Abstract

The problem of estimating spectral reflectances from the responses of a digital camera has received considerable attention recently. This problem can be cast as a regularized regression problem or as a statistical inversion problem. We discuss some previously suggested estimation methods based on critically undersampled RGB measurements and describe some relations between them. We concentrate mainly on those models that are using a priori information in the form of high-resolution measurements. We use the “kernel machine” framework in our evaluations and concentrate on the use of multiple illuminations and on the investigation of the performance of global and locally adapted estimation methods. We also introduce a nonlinear transformation of reflectance values to ensure that the estimated reflection spectra fulfill physically motivated boundary conditions. The reported experimental results are derived from measured and simulated camera responses from the Munsell Matte, NCS, and Pantone data sets.

© 2008 Optical Society of America

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  1. F. H. Imai and R. S. Berns, “Spectral estimation using trichromatic digital cameras,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society for Imaging Science and Technology, Society of Multispectral Imaging of Japan, 1999), pp. 42-49.
  2. J.-I. Park, M.-H. Lee, M. D. Grossberg, and S. K. Nayar, “Multispectral imaging using multiplexed illumination,” in ICCV 2007, Eleventh IEEE International Conference on Computer Vision (IEEE, 2007), pp. 14-21.
  3. J. M. Dicarlo, F. Xiao, and B. A. Wandell, “Illuminating illumination,” in The 9th Color Imaging Conference: Color Science and Engineering: Systems, Technologies, Applications (The Society for Imaging Science and Technology, Society of Multispectral Imaging of Japan, 2001), pp. 27-34.
  4. W. Menke, Geophysical Data Analysis: Discrete Inverse Theory (Academic, 1989).
  5. J. B. Cohen and W. E. Kappauf, “Metameric color stimuli, fundamental metamers and Wyszecki's metameric blacks,” Am. J. Psychol. 95, 537-564 (1982).
    [CrossRef] [PubMed]
  6. J. B. Cohen and W. E. Kappauf, “Color mixture and fundamental metamers: theory, algebra, geometry, application,” Am. J. Psychol. 98, 171-259 (1985).
    [CrossRef]
  7. P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetric characterization of novel multiple channel sensors for imaging and metrology,” J. Electron. Imaging 8, 342-353 (1999).
    [CrossRef]
  8. W. K. Pratt and C. E. Mancill, “Spectral estimation techniques for the spectral calibration of color image scanner,” Appl. Opt. 15, 73-75 (1976).
    [CrossRef] [PubMed]
  9. 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]
  10. F. Ayala, J. F. Echávarri, and P. Renet, “Use of three tristimulus values from surface reflectance spectra to calculate the principal components for reconstructing these spectra by using only three eigenvectors,” J. Opt. Soc. Am. A 23, 2020-2026 (2006).
    [CrossRef]
  11. H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, “System design for accurately estimating the reflectance spectra of art paintings,” Appl. Opt. 39, 6621-6632 (2000).
    [CrossRef]
  12. Å. Björck, Numerical Methods for Least Squares Problems (SIAM, 1996).
    [CrossRef]
  13. J. Hernández-Andrés, J. Romero, A. Garca-Beltran, and J. L. Nieves, “Testing linear models on spectral daylight measurements,” Appl. Opt. 37, 971-977 (1998).
    [CrossRef]
  14. M. A. López-Álvarez, J. Hernández-Andrés, E. 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]
  15. 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]
  16. J. Parkkinen, J. Hallikainen, and T. Jääskeläinen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318-322 (1989).
    [CrossRef]
  17. D. R. Connah and J. Y. Hardeberg, “Spectral recovery using polynomial models,” Proc. SPIE 5667, 65-75 (2005).
    [CrossRef]
  18. J. Y. Hardeberg, Acquisition and Reproduction of Color Images--Colorimetric and Multispectral Approaches (Dissertation.com, 2001).
  19. 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]
  20. T. Jetsu, V. Heikkinen, J. Parkkinen, M. Hauta-Kasari, B. Martinkauppi, S. D. Lee, H. W. Ok, and C. Y. Kim, “Color calibration of digital camera using polynomial transformation,” in CGIV, Third European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 163-166.
  21. V. Heikkinen, T. Jetsu, J. Parkkinen, M. Hauta-Kasari, Timo Jääaskeläinen, and S. D. Lee, “Regularized learning framework in estimation of reflectance spectra from camera responses,” J. Opt. Soc. Am. A 24, 2673-2683 (2007).
    [CrossRef]
  22. V. Vapnik, Statistical Learning Theory (Wiley, 1998).
  23. B. Schölkopf and A. J. Smola, Learning With Kernels (MIT, 2002).
  24. G. Wahba, Spline Models for Observational Data, Vol. 59 of SIAM CBMS-NSF Regional Conference Series in Applied Mathematics (SIAM, 1990).
    [CrossRef]
  25. T. Poggio and F. Girosi, “Networks for approximation and learning,” Proc. IEEE 78, 1481-1497 (1990).
    [CrossRef]
  26. J. M. Dicarlo and B. A. Wandell, “Spectral estimation theory: beyond linear but before Bayesian,” J. Opt. Soc. Am. A 20, 1261-1270 (2003).
    [CrossRef]
  27. T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference and Prediction (Springer-Verlag, 2001).
  28. H.-L. Shen and J. H. Xin, “Spectral characterization of a color scanner by adaptive estimation,” J. Opt. Soc. Am. A 21, 1125-1130 (2004).
    [CrossRef]
  29. H.-L. Shen and J. H. Xin, “Spectral characterization of a color scanner based on optimized adaptive estimation,” J. Opt. Soc. Am. A 23, 1566-1569 (2006).
    [CrossRef]
  30. Y. Murakami, T. Obi, M. Yamaguchi, and N. Ohyama, “Nonlinear estimation of spectral reflectance on Gaussian mixture distribution for color image reproduction,” Appl. Opt. 41, 4840-4847 (2002).
    [CrossRef] [PubMed]
  31. O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381-388 (2006).
    [CrossRef]
  32. P. L. Vora and H. J. Trussell, “Measures of goodness of a set of color scanning filters,” J. Opt. Soc. Am. A 10, 1499-1508 (1993).
    [CrossRef]
  33. G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins U. Press, 1996).
  34. M. Solli, M. Andersson, R. Lenz, and B. Kruse, “Color measurements with a consumer digital camera using spectral estimation techniques,” in Proceedings of 14th Scandinavian Conference on Image Analysis, Vol. 3540 ofLecture Notes in Computer science (Springer, 2005), pp. 110-114.
  35. N. Shimano, K. Terai, and M. Hironaga, “Recovery of spectral reflectances of objects being imaged by multispectral cameras,” J. Opt. Soc. Am. A 24, 3211-3219 (2007).
    [CrossRef]
  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. N. Ohta and A. R. Robertson, Colorimetry: Fundamentals and Applications, The Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2005).
    [CrossRef]
  38. 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]
  39. Y. Murakami, K. Letomi, M. Yamaguchi, and N. Ohyama, “Maximum a posteriori estimation of spectral reflectance from color image and multipoint spectral measurements,” Appl. Opt. 46, 7068-7082 (2007).
    [CrossRef] [PubMed]

