skinner, R. M. Eustice, and et al., “WaterGAN: Unsupervised generative network to enable real-time color correction of monocular underwater images,” IEEE Robot. Autom. Lett. 3(1), 387–394 (2018).
[Crossref]

Sowmya, A.

M. Yang and A. Sowmya, “An underwater color image quality evaluation metric,” IEEE Trans. Image Process. 24(12), 6062–6071 (2015).
[Crossref]

Sun, J.

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]

Sundgren, D.

J. Åhlén, D. Sundgren, and E. Bengtsson, “Application of underwater hyper spectral data for color correction purposes,” Pattern Recognit. Image Anal. 17(1), 170–173 (2007).
[Crossref]

Tan, R. T.

R. T. Tan, “Visibility in bad weather from a single image,” in Proc. of IEEE CVPR, 1–8 (2008).

Tang, X.

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]

Tang, Y.

C. Li, J. Guo, S. Chen, Y. Tang, Y. Pang, and J. Wang, “Underwater image restoration based on minimum information loss principle and optical properties of underwater imaging,” IEEE International Conference on Image Processing , ICIP, 1993–1997 (2016).

Tighe, J.

K. Wang, E. Dunn, J. Tighe, and J. M. Frahm, “Combining semantic scene priors and haze removal for single image depth estimation,” in Proc. of IEEE WACV, 800–807 (2014).

Vadali, S. R. K.

S. Ghosh, R. Ray, S. R. K. Vadali, and S. N. Shome, “Light-Particle interaction in underwater: a modified PSF,” Communications and Signal Processing (ICCSP), 2014 International Conference on. IEEE (2014).

Vo, D. T.

K. B. Gibson, D. T. Vo, and T. Q. Nguyen, “An investigation of dehazing effects on image and video coding,” IEEE Trans. Image Process. 21(2), 662–673 (2012).
[Crossref]

Volent, Z.

G. Johnsen, Z. Volent, E. Sakshaug, F. Sigernes, and L. H. Pettersson, “Remote sensing in the Barents Sea,” in Ecosystem Barents sea, E. Sakshaug, G. Johnsen, and K. Kovacs, (eds.), (Tapir Academic Press, 2009), pp. 139–166.

Wang, J.

C. Li, J. Guo, S. Chen, Y. Tang, Y. Pang, and J. Wang, “Underwater image restoration based on minimum information loss principle and optical properties of underwater imaging,” IEEE International Conference on Image Processing , ICIP, 1993–1997 (2016).

Wang, K.

K. Wang, E. Dunn, J. Tighe, and J. M. Frahm, “Combining semantic scene priors and haze removal for single image depth estimation,” in Proc. of IEEE WACV, 800–807 (2014).

Wang, T.

S. Zhang, T. Wang, J. Dong, and et al., “Underwater image enhancement via extended multi-scale Retinex,” Neurocomputing 245, 1–9 (2017).
[Crossref]

Xiao, C.

J. Yu, C. Xiao, and D. Li, “Physics-based fast single image fog removal,” Proc. IEEE ICSP 37(2), 1048–1052 (2011).

Yang, M.

M. Yang and A. Sowmya, “An underwater color image quality evaluation metric,” IEEE Trans. Image Process. 24(12), 6062–6071 (2015).
[Crossref]

Yeh, C. H.

C. H. Yeh, L. W. Kang, C. Y. Lin, and C. Y. Lin, “Efficient image/video dehazing through haze density analysis based on pixel-based dark channel prior,” Proc. IEEE ISIC 238, 14–16 (2012).

Yu, J.

J. Yu, C. Xiao, and D. Li, “Physics-based fast single image fog removal,” Proc. IEEE ICSP 37(2), 1048–1052 (2011).

Zawawi Talib, A.

K. Iqbal, R. Abdul Salam, A. Osman, and A. Zawawi Talib, “Underwater image enhancement using an integrated colour model,” Int. J. Comp. Sci. 34, 2 (2007).

Zhang, H.

B. Zheng, H. Zhang, H. Zheng, and T. A. Gulliver, “Underwater Imaging Based on Inhomogeneous Illumination,” 2011 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PacRim), 873–876 (2011).

Zhang, S.

S. Zhang, T. Wang, J. Dong, and et al., “Underwater image enhancement via extended multi-scale Retinex,” Neurocomputing 245, 1–9 (2017).
[Crossref]

Zhao, X.

Y. T. Peng, X. Zhao, and P. C. Cosman, “Single underwater image enhancement using depth estimation based on blurriness,” Image Processing (ICIP), 2015 IEEE International Conference on, IEEE (2015).

Zheng, B.

B. Zheng, H. Zhang, H. Zheng, and T. A. Gulliver, “Underwater Imaging Based on Inhomogeneous Illumination,” 2011 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PacRim), 873–876 (2011).

