Abstract

Acquisition of spectral information of objects being imaged through the use of sensor responses is important to reproduce color images under various illuminations. In the past several models have been proposed to recover the spectral reflectances from sensor responses. The accuracy of the spectral reflectances recovered by five different models is compared by using multispectral cameras. It is shown that the Wiener estimation that uses the noise variance estimated as proposed in IEEE Trans. Image Process. 15, 1848 (2006) recovers the spectral reflectances more accurately than the others when the test samples are different from learning samples.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  4. H. C. Lee, E. J. Breneman, and C. P. Schulte, "Modeling light reflection for computer color vision," IEEE Trans. Pattern Anal. Mach. Intell. 12, 79-86 (1990).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  8. J. Ho, B. V. Funt, and M. S. Drew, "Separating a color signal into illumination and surface reflectance components: theory and applications," IEEE Trans. Pattern Anal. Mach. Intell. 12, 966-977 (1990).
    [CrossRef]
  9. G. Iverson and M. D'Zumura, "Criteria for color constancy in trichromatic linear models," J. Opt. Soc. Am. A 11, 1970-1975 (1994).
    [CrossRef]
  10. A. Rosenfeld and A. C. Kak, Digital Picture Processing, 2nd ed. (Academic, 1982).
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. J. P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, "Characteristic spectra of Munsell colors," J. Opt. Soc. Am. A 6, 318-322 (1989).
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    [CrossRef]
  17. A. A. Afifi and S. P. Azen, Statistical Analysis, (Academic, 1972), Chap. 3.
  18. Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, "Using the matrix R method for spectral image archives," in Proceedings of The 10th Congress of the International Colour Association(AIC'5) (International Colour Association, 2005), pp. 469-472.
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    [CrossRef]
  20. D. Connah, J. Y. Hardeberg, and S. Westland, "Comparison of linear spectral reconstruction methods for multispectral imaging," Proceedings of IEEE's International Conference on Image Processing (IEEE, 2004), pp. 1497-1500.
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    [CrossRef]
  23. J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. H. Andrés, and J. Romero, "Multispectral synthesis of daylight using a commercial digital CCD camera," Appl. Opt. 44, 5696-5703 (2005).
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  26. M. A. López-Álvarez, J. Hernández-Andrés, Eva. M. Valero, and J. Romero, "Selecting algorithms, sensors and linear bases for optimum spectral recovery of skylight," J. Opt. Soc. Am. A 24, 942-956 (2007).
    [CrossRef]
  27. V. Cheung, S. Westland, C. Li, J. Hardeberg, and D. Connah, "Characterization of trichromatic color cameras by using a new multispectral imaging technique," J. Opt. Soc. Am. A 22, 1231-1240 (2005).
    [CrossRef]
  28. M. Shi and G. Healey, "Using reflectance models for color scanner calibration," J. Opt. Soc. Am. A 19, 645-656 (2002).
    [CrossRef]
  29. F. H. Imai, R. S. Berns, and D.-Y. Tzeng, "A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system," J. Imaging Sci. Technol. 44, 280-287 (2000).
  30. G. D. Finlayson and P. Morovic, "Metamer sets," J. Opt. Soc. Am. A 22, 810-819 (2006).
    [CrossRef]
  31. P. Morovic and G. D. Finlayson, "Metamer-set-based approach to estimating surface reflectance from camera RGB," J. Opt. Soc. Am. A 23, 1814-1822 (2006).
    [CrossRef]
  32. A. Alsam and D. Connah, "Recovering natural reflectances with convexity," Proceedings of the 10th Congress of the International Colour Association (AIC'5) (International Colour Association, 2005), pp. 1677-1680.
  33. A. Mansouri, F. S. Marzani, and P. Gouton, "Neural networks in two cascade algorithms for spectral reflectance reconstruction," in Proceedings of IEEE International Conference on Image Processing (IEEE, 2005), pp. 2053-2056.
  34. N. Shimano, "Recovery of spectral reflectances of an art painting without prior knowledge of objects being imaged," in Proceedings of The 10th Congress of the International Colour Association (International Color Association, 2005), pp. 375-378.
  35. N. Shimano, "Estimation of noise variance of a multispectral image acquisition system," Proc. SPIE 6062, 60620B-1-60620B-8 (2006).
  36. N. Shimano, "Recovery of spectral reflectances of objects being imaged without prior knowledge," IEEE Trans. Image Process. 15, 1848-1856 (2006).
    [CrossRef] [PubMed]
  37. G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, 1996), p. 55.
  38. N. Shimano, "Suppresion of noise effects in color correction by spectral sensitivities of image sensors," Opt. Rev. 8, 71-77 (2002).
    [CrossRef]
  39. N. Shimano, "Application of a colorimetric evaluation model to multispectral color image acquisition systems," J. Imaging Sci. Technol. 49, 588-593 (2006).
  40. N. Shimano, "Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise," Opt. Eng. 45, 013201 (2006).
    [CrossRef]