2007 (4)

2006 (5)

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

F. Ayala, J. F. Echávarri, and P. Renet, “Use of three tristimulus values from surface reflectance spectra to calculate the principal components for reconstructing these spectra by using only three eigenvectors,” J. Opt. Soc. Am. A 23, 2020-2026 (2006).
[CrossRef]

O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381-388 (2006).
[CrossRef]

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, “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 (2)

2004 (1)

2003 (1)

2002 (1)

2000 (1)

1999 (1)

P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetric characterization of novel multiple channel sensors for imaging and metrology,” J. Electron. Imaging 8, 342-353 (1999).
[CrossRef]

1998 (1)

1993 (1)

1990 (1)

T. Poggio and F. Girosi, “Networks for approximation and learning,” Proc. IEEE 78, 1481-1497 (1990).
[CrossRef]

1989 (1)

1986 (2)

1985 (1)

J. B. Cohen and W. E. Kappauf, “Color mixture and fundamental metamers: theory, algebra, geometry, application,” Am. J. Psychol. 98, 171-259 (1985).
[CrossRef]

1982 (1)

J. B. Cohen and W. E. Kappauf, “Metameric color stimuli, fundamental metamers and Wyszecki's metameric blacks,” Am. J. Psychol. 95, 537-564 (1982).
[CrossRef] [PubMed]

1976 (1)

Andersson, M.

