Abstract

In a previous work [Appl. Opt. 44, 5688 (2005) ] we found the optimum sensors for a planned multispectral system for measuring skylight in the presence of noise by adapting a linear spectral recovery algorithm proposed by Maloney and Wandell [J. Opt. Soc. Am. A 3, 29 (1986) ]. Here we continue along these lines by simulating the responses of three to five Gaussian sensors and recovering spectral information from noise-affected sensor data by trying out four different estimation algorithms, three different sizes for the training set of spectra, and various linear bases. We attempt to find the optimum combination of sensors, recovery method, linear basis, and matrix size to recover the best skylight spectral power distributions from colorimetric and spectral (in the visible range) points of view. We show how all these parameters play an important role in the practical design of a real multispectral system and how to obtain several relevant conclusions from simulating the behavior of sensors in the presence of noise.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. M. Goody and Y. L. Yung, Atmospheric Radiation, Theoretical Basis, 2nd ed. (Oxford U. Press, 1995), Chap. 5.
  2. J. Y. Hardeberg, "Acquisition and reproduction of color images: colorimetric and multispectral approaches," Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 121-174.
  3. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equations of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).
    [CrossRef]
  4. M. A. López-Álvarez, J. Hernández-Andrés, J. Romero, and R. L. Lee Jr., "Designing a practical system for spectral imaging of skylight," Appl. Opt. 44, 5688-5695 (2005).
    [CrossRef] [PubMed]
  5. M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. L. Nieves, "Colorimetric and spectral combined metric for the optimization of multispectral systems," in Proceedings of the 10th Congress of the International Colour Association (AIC'05) (AIC, 2005), pp. 1685-1688.
  6. 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]
  7. D. H. Marimont and B. A. Wandell, "Linear models of surface and illuminant spectra," J. Opt. Soc. Am. A 9, 1905-1913 (1992).
    [CrossRef] [PubMed]
  8. J. Romero, A. García-Beltrán, and J. Hernández-Andrés, "Linear bases for representation of natural and artificial illuminants," J. Opt. Soc. Am. A 14, 1007-1014 (1997).
    [CrossRef]
  9. G. Buchsbaum and O. Bloch, "Color categories revealed by non-negative matrix factorization of Munsell color spectra," Vision Res. 42, 559-563 (2002).
    [CrossRef] [PubMed]
  10. P. O. Hoyer, "Non-negative factorization with sparseness constraints," J. Mach. Learn. Res. 5, 1457-1469 (2004).
  11. D. D. Lee and H. S. Seung, "Learning the parts of objects by non-negative matrix factorization," Nature (London) 401, 788-793 (1999).
    [CrossRef]
  12. A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, 1st ed. (Wiley, 2001), pp. 147-292.
  13. T. W. Lee, M. Girolami, and T. J. Sejnowski, "Independent component analysis using an extended infomax algorithm for mixed sub-Gaussian and super-Gaussian sources," Neural Comput. 11, 417-441 (1999).
    [CrossRef] [PubMed]
  14. D. Connah, S. Westland, and M. G. A. Thomson, "Optimization of a multispectral imaging system," in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 619-622.
  15. 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 of Multispectral Imaging of Japan, 1999), pp. 42-48.
  16. M. Shi and G. Healey, "Using reflectance models for color scanner calibration," J. Opt. Soc. Am. A 19, 645-656 (2002).
    [CrossRef]
  17. H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, "System design for accurately estimating spectral reflectance of art paintings," Appl. Opt. 39, 6621-6632 (2000).
    [CrossRef]
  18. W. K. Pratt and C. E. Mancill, "Spectral estimation techniques for the spectral calibration of a color image scanner," Appl. Opt. 15, 73-75 (1976).