2007 (1)

2006 (7)

G. D. Finlayson and P. Morovic, "Metamer sets," J. Opt. Soc. Am. A 22, 810-819 (2006).
[CrossRef]

P. Morovic and G. D. Finlayson, "Metamer-set-based approach to estimating surface reflectance from camera RGB," J. Opt. Soc. Am. A 23, 1814-1822 (2006).
[CrossRef]

N. Shimano, "Estimation of noise variance of a multispectral image acquisition system," Proc. SPIE 6062, 60620B-1-60620B-8 (2006).

N. Shimano, "Recovery of spectral reflectances of objects being imaged without prior knowledge," IEEE Trans. Image Process. 15, 1848-1856 (2006).
[CrossRef] [PubMed]

H. L. Shen and H. H. Xin, "Spectral characterization of a color scanner based on optimized adaptive estimation," J. Opt. Soc. Am. A 23, 1566-1569 (2006).
[CrossRef]

N. Shimano, "Application of a colorimetric evaluation model to multispectral color image acquisition systems," J. Imaging Sci. Technol. 49, 588-593 (2006).

N. Shimano, "Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise," Opt. Eng. 45, 013201 (2006).
[CrossRef]

2005 (3)

2002 (3)

M. Shi and G. Healey, "Using reflectance models for color scanner calibration," J. Opt. Soc. Am. A 19, 645-656 (2002).
[CrossRef]

K. Martinez, J. Cupitt, D. Saunders, and R. Pillay, "Ten years of art imaging research," Proc. IEEE 90, 28-41 (2002).
[CrossRef]

N. Shimano, "Suppresion of noise effects in color correction by spectral sensitivities of image sensors," Opt. Rev. 8, 71-77 (2002).
[CrossRef]

2000 (2)

F. H. Imai, R. S. Berns, and D.-Y. Tzeng, "A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system," J. Imaging Sci. Technol. 44, 280-287 (2000).

H. Haneishi, T. Hasegawa, N. A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, "System design for accurately estimating the spectral reflectance of art paintings," Appl. Opt. 39, 6621-6632 (2000).
[CrossRef]

1998 (1)

Y. Miyake and Y. Yokoyama, "Obtaining and reproduction of accurate color images based on human perception," Proc. SPIE 3300, 190-197 (1998).
[CrossRef]

1997 (1)

G. Sharma and H. J. Trussell, "Figures of merit for color scanners," IEEE Trans. Image Process. 6, 990-1001 (1997).
[CrossRef] [PubMed]

1994 (2)

1992 (1)

1990 (3)

G. J. Klinker, S. A. Shafer, and T. Kanade, "A physical approach to color image understanding," Int. J. Comput. Vis. 4, 7-38 (1990).
[CrossRef]

H. C. Lee, E. J. Breneman, and C. P. Schulte, "Modeling light reflection for computer color vision," IEEE Trans. Pattern Anal. Mach. Intell. 12, 79-86 (1990).
[CrossRef]

J. Ho, B. V. Funt, and M. S. Drew, "Separating a color signal into illumination and surface reflectance components: theory and applications," IEEE Trans. Pattern Anal. Mach. Intell. 12, 966-977 (1990).
[CrossRef]

1989 (1)

1986 (2)

1964 (1)

J. Cohen, "Dependency of spectral reflectance curves of the Munsell color chips," Psychon. Sci. 1, 369-370 (1964).

Afifi, A. A.