M. Solli, M. Andersson, R. Lenz, and B. Kruse, “Color measurements with a consumer digital camera using spectral estimation techniques,” in Proceedings of 14th Scandinavian Conference on Image Analysis, Vol. 3540 ofLecture Notes in Computer science (Springer, 2005), pp. 110-114.

Ayala, F.

Berns, R. S.

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

Björck, Å.

Å. Björck, Numerical Methods for Least Squares Problems (SIAM, 1996).
[CrossRef]

Cheung, V.

Cohen, J. B.

J. B. Cohen and W. E. Kappauf, “Color mixture and fundamental metamers: theory, algebra, geometry, application,” Am. J. Psychol. 98, 171-259 (1985).
[CrossRef]

J. B. Cohen and W. E. Kappauf, “Metameric color stimuli, fundamental metamers and Wyszecki's metameric blacks,” Am. J. Psychol. 95, 537-564 (1982).
[CrossRef] [PubMed]

Connah, D.

Connah, D. R.

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

Dicarlo, J. M.

J. M. Dicarlo and B. A. Wandell, “Spectral estimation theory: beyond linear but before Bayesian,” J. Opt. Soc. Am. A 20, 1261-1270 (2003).
[CrossRef]

J. M. Dicarlo, F. Xiao, and B. A. Wandell, “Illuminating illumination,” in The 9th Color Imaging Conference: Color Science and Engineering: Systems, Technologies, Applications (The Society for Imaging Science and Technology, Society of Multispectral Imaging of Japan, 2001), pp. 27-34.

Echávarri, J. F.

Friedman, J.

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference and Prediction (Springer-Verlag, 2001).

Garca-Beltran, A.

Girosi, F.

T. Poggio and F. Girosi, “Networks for approximation and learning,” Proc. IEEE 78, 1481-1497 (1990).
[CrossRef]

Golub, G. H.

G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins U. Press, 1996).

Grossberg, M. D.

J.-I. Park, M.-H. Lee, M. D. Grossberg, and S. K. Nayar, “Multispectral imaging using multiplexed illumination,” in ICCV 2007, Eleventh IEEE International Conference on Computer Vision (IEEE, 2007), pp. 14-21.

Hallikainen, J.

Haneishi, H.

Hardeberg, J.

Hardeberg, J. Y.

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

J. Y. Hardeberg, Acquisition and Reproduction of Color Images--Colorimetric and Multispectral Approaches (Dissertation.com, 2001).

Hasegawa, T.

Hastie, T.

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference and Prediction (Springer-Verlag, 2001).

Hauta-Kasari, M.

V. Heikkinen, T. Jetsu, J. Parkkinen, M. Hauta-Kasari, Timo Jääaskeläinen, and S. D. Lee, “Regularized learning framework in estimation of reflectance spectra from camera responses,” J. Opt. Soc. Am. A 24, 2673-2683 (2007).
[CrossRef]

T. Jetsu, V. Heikkinen, J. Parkkinen, M. Hauta-Kasari, B. Martinkauppi, S. D. Lee, H. W. Ok, and C. Y. Kim, “Color calibration of digital camera using polynomial transformation,” in CGIV, Third European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 163-166.

Heikkinen, V.

V. Heikkinen, T. Jetsu, J. Parkkinen, M. Hauta-Kasari, Timo Jääaskeläinen, and S. D. Lee, “Regularized learning framework in estimation of reflectance spectra from camera responses,” J. Opt. Soc. Am. A 24, 2673-2683 (2007).
[CrossRef]

T. Jetsu, V. Heikkinen, J. Parkkinen, M. Hauta-Kasari, B. Martinkauppi, S. D. Lee, H. W. Ok, and C. Y. Kim, “Color calibration of digital camera using polynomial transformation,” in CGIV, Third European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 163-166.