    [CrossRef] [PubMed]
  19. J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. Hernández-Andrés, and J. Romero, "Multispectral synthesis of daylight using a commercial digital CCD camera," Appl. Opt. 44, 5696-5703 (2005).
    [CrossRef] [PubMed]
  20. D. C. Day, "Filter selection for spectral estimation using a trichromatic camera," M.Sc. dissertation (Rochester Institute of Technology, 2003), http://www.art-si.org/PDFs/Acquisition/DCDayMSThesis03.pdf.
  21. N. Shimano, "Evaluation of a multispectral image acquisition system aimed at reconstruction of spectral reflectances," Opt. Eng. (Bellingham) 44, 107005 (2005).
    [CrossRef]
  22. N. Shimano, "Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise," Opt. Eng. (Bellingham) 45, 013201 (2006).
    [CrossRef]
  23. N. Shimano, "Suppression of noise effects in color correction by spectral sensitivities of image sensors," Opt. Rev. 9, 81-88 (2002).
    [CrossRef]
  24. M. A. López-Álvarez, J. Hernández-Andrés, J. L. Nieves, and J. Romero, "Influence of the recovery method on the optimum sensors for spectral imaging of skylight," Proc. SPIE 6062, 6062-9 (2006).
  25. V. Cheung, C. Li, S. Westland, J. Y. Hardeberg, and D. R. Connah, "Characterization of trichromatic color cameras by using a new multispectral imaging technique," J. Opt. Soc. Am. A 22, 1231-1240 (2005).
    [CrossRef]
  26. M. Vilaseca, J. Pujol, and M. Arjona, "Illuminant influence on the reconstruction of near-infrared spectra," J. Imaging Sci. Technol. 48, 111-119 (2003).
  27. D. Connah, S. Westland, and M. G. A. Thomson, "Recovering spectral information using digital camera systems," Color Technol. 117, 309-312 (2001).
    [CrossRef]
  28. P. D. Burns and R. S. Berns, "Quantization in multispectral color image acquisition," in Proceedings of the IS&T 7th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, 1999), pp. 32-35.
  29. J. Hernández-Andrés, J. Romero, and R. L. Lee, Jr., "Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain," J. Opt. Soc. Am. A 18, 412-420 (2001).
    [CrossRef]
  30. S. M. Sze, Physics of Semiconductor Devices, 2nd ed. (Wiley, 1981), pp. 362-510.
  31. S. Franco, Design with Operational Amplifiers and Analog Integrated Circuits, 3rd ed. (McGraw-Hill, 2002), pp. 311-346.
  32. R. A. Yotter and D. M. Wilson, "A review of photodetectors for sensing light-emitting reporters in biological systems," IEEE Sens. J. 3, pp. 288-303 (2003).
    [CrossRef]
  33. P. Alotto, A. Caiti, G. Molinari, and M. Repetto, "A multiquadrics-based algorithm for the acceleration of simulated annealing optimization procedures," IEEE Trans. Magn. 32, 1198-1201 (1996).
    [CrossRef]
  34. F. H. Imai, M. R. Rosen, and R. S. Berns, "Comparative study of metrics for spectral match quality," in Proceedings of the 1st European Conference on Colour in Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 492-496.
  35. J. A. S. Viggiano, "Metrics for evaluating spectral matches: a quantitative comparison," in Proceedings of the 2nd European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2004), pp. 286-291.
  36. J. J. Michalsky, "Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability," Sol. Energy 34, 439-445 (1985).
    [CrossRef]
  37. J. Y. Hardeberg, "Acquisition and reproduction of color images: colorimetric and multispectral approaches," Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 134-138.
  38. B. P. Lathi, Modern Digital and Analog Communication Systems, 2nd ed. (Oxford U. Press, 1989), pp. 132-212.
  39. W. Xiong and B. Funt, "Independent component analysis and nonnegative linear model analysis of illuminant and reflectance spectra," in Proceedings of the 10th Congress of the International Colour Association (AIC'05) (AIC, 2005), pp. 503-506.
  40. E. K. Oxtoby, D. H. Foster, K. Amano, and S. M. C. Nascimento, "How many basis functions are needed to reproduce coloured patterns under illuminant changes?," Perception31, Suppl., 66 (2002).