A. A. Afifi and S. P. Azen, Statistical Analysis, (Academic, 1972), Chap. 3.

Alsam, A.

A. Alsam and D. Connah, "Recovering natural reflectances with convexity," Proceedings of the 10th Congress of the International Colour Association (AIC'5) (International Colour Association, 2005), pp. 1677-1680.

Andrés, J. H.

Azen, S. P.

A. A. Afifi and S. P. Azen, Statistical Analysis, (Academic, 1972), Chap. 3.

Berns, R. S.

F. H. Imai, R. S. Berns, and D.-Y. Tzeng, "A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system," J. Imaging Sci. Technol. 44, 280-287 (2000).

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, "Using the matrix R method for spectral image archives," in Proceedings of The 10th Congress of the International Colour Association(AIC'5) (International Colour Association, 2005), pp. 469-472.

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, "Methods of spectral reflectance reconstruction for a Sinarback 54 digital camera," Munsell Color Science Laboratory Technical Report December 2004, (Munsell Color Science Laboratory, 2004), pp. 1-36.

F. H. Imai and R. S. Berns, "Spectral estimation using trichromatic digital cameras," in Proceedings of International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives, (Society of Multispectral Imaging, 1999), pp. 42-49.

Breneman, E. J.

H. C. Lee, E. J. Breneman, and C. P. Schulte, "Modeling light reflection for computer color vision," IEEE Trans. Pattern Anal. Mach. Intell. 12, 79-86 (1990).
[CrossRef]

Cheung, V.

Cohen, J.

J. Cohen, "Dependency of spectral reflectance curves of the Munsell color chips," Psychon. Sci. 1, 369-370 (1964).

Connah, D.

D. Connah and J. Y. Hardeberg, "Spectral recovery using polynomial models," Proc. SPIE 5667, 65-75 (2005).
[CrossRef]

V. Cheung, S. Westland, C. Li, J. Hardeberg, and D. Connah, "Characterization of trichromatic color cameras by using a new multispectral imaging technique," J. Opt. Soc. Am. A 22, 1231-1240 (2005).
[CrossRef]

A. Alsam and D. Connah, "Recovering natural reflectances with convexity," Proceedings of the 10th Congress of the International Colour Association (AIC'5) (International Colour Association, 2005), pp. 1677-1680.

D. Connah, J. Y. Hardeberg, and S. Westland, "Comparison of linear spectral reconstruction methods for multispectral imaging," Proceedings of IEEE's International Conference on Image Processing (IEEE, 2004), pp. 1497-1500.

Cupitt, J.

K. Martinez, J. Cupitt, D. Saunders, and R. Pillay, "Ten years of art imaging research," Proc. IEEE 90, 28-41 (2002).
[CrossRef]

Daniel, J. W.

B. Noble and J. W. Daniel, Applied Linear Algebra, 3rd. ed (Prentice-Hall, 1988), pp. 338-346.

Dannemiller, J. L.

Drew, M. S.

J. Ho, B. V. Funt, and M. S. Drew, "Separating a color signal into illumination and surface reflectance components: theory and applications," IEEE Trans. Pattern Anal. Mach. Intell. 12, 966-977 (1990).
[CrossRef]

D'Zumura, M.

Fairchild, M. D.

M. D. Fairchild, Color Appearance Models (Addison-Wesley, 1997).

Finlayson, G. D.

Funt, B. V.