Hernández-Andrés, J.

Herzog, P. G.

P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetric characterization of novel multiple channel sensors for imaging and metrology,” J. Electron. Imaging 8, 342-353 (1999).
[CrossRef]

Hironaga, M.

Hosoi, A.

Imai, F. H.

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

Jääaskeläinen, Timo

Jääskeläinen, T.

O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381-388 (2006).
[CrossRef]

J. Parkkinen, J. Hallikainen, and T. Jääskeläinen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318-322 (1989).
[CrossRef]

Jetsu, T.

V. Heikkinen, T. Jetsu, J. Parkkinen, M. Hauta-Kasari, Timo Jääaskeläinen, and S. D. Lee, “Regularized learning framework in estimation of reflectance spectra from camera responses,” J. Opt. Soc. Am. A 24, 2673-2683 (2007).
[CrossRef]

T. Jetsu, V. Heikkinen, J. Parkkinen, M. Hauta-Kasari, B. Martinkauppi, S. D. Lee, H. W. Ok, and C. Y. Kim, “Color calibration of digital camera using polynomial transformation,” in CGIV, Third European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 163-166.

Kappauf, W. E.

J. B. Cohen and W. E. Kappauf, “Color mixture and fundamental metamers: theory, algebra, geometry, application,” Am. J. Psychol. 98, 171-259 (1985).
[CrossRef]

J. B. Cohen and W. E. Kappauf, “Metameric color stimuli, fundamental metamers and Wyszecki's metameric blacks,” Am. J. Psychol. 95, 537-564 (1982).
[CrossRef] [PubMed]

Kim, C. Y.

T. Jetsu, V. Heikkinen, J. Parkkinen, M. Hauta-Kasari, B. Martinkauppi, S. D. Lee, H. W. Ok, and C. Y. Kim, “Color calibration of digital camera using polynomial transformation,” in CGIV, Third European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 163-166.

Knipp, D.

P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetric characterization of novel multiple channel sensors for imaging and metrology,” J. Electron. Imaging 8, 342-353 (1999).
[CrossRef]

Kohonen, O.

O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381-388 (2006).
[CrossRef]

König, F.

P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetric characterization of novel multiple channel sensors for imaging and metrology,” J. Electron. Imaging 8, 342-353 (1999).
[CrossRef]

Kruse, B.

M. Solli, M. Andersson, R. Lenz, and B. Kruse, “Color measurements with a consumer digital camera using spectral estimation techniques,” in Proceedings of 14th Scandinavian Conference on Image Analysis, Vol. 3540 ofLecture Notes in Computer science (Springer, 2005), pp. 110-114.

Lee, M.-H.

J.-I. Park, M.-H. Lee, M. D. Grossberg, and S. K. Nayar, “Multispectral imaging using multiplexed illumination,” in ICCV 2007, Eleventh IEEE International Conference on Computer Vision (IEEE, 2007), pp. 14-21.

Lee, S. D.

V. Heikkinen, T. Jetsu, J. Parkkinen, M. Hauta-Kasari, Timo Jääaskeläinen, and S. D. Lee, “Regularized learning framework in estimation of reflectance spectra from camera responses,” J. Opt. Soc. Am. A 24, 2673-2683 (2007).
[CrossRef]

T. Jetsu, V. Heikkinen, J. Parkkinen, M. Hauta-Kasari, B. Martinkauppi, S. D. Lee, H. W. Ok, and C. Y. Kim, “Color calibration of digital camera using polynomial transformation,” in CGIV, Third European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 163-166.

Lenz, R.

M. Solli, M. Andersson, R. Lenz, and B. Kruse, “Color measurements with a consumer digital camera using spectral estimation techniques,” in Proceedings of 14th Scandinavian Conference on Image Analysis, Vol. 3540 ofLecture Notes in Computer science (Springer, 2005), pp. 110-114.

Letomi, K.

Li, C.