Zheng, H.

B. Zheng, H. Zhang, H. Zheng, and T. A. Gulliver, “Underwater Imaging Based on Inhomogeneous Illumination,” 2011 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PacRim), 873–876 (2011).

Zhu, J. Y.

J. Y. Zhu, T. Park, and P. Isola, et al., “Unpaired image-to-image translation using cycle-consistent adversarial networks,” arXiv preprint, (2017).

Zhuang, P.

X. Fu, P. Zhuang, Y. Huang, and et al., “A retinex-based enhancing approach for single underwater image, “ Image Processing (ICIP), 2014 IEEE International Conference on., IEEE, 4572–4576 (2014).

ACM Trans. Graphics (1)

R. Fattal, “Single image dehazing,” ACM Trans. Graphics 27(3), 1 (2008).
[Crossref]

Acta Opt. Sin. (1)

Y. Nie and Z. Y. He, “Underwater imaging and real-time optical image processing under illumination by light sources with different wavelengths,” Acta Opt. Sin. 34(7), 0710002 (2014).
[Crossref]

Appl. Opt. (1)

Eng. Appl. Artif. Intell. (1)

F. C. Cheng, C. C. Cheng, P. H. Lin, and S. C. Huang, “A hierarchical airlight estimation method for image fog removal,” Eng. Appl. Artif. Intell. 43, 27–34 (2015).
[Crossref]

Expert Syst. Appl. (1)

A. T. Çelebi and S. Ertürk, “Visual enhancement of underwater images using Empirical Mode Decomposition,” Expert Syst. Appl. 39(1), 800–805 (2012).
[Crossref]

ICES J. Mar. Sci. (1)

T. Johnsen, H. A. Bouman, S. Sathyendranath, and E. Devred, “Regional-scale changes in diatom distribution in the Humboldt upwelling system as revealed by remote sensing: implications for fisheries,” ICES J. Mar. Sci. 68(4), 729–736 (2011).
[Crossref]

IEEE J. Oceanic Eng. (1)

J. S. Jaffe, “Underwater optical imaging: The past, the present, and the prospects,” IEEE J. Oceanic Eng. 40(3), 683–700 (2015).
[Crossref]

IEEE Robot. Autom. Lett. (1)

J. Li, K. A. Skinner, R. M. Eustice, and et al., “WaterGAN: Unsupervised generative network to enable real-time color correction of monocular underwater images,” IEEE Robot. Autom. Lett. 3(1), 387–394 (2018).
[Crossref]

IEEE Signal Process. Lett. (1)

C. Li, J. Guo, and C. Guo, “Emerging from water: Underwater image color correction based on weakly supervised color transfer,” IEEE Signal Process. Lett. 25(3), 323–327 (2018).
[Crossref]

IEEE Trans. Image Process. (5)

J. Y. Chiang and Y. C. Chen, “Underwater image enhancement by wavelength compensation and dehazing,” IEEE Trans. Image Process. 21(4), 1756–1769 (2012).
[Crossref]

Y. T. Peng and P. C. Cosman, “Underwater image restoration based on image blurriness and light absorption,” IEEE Trans. Image Process. 26(4), 1579–1594 (2017).
[Crossref]

C. O. Ancuti, C. Ancuti, C. DeVleeschouwer, and P. Bekaert, “Color balance and fusion for underwater image enhancement,” IEEE Trans. Image Process. 27(1), 379–393 (2018).
[Crossref]

K. B. Gibson, D. T. Vo, and T. Q. Nguyen, “An investigation of dehazing effects on image and video coding,” IEEE Trans. Image Process. 21(2), 662–673 (2012).
[Crossref]

M. Yang and A. Sowmya, “An underwater color image quality evaluation metric,” IEEE Trans. Image Process. 24(12), 6062–6071 (2015).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (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]

Int. J. Comp. Sci. (1)

K. Iqbal, R. Abdul Salam, A. Osman, and A. Zawawi Talib, “Underwater image enhancement using an integrated colour model,” Int. J. Comp. Sci. 34, 2 (2007).

Int. J. Emerg. Technol. Adv. Eng. (1)

R. Rai, P. Gour, and B. Singh, “Underwater Image Segmentation using CLAHE Enhancement and Thresholding,” Int. J. Emerg. Technol. Adv. Eng. 2(1), 118–123 (2012).