J. Ho, B. V. Funt, and M. S. Drew, "Separating a color signal into illumination and surface reflectance components: theory and applications," IEEE Trans. Pattern Anal. Mach. Intell. 12, 966-977 (1990).
[CrossRef]

Golub, G. H.

G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, 1996), p. 55.

Gouton, P.

A. Mansouri, F. S. Marzani, and P. Gouton, "Neural networks in two cascade algorithms for spectral reflectance reconstruction," in Proceedings of IEEE International Conference on Image Processing (IEEE, 2005), pp. 2053-2056.

Hallikainen, J.

Haneishi, H.

Hardeberg, J.

Hardeberg, J. Y.

D. Connah and J. Y. Hardeberg, "Spectral recovery using polynomial models," Proc. SPIE 5667, 65-75 (2005).
[CrossRef]

D. Connah, J. Y. Hardeberg, and S. Westland, "Comparison of linear spectral reconstruction methods for multispectral imaging," Proceedings of IEEE's International Conference on Image Processing (IEEE, 2004), pp. 1497-1500.

Hasegawa, T.

Healey, G.

Hernández-Andrés, J.

Ho, J.

J. Ho, B. V. Funt, and M. S. Drew, "Separating a color signal into illumination and surface reflectance components: theory and applications," IEEE Trans. Pattern Anal. Mach. Intell. 12, 966-977 (1990).
[CrossRef]

Hosoi, N. A.

Imai, F. H.

F. H. Imai, R. S. Berns, and D.-Y. Tzeng, "A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system," J. Imaging Sci. Technol. 44, 280-287 (2000).

F. H. Imai and R. S. Berns, "Spectral estimation using trichromatic digital cameras," in Proceedings of International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives, (Society of Multispectral Imaging, 1999), pp. 42-49.

Iverson, G.

Jaaskelainen, T.

Kak, A. C.

A. Rosenfeld and A. C. Kak, Digital Picture Processing, 2nd ed. (Academic, 1982).

Kanade, T.

G. J. Klinker, S. A. Shafer, and T. Kanade, "A physical approach to color image understanding," Int. J. Comput. Vis. 4, 7-38 (1990).
[CrossRef]

Klinker, G. J.

G. J. Klinker, S. A. Shafer, and T. Kanade, "A physical approach to color image understanding," Int. J. Comput. Vis. 4, 7-38 (1990).
[CrossRef]

Lee, H. C.

H. C. Lee, E. J. Breneman, and C. P. Schulte, "Modeling light reflection for computer color vision," IEEE Trans. Pattern Anal. Mach. Intell. 12, 79-86 (1990).
[CrossRef]

Li, C.

Loan, C. F. V.

G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, 1996), p. 55.

López-Álvarez, M. A.

Maloney, L. T.

Mansouri, A.

A. Mansouri, F. S. Marzani, and P. Gouton, "Neural networks in two cascade algorithms for spectral reflectance reconstruction," in Proceedings of IEEE International Conference on Image Processing (IEEE, 2005), pp. 2053-2056.

Martinez, K.

K. Martinez, J. Cupitt, D. Saunders, and R. Pillay, "Ten years of art imaging research," Proc. IEEE 90, 28-41 (2002).
[CrossRef]

Marzani, F. S.

A. Mansouri, F. S. Marzani, and P. Gouton, "Neural networks in two cascade algorithms for spectral reflectance reconstruction," in Proceedings of IEEE International Conference on Image Processing (IEEE, 2005), pp. 2053-2056.

Miyake, Y.

Morovic, P.

Nascimento, S. M. C.

Nezamabadi, M.

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, "Methods of spectral reflectance reconstruction for a Sinarback 54 digital camera," Munsell Color Science Laboratory Technical Report December 2004, (Munsell Color Science Laboratory, 2004), pp. 1-36.

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, "Using the matrix R method for spectral image archives," in Proceedings of The 10th Congress of the International Colour Association(AIC'5) (International Colour Association, 2005), pp. 469-472.