López-Álvarez, M. A.

Maloney, L. T.

Mancill, C. E.

Martinkauppi, B.

T. Jetsu, V. Heikkinen, J. Parkkinen, M. Hauta-Kasari, B. Martinkauppi, S. D. Lee, H. W. Ok, and C. Y. Kim, “Color calibration of digital camera using polynomial transformation,” in CGIV, Third European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 163-166.

Menke, W.

W. Menke, Geophysical Data Analysis: Discrete Inverse Theory (Academic, 1989).

Miyake, Y.

Murakami, Y.

Nayar, S. K.

J.-I. Park, M.-H. Lee, M. D. Grossberg, and S. K. Nayar, “Multispectral imaging using multiplexed illumination,” in ICCV 2007, Eleventh IEEE International Conference on Computer Vision (IEEE, 2007), pp. 14-21.

Nieves, J. L.

Obi, T.

Ohta, N.

N. Ohta and A. R. Robertson, Colorimetry: Fundamentals and Applications, The Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2005).
[CrossRef]

Ohyama, N.

Ok, H. W.

T. Jetsu, V. Heikkinen, J. Parkkinen, M. Hauta-Kasari, B. Martinkauppi, S. D. Lee, H. W. Ok, and C. Y. Kim, “Color calibration of digital camera using polynomial transformation,” in CGIV, Third European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 163-166.

Park, J.-I.

J.-I. Park, M.-H. Lee, M. D. Grossberg, and S. K. Nayar, “Multispectral imaging using multiplexed illumination,” in ICCV 2007, Eleventh IEEE International Conference on Computer Vision (IEEE, 2007), pp. 14-21.

Parkkinen, J.

V. Heikkinen, T. Jetsu, J. Parkkinen, M. Hauta-Kasari, Timo Jääaskeläinen, and S. D. Lee, “Regularized learning framework in estimation of reflectance spectra from camera responses,” J. Opt. Soc. Am. A 24, 2673-2683 (2007).
[CrossRef]

O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381-388 (2006).
[CrossRef]

J. Parkkinen, J. Hallikainen, and T. Jääskeläinen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318-322 (1989).
[CrossRef]

T. Jetsu, V. Heikkinen, J. Parkkinen, M. Hauta-Kasari, B. Martinkauppi, S. D. Lee, H. W. Ok, and C. Y. Kim, “Color calibration of digital camera using polynomial transformation,” in CGIV, Third European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 163-166.

Poggio, T.

T. Poggio and F. Girosi, “Networks for approximation and learning,” Proc. IEEE 78, 1481-1497 (1990).
[CrossRef]

Pratt, W. K.

Renet, P.

Robertson, A. R.

N. Ohta and A. R. Robertson, Colorimetry: Fundamentals and Applications, The Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2005).
[CrossRef]

Romero, J.

Schölkopf, B.

B. Schölkopf and A. J. Smola, Learning With Kernels (MIT, 2002).

Shen, H.-L.

Shimano, N.

N. Shimano, K. Terai, and M. Hironaga, “Recovery of spectral reflectances of objects being imaged by multispectral cameras,” J. Opt. Soc. Am. A 24, 3211-3219 (2007).
[CrossRef]

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, “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]

Smola, A. J.

B. Schölkopf and A. J. Smola, Learning With Kernels (MIT, 2002).

Solli, M.

M. Solli, M. Andersson, R. Lenz, and B. Kruse, “Color measurements with a consumer digital camera using spectral estimation techniques,” in Proceedings of 14th Scandinavian Conference on Image Analysis, Vol. 3540 ofLecture Notes in Computer science (Springer, 2005), pp. 110-114.

Stiebig, H.

P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetric characterization of novel multiple channel sensors for imaging and metrology,” J. Electron. Imaging 8, 342-353 (1999).
[CrossRef]

Terai, K.

Tibshirani, R.

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference and Prediction (Springer-Verlag, 2001).

Trussell, H. J.

Tsumura, N.

Valero, E. M.

Van Loan, C. F.

G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins U. Press, 1996).

Vapnik, V.