2006

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

M. A. López-Álvarez, J. Hernández-Andrés, J. L. Nieves, and J. Romero, "Influence of the recovery method on the optimum sensors for spectral imaging of skylight," Proc. SPIE 6062, 6062-9 (2006).

2005

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

J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. Hernández-Andrés, and J. Romero, "Multispectral synthesis of daylight using a commercial digital CCD camera," Appl. Opt. 44, 5696-5703 (2005).
[CrossRef] [PubMed]

N. Shimano, "Evaluation of a multispectral image acquisition system aimed at reconstruction of spectral reflectances," Opt. Eng. (Bellingham) 44, 107005 (2005).
[CrossRef]

M. A. López-Álvarez, J. Hernández-Andrés, J. Romero, and R. L. Lee Jr., "Designing a practical system for spectral imaging of skylight," Appl. Opt. 44, 5688-5695 (2005).
[CrossRef] [PubMed]

M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. L. Nieves, "Colorimetric and spectral combined metric for the optimization of multispectral systems," in Proceedings of the 10th Congress of the International Colour Association (AIC'05) (AIC, 2005), pp. 1685-1688.

W. Xiong and B. Funt, "Independent component analysis and nonnegative linear model analysis of illuminant and reflectance spectra," in Proceedings of the 10th Congress of the International Colour Association (AIC'05) (AIC, 2005), pp. 503-506.

2004

P. O. Hoyer, "Non-negative factorization with sparseness constraints," J. Mach. Learn. Res. 5, 1457-1469 (2004).

J. A. S. Viggiano, "Metrics for evaluating spectral matches: a quantitative comparison," in Proceedings of the 2nd European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2004), pp. 286-291.

2003

R. A. Yotter and D. M. Wilson, "A review of photodetectors for sensing light-emitting reporters in biological systems," IEEE Sens. J. 3, pp. 288-303 (2003).
[CrossRef]

D. C. Day, "Filter selection for spectral estimation using a trichromatic camera," M.Sc. dissertation (Rochester Institute of Technology, 2003), http://www.art-si.org/PDFs/Acquisition/DCDayMSThesis03.pdf.

M. Vilaseca, J. Pujol, and M. Arjona, "Illuminant influence on the reconstruction of near-infrared spectra," J. Imaging Sci. Technol. 48, 111-119 (2003).

2002

N. Shimano, "Suppression of noise effects in color correction by spectral sensitivities of image sensors," Opt. Rev. 9, 81-88 (2002).
[CrossRef]

S. Franco, Design with Operational Amplifiers and Analog Integrated Circuits, 3rd ed. (McGraw-Hill, 2002), pp. 311-346.

D. Connah, S. Westland, and M. G. A. Thomson, "Optimization of a multispectral imaging system," in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 619-622.

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

G. Buchsbaum and O. Bloch, "Color categories revealed by non-negative matrix factorization of Munsell color spectra," Vision Res. 42, 559-563 (2002).
[CrossRef] [PubMed]

E. K. Oxtoby, D. H. Foster, K. Amano, and S. M. C. Nascimento, "How many basis functions are needed to reproduce coloured patterns under illuminant changes?," Perception31, Suppl., 66 (2002).

F. H. Imai, M. R. Rosen, and R. S. Berns, "Comparative study of metrics for spectral match quality," in Proceedings of the 1st European Conference on Colour in Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 492-496.

2001

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, 1st ed. (Wiley, 2001), pp. 147-292.

J. Hernández-Andrés, J. Romero, and R. L. Lee, Jr., "Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain," J. Opt. Soc. Am. A 18, 412-420 (2001).
[CrossRef]

D. Connah, S. Westland, and M. G. A. Thomson, "Recovering spectral information using digital camera systems," Color Technol. 117, 309-312 (2001).
[CrossRef]

2000

1999

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 of Multispectral Imaging of Japan, 1999), pp. 42-48.