Nieves, J. L.

Noble, B.

B. Noble and J. W. Daniel, Applied Linear Algebra, 3rd. ed (Prentice-Hall, 1988), pp. 338-346.

Parkkinen, J. P. S.

Pillay, R.

K. Martinez, J. Cupitt, D. Saunders, and R. Pillay, "Ten years of art imaging research," Proc. IEEE 90, 28-41 (2002).
[CrossRef]

Romero, J.

Rosenfeld, A.

A. Rosenfeld and A. C. Kak, Digital Picture Processing, 2nd ed. (Academic, 1982).

Saunders, D.

K. Martinez, J. Cupitt, D. Saunders, and R. Pillay, "Ten years of art imaging research," Proc. IEEE 90, 28-41 (2002).
[CrossRef]

Schulte, C. P.

H. C. Lee, E. J. Breneman, and C. P. Schulte, "Modeling light reflection for computer color vision," IEEE Trans. Pattern Anal. Mach. Intell. 12, 79-86 (1990).
[CrossRef]

Shafer, S. A.

G. J. Klinker, S. A. Shafer, and T. Kanade, "A physical approach to color image understanding," Int. J. Comput. Vis. 4, 7-38 (1990).
[CrossRef]

Sharma, G.

G. Sharma and H. J. Trussell, "Figures of merit for color scanners," IEEE Trans. Image Process. 6, 990-1001 (1997).
[CrossRef] [PubMed]

Shen, H. L.

Shi, M.

Shimano, N.

N. Shimano, "Estimation of noise variance of a multispectral image acquisition system," Proc. SPIE 6062, 60620B-1-60620B-8 (2006).

N. Shimano, "Recovery of spectral reflectances of objects being imaged without prior knowledge," IEEE Trans. Image Process. 15, 1848-1856 (2006).
[CrossRef] [PubMed]

N. Shimano, "Application of a colorimetric evaluation model to multispectral color image acquisition systems," J. Imaging Sci. Technol. 49, 588-593 (2006).

N. Shimano, "Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise," Opt. Eng. 45, 013201 (2006).
[CrossRef]

N. Shimano, "Suppresion of noise effects in color correction by spectral sensitivities of image sensors," Opt. Rev. 8, 71-77 (2002).
[CrossRef]

N. Shimano, "Recovery of spectral reflectances of an art painting without prior knowledge of objects being imaged," in Proceedings of The 10th Congress of the International Colour Association (International Color Association, 2005), pp. 375-378.

Slater, D.

Taplin, L. A.

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, "Using the matrix R method for spectral image archives," in Proceedings of The 10th Congress of the International Colour Association(AIC'5) (International Colour Association, 2005), pp. 469-472.

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, "Methods of spectral reflectance reconstruction for a Sinarback 54 digital camera," Munsell Color Science Laboratory Technical Report December 2004, (Munsell Color Science Laboratory, 2004), pp. 1-36.

Trussell, H. J.

G. Sharma and H. J. Trussell, "Figures of merit for color scanners," IEEE Trans. Image Process. 6, 990-1001 (1997).
[CrossRef] [PubMed]

Tsumura, N.

Tzeng, D.-Y.

F. H. Imai, R. S. Berns, and D.-Y. Tzeng, "A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system," J. Imaging Sci. Technol. 44, 280-287 (2000).

Valero, E. M.

Valero, Eva. M.

Wandell, B. A.

Westland, S.

V. Cheung, S. Westland, C. Li, J. Hardeberg, and D. Connah, "Characterization of trichromatic color cameras by using a new multispectral imaging technique," J. Opt. Soc. Am. A 22, 1231-1240 (2005).
[CrossRef]

D. Connah, J. Y. Hardeberg, and S. Westland, "Comparison of linear spectral reconstruction methods for multispectral imaging," Proceedings of IEEE's International Conference on Image Processing (IEEE, 2004), pp. 1497-1500.

Xin, H. H.