V. Vapnik, Statistical Learning Theory (Wiley, 1998).

Vora, P. L.

Wahba, G.

G. Wahba, Spline Models for Observational Data, Vol. 59 of SIAM CBMS-NSF Regional Conference Series in Applied Mathematics (SIAM, 1990).
[CrossRef]

Wandell, B. A.

J. M. Dicarlo and B. A. Wandell, “Spectral estimation theory: beyond linear but before Bayesian,” J. Opt. Soc. Am. A 20, 1261-1270 (2003).
[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]

J. M. Dicarlo, F. Xiao, and B. A. Wandell, “Illuminating illumination,” in The 9th Color Imaging Conference: Color Science and Engineering: Systems, Technologies, Applications (The Society for Imaging Science and Technology, Society of Multispectral Imaging of Japan, 2001), pp. 27-34.

Westland, S.

Xiao, F.

J. M. Dicarlo, F. Xiao, and B. A. Wandell, “Illuminating illumination,” in The 9th Color Imaging Conference: Color Science and Engineering: Systems, Technologies, Applications (The Society for Imaging Science and Technology, Society of Multispectral Imaging of Japan, 2001), pp. 27-34.

Xin, J. H.

Yamaguchi, M.

Yokoyama, Y.

Am. J. Psychol. (2)

J. B. Cohen and W. E. Kappauf, “Metameric color stimuli, fundamental metamers and Wyszecki's metameric blacks,” Am. J. Psychol. 95, 537-564 (1982).
[CrossRef] [PubMed]

J. B. Cohen and W. E. Kappauf, “Color mixture and fundamental metamers: theory, algebra, geometry, application,” Am. J. Psychol. 98, 171-259 (1985).
[CrossRef]

Appl. Opt. (5)

Color Res. Appl. (1)

O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381-388 (2006).
[CrossRef]

IEEE Trans. Image Process. (1)

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

J. Electron. Imaging (1)

P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetric characterization of novel multiple channel sensors for imaging and metrology,” J. Electron. Imaging 8, 342-353 (1999).
[CrossRef]

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

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]

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. Parkkinen, J. Hallikainen, and T. Jääskeläinen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318-322 (1989).
[CrossRef]

P. L. Vora and H. J. Trussell, “Measures of goodness of a set of color scanning filters,” J. Opt. Soc. Am. A 10, 1499-1508 (1993).
[CrossRef]

J. M. Dicarlo and B. A. Wandell, “Spectral estimation theory: beyond linear but before Bayesian,” J. Opt. Soc. Am. A 20, 1261-1270 (2003).
[CrossRef]

H.-L. Shen and J. H. Xin, “Spectral characterization of a color scanner by adaptive estimation,” J. Opt. Soc. Am. A 21, 1125-1130 (2004).
[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]

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

F. Ayala, J. F. Echávarri, and P. Renet, “Use of three tristimulus values from surface reflectance spectra to calculate the principal components for reconstructing these spectra by using only three eigenvectors,” J. Opt. Soc. Am. A 23, 2020-2026 (2006).
[CrossRef]

M. A. López-Álvarez, J. Hernández-Andrés, E. 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. Heikkinen, T. Jetsu, J. Parkkinen, M. Hauta-Kasari, Timo Jääaskeläinen, and S. D. Lee, “Regularized learning framework in estimation of reflectance spectra from camera responses,” J. Opt. Soc. Am. A 24, 2673-2683 (2007).
[CrossRef]

N. Shimano, K. Terai, and M. Hironaga, “Recovery of spectral reflectances of objects being imaged by multispectral cameras,” J. Opt. Soc. Am. A 24, 3211-3219 (2007).
[CrossRef]

Opt. Eng. (1)

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]

Proc. IEEE (1)

T. Poggio and F. Girosi, “Networks for approximation and learning,” Proc. IEEE 78, 1481-1497 (1990).
[CrossRef]

Proc. SPIE (1)

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

Other (14)

J. Y. Hardeberg, Acquisition and Reproduction of Color Images--Colorimetric and Multispectral Approaches (Dissertation.com, 2001).