T. W. Lee, M. Girolami, and T. J. Sejnowski, "Independent component analysis using an extended infomax algorithm for mixed sub-Gaussian and super-Gaussian sources," Neural Comput. 11, 417-441 (1999).
[CrossRef] [PubMed]

D. D. Lee and H. S. Seung, "Learning the parts of objects by non-negative matrix factorization," Nature (London) 401, 788-793 (1999).
[CrossRef]

J. Y. Hardeberg, "Acquisition and reproduction of color images: colorimetric and multispectral approaches," Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 121-174.

P. D. Burns and R. S. Berns, "Quantization in multispectral color image acquisition," in Proceedings of the IS&T 7th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, 1999), pp. 32-35.

J. Y. Hardeberg, "Acquisition and reproduction of color images: colorimetric and multispectral approaches," Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 134-138.

1997

1996

P. Alotto, A. Caiti, G. Molinari, and M. Repetto, "A multiquadrics-based algorithm for the acceleration of simulated annealing optimization procedures," IEEE Trans. Magn. 32, 1198-1201 (1996).
[CrossRef]

1995

R. M. Goody and Y. L. Yung, Atmospheric Radiation, Theoretical Basis, 2nd ed. (Oxford U. Press, 1995), Chap. 5.

1992

1989

B. P. Lathi, Modern Digital and Analog Communication Systems, 2nd ed. (Oxford U. Press, 1989), pp. 132-212.

1986

1985

J. J. Michalsky, "Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability," Sol. Energy 34, 439-445 (1985).
[CrossRef]

1981

S. M. Sze, Physics of Semiconductor Devices, 2nd ed. (Wiley, 1981), pp. 362-510.

1976

1953

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equations of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).
[CrossRef]

Alotto, P.

P. Alotto, A. Caiti, G. Molinari, and M. Repetto, "A multiquadrics-based algorithm for the acceleration of simulated annealing optimization procedures," IEEE Trans. Magn. 32, 1198-1201 (1996).
[CrossRef]

Amano, K.

E. K. Oxtoby, D. H. Foster, K. Amano, and S. M. C. Nascimento, "How many basis functions are needed to reproduce coloured patterns under illuminant changes?," Perception31, Suppl., 66 (2002).

Arjona, M.

M. Vilaseca, J. Pujol, and M. Arjona, "Illuminant influence on the reconstruction of near-infrared spectra," J. Imaging Sci. Technol. 48, 111-119 (2003).

Berns, R. S.

F. H. Imai, M. R. Rosen, and R. S. Berns, "Comparative study of metrics for spectral match quality," in Proceedings of the 1st European Conference on Colour in Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 492-496.

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 of Multispectral Imaging of Japan, 1999), pp. 42-48.

P. D. Burns and R. S. Berns, "Quantization in multispectral color image acquisition," in Proceedings of the IS&T 7th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, 1999), pp. 32-35.

Bloch, O.

G. Buchsbaum and O. Bloch, "Color categories revealed by non-negative matrix factorization of Munsell color spectra," Vision Res. 42, 559-563 (2002).
[CrossRef] [PubMed]

Buchsbaum, G.

G. Buchsbaum and O. Bloch, "Color categories revealed by non-negative matrix factorization of Munsell color spectra," Vision Res. 42, 559-563 (2002).
[CrossRef] [PubMed]

Burns, P. D.

P. D. Burns and R. S. Berns, "Quantization in multispectral color image acquisition," in Proceedings of the IS&T 7th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, 1999), pp. 32-35.

Caiti, A.

P. Alotto, A. Caiti, G. Molinari, and M. Repetto, "A multiquadrics-based algorithm for the acceleration of simulated annealing optimization procedures," IEEE Trans. Magn. 32, 1198-1201 (1996).
[CrossRef]

Cheung, V.

Connah, D.

D. Connah, S. Westland, and M. G. A. Thomson, "Optimization of a multispectral imaging system," in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 619-622.

D. Connah, S. Westland, and M. G. A. Thomson, "Recovering spectral information using digital camera systems," Color Technol. 117, 309-312 (2001).
[CrossRef]

Connah, D. R.

Day, D. C.