J. Vis. Commun. Image Rep. (1)

A. Galdran, D. Pardo, A. Picón, and A. Alvarez-Gila, “Automatic Red-Channel underwater image restoration,” J. Vis. Commun. Image Rep. 26, 132–145 (2015).
[Crossref]

Limnol. Oceanogr. (2)

C. L. Gallegos, D. L. Correll, and J. W. Pierce, “Modeling spectral diffuse attenuation, absorption, and scattering coefficients in a turbid estuary,” Limnol. Oceanogr. 35(7), 1486–1502 (1990).
[Crossref]

R. J. Davies-Colley, “Measuring water clarity with a black disk,” Limnol. Oceanogr. 33(4), 616–623 (1988).
[Crossref]

Neurocomputing (1)

S. Zhang, T. Wang, J. Dong, and et al., “Underwater image enhancement via extended multi-scale Retinex,” Neurocomputing 245, 1–9 (2017).
[Crossref]

Ocean Optics (1)

B. L. McGlamery, “A computer model for underwater camera systems,” Ocean Optics 0208, 221–231 (1980).
[Crossref]

Pattern Recognit. Image Anal. (1)

J. Åhlén, D. Sundgren, and E. Bengtsson, “Application of underwater hyper spectral data for color correction purposes,” Pattern Recognit. Image Anal. 17(1), 170–173 (2007).
[Crossref]

Proc. IEEE ICSP (1)

J. Yu, C. Xiao, and D. Li, “Physics-based fast single image fog removal,” Proc. IEEE ICSP 37(2), 1048–1052 (2011).

Proc. IEEE ISIC (1)

C. H. Yeh, L. W. Kang, C. Y. Lin, and C. Y. Lin, “Efficient image/video dehazing through haze density analysis based on pixel-based dark channel prior,” Proc. IEEE ISIC 238, 14–16 (2012).

Other (23)

R. T. Tan, “Visibility in bad weather from a single image,” in Proc. of IEEE CVPR, 1–8 (2008).

K. Wang, E. Dunn, J. Tighe, and J. M. Frahm, “Combining semantic scene priors and haze removal for single image depth estimation,” in Proc. of IEEE WACV, 800–807 (2014).

Imatest, Accessed: Jan. 3, 2015. [Online]. Available: http://www.imatest.com/ .

F. Petit, A.-S. Capelle-Laize, and P. Carre, “Underwater image enhancement by attenuation inversion with quaternions,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP ‘09), 1177–1180, (2009).

G. Dudek, “Color correction of underwater images for aquatic robot inspection,” International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition Springer, Berlin, Heidelberg, 60–73 (2005).

C. O. Ancuti, C. Ancuti, T. Haber, and P. Bekaert, “Enhancing underwater image and videos by fusion,” In Proc. CVPR, 81–88 (2012).

K. Iqbal, M. Odetayo, A. James, and R. Abdul Salam, “Enhancing the low quality images using unsupervised colour correction method,’’ in IEEE International Conference on Systems Man and Cybernetics (SMC) (2010).

X. Fu, P. Zhuang, Y. Huang, and et al., “A retinex-based enhancing approach for single underwater image, “ Image Processing (ICIP), 2014 IEEE International Conference on., IEEE, 4572–4576 (2014).

D. Jia and Y. Ge, “Underwater Image De-Noising Algorithm Based On Nonsubsampled Contourlet Transform And Total Variation,” 2012 International Conference on Computer Science and Information Processing (CSIP), 76–80 (2012).

A. Arnold-Bos, J. P. Malkasse, and G. Kerven, “A preprocessing framework for automatic underwater images denoising,” in Proceedings of the European Conference on Propagation and Systems, Brest, France (2005).

S. Bazeille, I. Quidu, L. Jaulin, and J. P. Malkasse, “Automatic underwater image pre-processing,” in Proceedings of the Characterizations du Milieu Marin (CMM ‘06), 16–19 (2006).

M. Chambah, D. Semani, A. Renouf, P. Courtellemont, and A. Rizzi, “Underwater color constancy: enhancement of automatic live fish recognition,” in Color Imaging IX: Processing, Hardcopy, and Applications, Proceedings of SPIE, 5293, 157–168 (2003).

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Figures (14)