V. Vapnik, Statistical Learning Theory (Wiley, 1998).

B. Schölkopf and A. J. Smola, Learning With Kernels (MIT, 2002).

G. Wahba, Spline Models for Observational Data, Vol. 59 of SIAM CBMS-NSF Regional Conference Series in Applied Mathematics (SIAM, 1990).
[CrossRef]

T. Jetsu, V. Heikkinen, J. Parkkinen, M. Hauta-Kasari, B. Martinkauppi, S. D. Lee, H. W. Ok, and C. Y. Kim, “Color calibration of digital camera using polynomial transformation,” in CGIV, Third European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 163-166.

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference and Prediction (Springer-Verlag, 2001).

N. Ohta and A. R. Robertson, Colorimetry: Fundamentals and Applications, The Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2005).
[CrossRef]

Å. Björck, Numerical Methods for Least Squares Problems (SIAM, 1996).
[CrossRef]

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

J.-I. Park, M.-H. Lee, M. D. Grossberg, and S. K. Nayar, “Multispectral imaging using multiplexed illumination,” in ICCV 2007, Eleventh IEEE International Conference on Computer Vision (IEEE, 2007), pp. 14-21.

J. M. Dicarlo, F. Xiao, and B. A. Wandell, “Illuminating illumination,” in The 9th Color Imaging Conference: Color Science and Engineering: Systems, Technologies, Applications (The Society for Imaging Science and Technology, Society of Multispectral Imaging of Japan, 2001), pp. 27-34.

W. Menke, Geophysical Data Analysis: Discrete Inverse Theory (Academic, 1989).

G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins U. Press, 1996).

M. Solli, M. Andersson, R. Lenz, and B. Kruse, “Color measurements with a consumer digital camera using spectral estimation techniques,” in Proceedings of 14th Scandinavian Conference on Image Analysis, Vol. 3540 ofLecture Notes in Computer science (Springer, 2005), pp. 110-114.

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Figures (7)

Fig. 1
Fig. 1

Fluorescent and tungsten illuminations.

Fig. 2
Fig. 2

RGB sensitivities weighted by fluorescent (dashed) and tungsten (solid) illuminations.

Fig. 3
Fig. 3

Gaussian sensitivity system.

Fig. 4
Fig. 4

Example of an estimate for a Munsell spectrum using Wiener and Gaussian kernel models globally. Training set, Munsell I; illumination, tungsten.

Fig. 5
Fig. 5

Example of an estimate for a Munsell spectrum using Wiener and Gaussian kernel models globally. Training set, Pantone; illumination, tungsten.

Fig. 6
Fig. 6

Example of an estimate for a Munsell spectrum using Wiener and Gaussian kernel models globally. Training set, Pantone; illumination, tungsten and fluorescent.

Fig. 7
Fig. 7

Example of an estimate for a Munsell spectrum using Wiener and Gaussian kernel models globally. Training set, Pantone; illumination, tungsten and fluorescent.

Tables (10)

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Table 1 Similarities of Subspaces of Used Sets, Where k Denotes the Dimension of the Subspace a

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Table 2 Overview of Training and Test Sets

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Table 3 Average RMSE Values for the Simulated Munsell I/Munsell II Setting a

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Table 4 Average RMSE Values for the Simulated NCS/Munsell Setting a

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Table 5 Average RMSE Values for the Simulated Pantone/Munsell Setting a

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Table 6 Average Δ E Values for Simulated Settings a

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Table 7 Average RMSE Values for the Gaussian Six-Sensitivity System a

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Table 8 Average RMSE Values for the Munsell Sets a

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Table 9 RMSE Values for the Munsell Sets a

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Table 10 RMSE Errors for the 15-Sample Munsell Clusters Corresponding to the Test Samples a

Equations (40)