D. C. Day, "Filter selection for spectral estimation using a trichromatic camera," M.Sc. dissertation (Rochester Institute of Technology, 2003), http://www.art-si.org/PDFs/Acquisition/DCDayMSThesis03.pdf.

Foster, D. H.

E. K. Oxtoby, D. H. Foster, K. Amano, and S. M. C. Nascimento, "How many basis functions are needed to reproduce coloured patterns under illuminant changes?," Perception31, Suppl., 66 (2002).

Franco, S.

S. Franco, Design with Operational Amplifiers and Analog Integrated Circuits, 3rd ed. (McGraw-Hill, 2002), pp. 311-346.

Funt, B.

W. Xiong and B. Funt, "Independent component analysis and nonnegative linear model analysis of illuminant and reflectance spectra," in Proceedings of the 10th Congress of the International Colour Association (AIC'05) (AIC, 2005), pp. 503-506.

García-Beltrán, A.

Girolami, M.

T. W. Lee, M. Girolami, and T. J. Sejnowski, "Independent component analysis using an extended infomax algorithm for mixed sub-Gaussian and super-Gaussian sources," Neural Comput. 11, 417-441 (1999).
[CrossRef] [PubMed]

Goody, R. M.

R. M. Goody and Y. L. Yung, Atmospheric Radiation, Theoretical Basis, 2nd ed. (Oxford U. Press, 1995), Chap. 5.

Haneishi, H.

Hardeberg, J. Y.

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

J. Y. Hardeberg, "Acquisition and reproduction of color images: colorimetric and multispectral approaches," Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 121-174.

J. Y. Hardeberg, "Acquisition and reproduction of color images: colorimetric and multispectral approaches," Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 134-138.

Hasegawa, T.

Healey, G.

Hernández-Andrés, J.

Hosoi, A.

Hoyer, P. O.

P. O. Hoyer, "Non-negative factorization with sparseness constraints," J. Mach. Learn. Res. 5, 1457-1469 (2004).

Hyvärinen, A.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, 1st ed. (Wiley, 2001), pp. 147-292.

Imai, F. H.

F. H. Imai, M. R. Rosen, and R. S. Berns, "Comparative study of metrics for spectral match quality," in Proceedings of the 1st European Conference on Colour in Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 492-496.

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 of Multispectral Imaging of Japan, 1999), pp. 42-48.

Karhunen, J.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, 1st ed. (Wiley, 2001), pp. 147-292.

Lathi, B. P.

B. P. Lathi, Modern Digital and Analog Communication Systems, 2nd ed. (Oxford U. Press, 1989), pp. 132-212.

Lee, D. D.

D. D. Lee and H. S. Seung, "Learning the parts of objects by non-negative matrix factorization," Nature (London) 401, 788-793 (1999).
[CrossRef]

Lee, R. L.

Lee, T. W.

T. W. Lee, M. Girolami, and T. J. Sejnowski, "Independent component analysis using an extended infomax algorithm for mixed sub-Gaussian and super-Gaussian sources," Neural Comput. 11, 417-441 (1999).
[CrossRef] [PubMed]

Li, C.

López-Álvarez, M. A.

M. A. López-Álvarez, J. Hernández-Andrés, J. L. Nieves, and J. Romero, "Influence of the recovery method on the optimum sensors for spectral imaging of skylight," Proc. SPIE 6062, 6062-9 (2006).

M. A. López-Álvarez, J. Hernández-Andrés, J. Romero, and R. L. Lee Jr., "Designing a practical system for spectral imaging of skylight," Appl. Opt. 44, 5688-5695 (2005).
[CrossRef] [PubMed]

M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. L. Nieves, "Colorimetric and spectral combined metric for the optimization of multispectral systems," in Proceedings of the 10th Congress of the International Colour Association (AIC'05) (AIC, 2005), pp. 1685-1688.

Maloney, L. T.

Mancill, C. E.

Marimont, D. H.

Metropolis, N.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equations of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).
[CrossRef]

Michalsky, J. J.

J. J. Michalsky, "Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability," Sol. Energy 34, 439-445 (1985).
[CrossRef]

Miyake, Y.