Fig. 1.
Fig. 1. The underwater imaging model.
Fig. 2.
Fig. 2. Fitted directional angles of the brightness of the background image: (a) column average intensity, (b) column cumulative intensity.
Fig. 3.
Fig. 3. The relationship between the background pixels and dark channel maximum area of the offshore underwater images. (a) The histogram of the ratios of the maximum area in the dark channel belonging to the true background light in 300 underwater images. (b) The histogram of the pixel values in the maximum area of the dark channel divided by the global maxima of the dark channel in 300 underwater images.
Fig. 4.
Fig. 4. Illuminance measurement.
Fig. 5.
Fig. 5. Illuminance distribution of the target panel under natural lighting conditions.
Fig. 6.
Fig. 6. The R-channel luminance distribution of the background areas in underwater images. (a)-(c) The original underwater background images, (d)-(f) the fitted R-channel luminance in the 3D view, (g)-(i) the fitted R-channel luminance in the plan view.
Fig. 7.
Fig. 7. Luminance distributions of the middle row in R, G, and B channels of the offshore underwater background images.
Fig. 8.
Fig. 8. The structure of the ANN model for the background light recognition.
Fig. 9.
Fig. 9. Examples of the background light estimation. (a) The original images, (b) the images obtained by the method proposed by Galdran et al. [26], (c) the images obtained by the method proposed by Peng et al. [28], (d) the images obtained by the method proposed by Li et al. [31] and (e) the images obtained by using our MLBE method.
Fig. 10.
Fig. 10. Comparisons of underwater image restoration results, from the up to the down are: original images, results of cited methods and improved results with MLBE used.
Fig. 11.
Fig. 11. Comparisons of underwater image restoration results, from the left to the right are: original images, results of cited methods and improved results with MLBE used.
Fig. 12.
Fig. 12. Tank and targets.
Fig. 13.
Fig. 13. Comparisons of underwater ColorChecker chart restorations results, from the left to the right are: original images, results of original methods and improved results with MLBE used.
Fig. 14.
Fig. 14. Comparisons of underwater Imatest SFRplus restorations results, from the left to the right are: original images, results of original methods and improved results with MLBE used.

Tables (3)

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Table 1. Quantitative Measurement Results

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Table 2. Imatest 4.3 SFR Analysis

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Table 3. Imatest 4.3 ColorChecker Analysis

Equations (28)

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E d = J c ( x ) e p λ d ( x ) ,
p λ = a λ + b λ .
t c ( x ) = e p λ d ( x ) .
E b ( x ) = B c ( x ) ( 1 e p λ d ( x ) ) ,
I c ( x ) = J c ( x ) t c ( x ) + ( 1 t c ( x ) ) B c ( x ) .
J c ( x ) = I c ( x ) B c ( x ) t c ( x ) + B c ( x ) .
L D C = min y Ω ( x ) ( min c R , G , B I c ( y ) ) ,
min y Ω ( x ) ( min c R , G , B J c ( y ) ) = 0.
L D C = B ~ c ( x ) ( 1 t ~ c ( x ) ) ,
B ~ c ( x ) = I c ( arg max x B s 0.1 % | I R ( x ) I B ( x ) | ) .
B ~ c ( x ) = ( I R ( x 0 ) , I G ( x 0 ) , I B ( x 0 ) ) I R ( x 0 ) I R ( x ) x .
B ~ c ( x ) = I c ( arg min x t ~ c ( x ) ) .
B ~ c ( x ) = 1 | S 0.1 | x S 0.1 I c ( x ) ,
B ~ c ( x ) = max y M D C Ψ ( x ) ( min z Ω ( y ) I c ( z ) ) ,
x D C ( i ) = { R D C ( i ) , G D C ( i ) , B D C ( i ) , V R G B ( i ) , V D C ( i ) , L D C ( i ) } .
{ B ~ c ( x ) = I c ( x ) , x M D C y ( i ) = 1 B ~ c ( x ) x N M D C y ( i ) = 1 i = M e a n z M D C y ( i ) = 1 ( I c ( z ) ) , o t h e r w i s e ,
t ~ c ( x ) = 1 min y Ω ( x ) ( min c { R , G , B } I c ( y ) B ~ c ( y ) ) .
D ( x ) = max x Ω , c R I c ( x ) max x Ω , c { G , B } I c ( x ) .
t ~ c ( x ) = D ( x ) + ( 1 max x D ( x ) ) .
t ~ c ( x ) = 1 min ( min y Ω ( x ) ( 1 I R ( y ) ) 1 B ~ R , min y Ω ( x ) I G ( y ) B ~ G , min y Ω ( x ) I B ( y ) B ~ B ) .
B ( x ) = 1 n i = 1 n ( | I ( x ) G r i , r i ( x ) | ) .
t ~ c ( x ) = max y Ω ( x ) B ( y ) .
t ~ R ( x ) max [ min y Ω ( x ) ( I R ( y ) B ~ R B ~ R ) , max y B s ( I R ( y ) B ~ R 255 B ~ R ) ] .
t ~ c ( x ) = ( t R ( x ) ) p c / p R , c { G , B } ,
p c p R = b c B ~ R b R B ~ c ,
b c = ( 0.00113 λ c + 1.62517 ) b ( 555 n m ) .
Δ E ab = ( ( L 2 L 1 ) 2 + ( a 2 a 1 ) 2 + ( b 2 b 1 ) 2 ) 1 / 2 ,
Δ C ab = ( ( a 2 a 1 ) 2 + ( b 2 b 1 ) 2 ) 1 / 2 ,

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