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

x i = Γ i ( ξ i Ω l ( λ ) r ( λ ) s i ( λ ) d λ + ϵ i ) ,
( C r ) i = r , w i = x i ,
M r 1 = { q q = r 1 + r q , r q N ( C ) }
x i Γ i ( ξ i Δ λ t = 1 n l ( λ t ) r ( λ t ) s i ( λ t ) + ϵ i ) ,
x W r .
arg min r ( W r x Z 2 + γ r M 2 ) ,
L = M 1 W T ( W M 1 W T + γ Z 1 ) 1 .
L = W T ( W W T + γ I k ) 1 = ( W T W + γ I n ) 1 W T .
x W r = W V k s b 1 + W V n k s b 2 = T b 1 + W V n k s b 2 .
r ̂ = Σ r r W T ( W Σ r r W T ) 1 ( x W r ¯ ) + r ¯ ,
arg min r ( W r x 2 2 + γ r Σ r r 1 2 ) ,
r ̂ = Σ r r W T ( W Σ r r W T + γ I ) 1 ( x W r ¯ ) + r ¯ .
arg min F j l Q ( r j , F ( Φ ( x j ) ) ) ,
arg min F j l r j F Φ ( x j ) 2 2 .
r ̂ = F Φ ( x ) = k = 1 N F k ϕ k ( x ) .
arg min F ( i l r i F Φ ( x i ) 2 2 + γ F F 2 ) ,
F x = R T X ( X T X + γ I k ) 1 x ,
Φ p : x R k ( 1 , x a 1 , , x a N 1 ) R N .
r ̂ = R T X Φ ( X Φ T X Φ + γ I N ) 1 Φ ( x ) = R T ( X Φ X Φ T + γ I l ) 1 X Φ Φ ( x ) = R T ( K + γ I l ) 1 κ x ,
r ̂ ( λ i ) = j = 1 l ( m = 1 l r m ( λ i ) ( K + γ I l ) m j 1 ) κ ( x , x j ) = j = 1 l b j ( λ i ) κ ( x , x j ) = m = 1 l r m ( λ i ) ( j = 1 l ( K + γ I l ) m j 1 κ ( x , x j ) ) = m = 1 l c m ( x ) r m ( λ i ) ,
r ̂ w = Σ r r W T ( W Σ r r W T + γ I k ) 1 x = R T R W T ( W R T R W T + γ I k ) 1 x = R T ( R W T W R T + γ I l ) 1 R W T x = R T ( K + γ I l ) 1 κ w x ,
K j m = κ w ( r j , r m ) = r j T W T W r m
κ w x = [ ( W r 1 ) T x , , ( W r l ) T x ] T .
K j m = κ g ( r j , r m ) = exp ( W r j W r m 2 2 2 σ 2 ) = exp ( 1 2 σ 2 r j r m W T W 2 ) .
( κ g x ) j = exp ( W r j x 2 2 2 σ 2 ) .
{ r i d ( x , W r i ) = x W r i 2 t x } ,
r ̃ = arctanh ( 2 r 1 ) ,
r = ( 1 + tanh ( r ̂ ) ) 2 .
S k ( D b 1 , D b 2 ) = i = 1 k ρ i 2 k ,
SNR = 10 log 10 X F 2 E n F 2 ,
S i i = 1 w i .
κ 1 ( r j , r m ) = exp ( 1 2 σ 2 S W r j S W r m 2 2 )
κ 2 ( r j , r m ) = ( S W r j ) T S W r m .
r ̂ = R ̃ T ( K + γ I l ) 1 κ x ,
κ 2 ( x j , x m ) = exp ( 1 2 γ 2 S x j S x m 2 2 )
κ 2 ( x j , x m ) = ( S x j ) T S x j ,
RMSE = ( r r ̃ 2 n ) 1 2 ,
R = U S V T , S = ( S k 0 0 0 ) ,
R = U ̃ S ̃ V T ,
A T ( A A T + γ I k ) 1 = U ̃ S ̃ V T ( V S ̃ 2 V T + γ I k ) 1 = U ̃ S ̃ V T V ( S ̃ 2 + γ I k ) 1 V T = U ̃ S ̃ ( S ̃ 2 + γ I k ) 1 V T = U ( S S T + γ I n ) 1 S V T = U ( S S T + γ I n ) 1 U T U S V T = ( U S V T V S T U T + γ I n ) 1 U S V T = ( A T A + γ I n ) 1 A T .

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