Molinari, G.

P. Alotto, A. Caiti, G. Molinari, and M. Repetto, "A multiquadrics-based algorithm for the acceleration of simulated annealing optimization procedures," IEEE Trans. Magn. 32, 1198-1201 (1996).
[CrossRef]

Nascimento, S. M. C.

J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. Hernández-Andrés, and J. Romero, "Multispectral synthesis of daylight using a commercial digital CCD camera," Appl. Opt. 44, 5696-5703 (2005).
[CrossRef] [PubMed]

E. K. Oxtoby, D. H. Foster, K. Amano, and S. M. C. Nascimento, "How many basis functions are needed to reproduce coloured patterns under illuminant changes?," Perception31, Suppl., 66 (2002).

Nieves, J. L.

M. A. López-Álvarez, J. Hernández-Andrés, J. L. Nieves, and J. Romero, "Influence of the recovery method on the optimum sensors for spectral imaging of skylight," Proc. SPIE 6062, 6062-9 (2006).

M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. L. Nieves, "Colorimetric and spectral combined metric for the optimization of multispectral systems," in Proceedings of the 10th Congress of the International Colour Association (AIC'05) (AIC, 2005), pp. 1685-1688.

J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. Hernández-Andrés, and J. Romero, "Multispectral synthesis of daylight using a commercial digital CCD camera," Appl. Opt. 44, 5696-5703 (2005).
[CrossRef] [PubMed]

Oja, E.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, 1st ed. (Wiley, 2001), pp. 147-292.

Oxtoby, E. K.

E. K. Oxtoby, D. H. Foster, K. Amano, and S. M. C. Nascimento, "How many basis functions are needed to reproduce coloured patterns under illuminant changes?," Perception31, Suppl., 66 (2002).

Pratt, W. K.

Pujol, J.

M. Vilaseca, J. Pujol, and M. Arjona, "Illuminant influence on the reconstruction of near-infrared spectra," J. Imaging Sci. Technol. 48, 111-119 (2003).

Repetto, M.

P. Alotto, A. Caiti, G. Molinari, and M. Repetto, "A multiquadrics-based algorithm for the acceleration of simulated annealing optimization procedures," IEEE Trans. Magn. 32, 1198-1201 (1996).
[CrossRef]

Romero, J.

Rosen, M. R.

F. H. Imai, M. R. Rosen, and R. S. Berns, "Comparative study of metrics for spectral match quality," in Proceedings of the 1st European Conference on Colour in Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 492-496.

Rosenbluth, A.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equations of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).
[CrossRef]

Rosenbluth, M.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equations of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).
[CrossRef]

Sejnowski, T. J.

T. W. Lee, M. Girolami, and T. J. Sejnowski, "Independent component analysis using an extended infomax algorithm for mixed sub-Gaussian and super-Gaussian sources," Neural Comput. 11, 417-441 (1999).
[CrossRef] [PubMed]

Seung, H. S.

D. D. Lee and H. S. Seung, "Learning the parts of objects by non-negative matrix factorization," Nature (London) 401, 788-793 (1999).
[CrossRef]

Shi, M.

Shimano, N.

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

N. Shimano, "Evaluation of a multispectral image acquisition system aimed at reconstruction of spectral reflectances," Opt. Eng. (Bellingham) 44, 107005 (2005).
[CrossRef]

N. Shimano, "Suppression of noise effects in color correction by spectral sensitivities of image sensors," Opt. Rev. 9, 81-88 (2002).
[CrossRef]

Sze, S. M.

S. M. Sze, Physics of Semiconductor Devices, 2nd ed. (Wiley, 1981), pp. 362-510.

Teller, A.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equations of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).
[CrossRef]

Teller, E.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equations of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).
[CrossRef]

Thomson, M. G. A.

D. Connah, S. Westland, and M. G. A. Thomson, "Optimization of a multispectral imaging system," in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 619-622.

D. Connah, S. Westland, and M. G. A. Thomson, "Recovering spectral information using digital camera systems," Color Technol. 117, 309-312 (2001).
[CrossRef]

Tsumura, N.