Yokoyama, Y.

Zhao, Y.

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, "Using the matrix R method for spectral image archives," in Proceedings of The 10th Congress of the International Colour Association(AIC'5) (International Colour Association, 2005), pp. 469-472.

Y. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, "Methods of spectral reflectance reconstruction for a Sinarback 54 digital camera," Munsell Color Science Laboratory Technical Report December 2004, (Munsell Color Science Laboratory, 2004), pp. 1-36.

Appl. Opt. (2)

IEEE Trans. Image Process. (2)

N. Shimano, "Recovery of spectral reflectances of objects being imaged without prior knowledge," IEEE Trans. Image Process. 15, 1848-1856 (2006).
[CrossRef] [PubMed]

G. Sharma and H. J. Trussell, "Figures of merit for color scanners," IEEE Trans. Image Process. 6, 990-1001 (1997).
[CrossRef] [PubMed]

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

H. C. Lee, E. J. Breneman, and C. P. Schulte, "Modeling light reflection for computer color vision," IEEE Trans. Pattern Anal. Mach. Intell. 12, 79-86 (1990).
[CrossRef]

J. Ho, B. V. Funt, and M. S. Drew, "Separating a color signal into illumination and surface reflectance components: theory and applications," IEEE Trans. Pattern Anal. Mach. Intell. 12, 966-977 (1990).
[CrossRef]

Int. J. Comput. Vis. (1)

G. J. Klinker, S. A. Shafer, and T. Kanade, "A physical approach to color image understanding," Int. J. Comput. Vis. 4, 7-38 (1990).
[CrossRef]

J. Imaging Sci. Technol. (2)

N. Shimano, "Application of a colorimetric evaluation model to multispectral color image acquisition systems," J. Imaging Sci. Technol. 49, 588-593 (2006).

F. H. Imai, R. S. Berns, and D.-Y. Tzeng, "A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system," J. Imaging Sci. Technol. 44, 280-287 (2000).

J. Opt. Soc. Am. A (12)

G. D. Finlayson and P. Morovic, "Metamer sets," J. Opt. Soc. Am. A 22, 810-819 (2006).
[CrossRef]

P. Morovic and G. D. Finlayson, "Metamer-set-based approach to estimating surface reflectance from camera RGB," J. Opt. Soc. Am. A 23, 1814-1822 (2006).
[CrossRef]

H. L. Shen and H. H. Xin, "Spectral characterization of a color scanner based on optimized adaptive estimation," J. Opt. Soc. Am. A 23, 1566-1569 (2006).
[CrossRef]

M. A. López-Álvarez, J. Hernández-Andrés, Eva. M. Valero, and J. Romero, "Selecting algorithms, sensors and linear bases for optimum spectral recovery of skylight," J. Opt. Soc. Am. A 24, 942-956 (2007).
[CrossRef]

V. Cheung, S. Westland, C. Li, J. Hardeberg, and D. Connah, "Characterization of trichromatic color cameras by using a new multispectral imaging technique," J. Opt. Soc. Am. A 22, 1231-1240 (2005).
[CrossRef]

M. Shi and G. Healey, "Using reflectance models for color scanner calibration," J. Opt. Soc. Am. A 19, 645-656 (2002).
[CrossRef]

L. T. Maloney and B. A. Wandell, "Color constancy: a method for recovering surface spectral reflectance," J. Opt. Soc. Am. A 3, 29-33 (1986).
[CrossRef] [PubMed]

G. Iverson and M. D'Zumura, "Criteria for color constancy in trichromatic linear models," J. Opt. Soc. Am. A 11, 1970-1975 (1994).
[CrossRef]

G. Healey and D. Slater, "Global color constancy: recognition of objects by use of illumination-invariant properties of color distributions," J. Opt. Soc. Am. A 11, 3003-3010 (1994).
[CrossRef]

L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small numbers of parameters," J. Opt. Soc. Am. A 3, 1673-1683 (1986).
[CrossRef] [PubMed]

J. P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, "Characteristic spectra of Munsell colors," J. Opt. Soc. Am. A 6, 318-322 (1989).
[CrossRef]

J. L. Dannemiller, "Spectral reflectance of natural objects: how many basis functions are necessary?" J. Opt. Soc. Am. A 9, 507-515 (1992).
[CrossRef]

Opt. Eng. (1)

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Figures (6)

Fig. 1
Fig. 1

Spectral sensitivities of a set of seven sensors used in the experiment.