Valero, E. M.

M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. L. Nieves, "Colorimetric and spectral combined metric for the optimization of multispectral systems," in Proceedings of the 10th Congress of the International Colour Association (AIC'05) (AIC, 2005), pp. 1685-1688.

J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. Hernández-Andrés, and J. Romero, "Multispectral synthesis of daylight using a commercial digital CCD camera," Appl. Opt. 44, 5696-5703 (2005).
[CrossRef] [PubMed]

Viggiano, J. A. S.

J. A. S. Viggiano, "Metrics for evaluating spectral matches: a quantitative comparison," in Proceedings of the 2nd European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2004), pp. 286-291.

Vilaseca, M.

M. Vilaseca, J. Pujol, and M. Arjona, "Illuminant influence on the reconstruction of near-infrared spectra," J. Imaging Sci. Technol. 48, 111-119 (2003).

Wandell, B. A.

Westland, S.

V. Cheung, C. Li, S. Westland, J. Y. Hardeberg, and D. R. 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, S. Westland, and M. G. A. Thomson, "Optimization of a multispectral imaging system," in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 619-622.

D. Connah, S. Westland, and M. G. A. Thomson, "Recovering spectral information using digital camera systems," Color Technol. 117, 309-312 (2001).
[CrossRef]

Wilson, D. M.

R. A. Yotter and D. M. Wilson, "A review of photodetectors for sensing light-emitting reporters in biological systems," IEEE Sens. J. 3, pp. 288-303 (2003).
[CrossRef]

Xiong, W.

W. Xiong and B. Funt, "Independent component analysis and nonnegative linear model analysis of illuminant and reflectance spectra," in Proceedings of the 10th Congress of the International Colour Association (AIC'05) (AIC, 2005), pp. 503-506.

Yokoyama, Y.

Yotter, R. A.

R. A. Yotter and D. M. Wilson, "A review of photodetectors for sensing light-emitting reporters in biological systems," IEEE Sens. J. 3, pp. 288-303 (2003).
[CrossRef]

Yung, Y. L.

R. M. Goody and Y. L. Yung, Atmospheric Radiation, Theoretical Basis, 2nd ed. (Oxford U. Press, 1995), Chap. 5.

Appl. Opt.

Color Technol.

D. Connah, S. Westland, and M. G. A. Thomson, "Recovering spectral information using digital camera systems," Color Technol. 117, 309-312 (2001).
[CrossRef]

IEEE Sens. J.

R. A. Yotter and D. M. Wilson, "A review of photodetectors for sensing light-emitting reporters in biological systems," IEEE Sens. J. 3, pp. 288-303 (2003).
[CrossRef]

IEEE Trans. Magn.

P. Alotto, A. Caiti, G. Molinari, and M. Repetto, "A multiquadrics-based algorithm for the acceleration of simulated annealing optimization procedures," IEEE Trans. Magn. 32, 1198-1201 (1996).
[CrossRef]

J. Chem. Phys.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equations of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).
[CrossRef]

J. Imaging Sci. Technol.

M. Vilaseca, J. Pujol, and M. Arjona, "Illuminant influence on the reconstruction of near-infrared spectra," J. Imaging Sci. Technol. 48, 111-119 (2003).

J. Mach. Learn. Res.

P. O. Hoyer, "Non-negative factorization with sparseness constraints," J. Mach. Learn. Res. 5, 1457-1469 (2004).

J. Opt. Soc. Am. A

Nature (London)

D. D. Lee and H. S. Seung, "Learning the parts of objects by non-negative matrix factorization," Nature (London) 401, 788-793 (1999).
[CrossRef]

Neural Comput.

T. W. Lee, M. Girolami, and T. J. Sejnowski, "Independent component analysis using an extended infomax algorithm for mixed sub-Gaussian and super-Gaussian sources," Neural Comput. 11, 417-441 (1999).
[CrossRef] [PubMed]

Opt. Eng. (Bellingham)

N. Shimano, "Evaluation of a multispectral image acquisition system aimed at reconstruction of spectral reflectances," Opt. Eng. (Bellingham) 44, 107005 (2005).
[CrossRef]

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

Opt. Rev.