Fig. 2
Fig. 2

Spectral power distribution of the Solax lamp.

Fig. 3
Fig. 3

MSE between recovered and measured spectral reflectances for the Shi–Healey model as a function of the number of basis vectors. Macbeth and Kodak represent the GretagMacbeth ColorChecker and the Kodak Q60 charts, respectively.

Fig. 4
Fig. 4

Typical examples of the spectral reflectances recovered by five different models. The recovered spectral reflectance was a patch number 13 (Blue) of the GretagMacbeth ColorChecker, using the learning samples of the Kodak Q60 and five sensors (the combination of channels 1, 2, 3, 4, and 6, where the channel number is counted from left to right in Fig. 1).

Fig. 5
Fig. 5

Typical examples of the singular values as a function of the dimension for the six-channel camera (only the first channel, the left channel in Fig. 1, was omitted) with the test samples of the GretagMacbeth ColorChecker and the learning samples of the Kodak Q60.

Fig. 6
Fig. 6

A Japanese art painting with 18 selected points used to evaluate the recovery performance.

Tables (6)

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Table 1 Required Prior Knowledge for Each Model a

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Table 2 Comparative Spectral Recovery Performance: GretagMacbeth ColorChecker Used as Samples for Both Learning and Test

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Table 3 Comparative Spectral Recovery Performance: Kodak Q60 Used as Samples for Both Test and Learning

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Table 4 Comparative Spectral Recovery Performance: Kodak Q60 Used as Samples for Learning and GretagMacbeth ColorChecker Used as Samples for Test

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Table 5 Comparative Spectral Recovery Performance: GretagMacbeth ColorChecker Used as Samples for Learning and Kodak Q60 Used as Samples for Test

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Table 6 Comparative Spectral Recovery Performance: GretagMacbeth ColorChecker Used as Samples for Learning and Japanese Art Painting Used as a Sample for Test

Equations (14)

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

p = S L r + e ,
W = R SS S L T ( S L R SS S L T + σ e 2 I ) 1 ,
Δ r = r V Λ 1 2 S L V T ( S L V S L V T + σ e 2 I ) 1 p .
E { Δ r 2 } = i = 1 N λ i i = 1 N j = 1 β λ i b i j 2 + i = 1 N j = 1 β σ e 4 + κ j v 2 σ 2 ( κ j v 2 + σ e 2 ) 2 λ i b i j 2 ,
MSE ( σ e 2 = 0 ) = i = 1 N λ i i = 1 N j = 1 β λ i b i j 2 + i = 1 N j = 1 β σ 2 κ j v 2 λ i b i j 2 .
σ ̂ 2 = MSE ( σ e 2 = 0 ) i = 1 N λ i + i = 1 N j = 1 β λ i b i j 2 i = 1 N j = 1 β λ i b i j 2 κ j v 2 .
W = R P + ,
r ̂ = ω 1 v 1 + ω 2 v 2 + + ω d v d = V ω ,
ω ̂ = ( S L V ) + p .
B = Ω P + .
p = S L V 1 ω 1 + S L V 2 ω 2 ,
r ̂ = V 1 ω 1 + V 2 ( S L V 2 ) 1 ( p S L V 1 ω 1 ) .
ω ̂ 1 = { V 1 V 2 ( S L V 2 ) 1 S L V 1 } + { r i V 2 ( S L V 2 ) 1 p } .
r ̂ = i = 1 M κ i ( s i + e i ) v i ,

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