N. Shimano, "Suppression of noise effects in color correction by spectral sensitivities of image sensors," Opt. Rev. 9, 81-88 (2002).
[CrossRef]

Sol. Energy

J. J. Michalsky, "Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability," Sol. Energy 34, 439-445 (1985).
[CrossRef]

Vision Res.

G. Buchsbaum and O. Bloch, "Color categories revealed by non-negative matrix factorization of Munsell color spectra," Vision Res. 42, 559-563 (2002).
[CrossRef] [PubMed]

Other

J. Y. Hardeberg, "Acquisition and reproduction of color images: colorimetric and multispectral approaches," Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 134-138.

B. P. Lathi, Modern Digital and Analog Communication Systems, 2nd ed. (Oxford U. Press, 1989), pp. 132-212.

W. Xiong and B. Funt, "Independent component analysis and nonnegative linear model analysis of illuminant and reflectance spectra," in Proceedings of the 10th Congress of the International Colour Association (AIC'05) (AIC, 2005), pp. 503-506.

E. K. Oxtoby, D. H. Foster, K. Amano, and S. M. C. Nascimento, "How many basis functions are needed to reproduce coloured patterns under illuminant changes?," Perception31, Suppl., 66 (2002).

F. H. Imai, M. R. Rosen, and R. S. Berns, "Comparative study of metrics for spectral match quality," in Proceedings of the 1st European Conference on Colour in Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 492-496.

J. A. S. Viggiano, "Metrics for evaluating spectral matches: a quantitative comparison," in Proceedings of the 2nd European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2004), pp. 286-291.

M. A. López-Álvarez, J. Hernández-Andrés, J. L. Nieves, and J. Romero, "Influence of the recovery method on the optimum sensors for spectral imaging of skylight," Proc. SPIE 6062, 6062-9 (2006).

P. D. Burns and R. S. Berns, "Quantization in multispectral color image acquisition," in Proceedings of the IS&T 7th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, 1999), pp. 32-35.

S. M. Sze, Physics of Semiconductor Devices, 2nd ed. (Wiley, 1981), pp. 362-510.

S. Franco, Design with Operational Amplifiers and Analog Integrated Circuits, 3rd ed. (McGraw-Hill, 2002), pp. 311-346.

D. Connah, S. Westland, and M. G. A. Thomson, "Optimization of a multispectral imaging system," in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 619-622.

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 of Multispectral Imaging of Japan, 1999), pp. 42-48.

R. M. Goody and Y. L. Yung, Atmospheric Radiation, Theoretical Basis, 2nd ed. (Oxford U. Press, 1995), Chap. 5.

J. Y. Hardeberg, "Acquisition and reproduction of color images: colorimetric and multispectral approaches," Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 121-174.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, 1st ed. (Wiley, 2001), pp. 147-292.

M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. L. Nieves, "Colorimetric and spectral combined metric for the optimization of multispectral systems," in Proceedings of the 10th Congress of the International Colour Association (AIC'05) (AIC, 2005), pp. 1685-1688.

D. C. Day, "Filter selection for spectral estimation using a trichromatic camera," M.Sc. dissertation (Rochester Institute of Technology, 2003), http://www.art-si.org/PDFs/Acquisition/DCDayMSThesis03.pdf.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

(a) Optimum three sensors, (b) four sensors, and (c) five sensors for Maloney–Wandell[6] method with m = 1567 training spectra. Equal numbers of sensors and PCA basis vectors are used. Solid curves denote SNR = 40 dB , and dashed curves denote SNR = 26 dB .

Fig. 2
Fig. 2

(a) Optimum three sensors, (b) four sensors, and (c) five sensors for Imai–Berns[15] method with m = 1567 training spectra. Equal numbers of sensors and PCA basis vectors are used. Solid curves denote for SNR = 40 dB , and dashed curves denote SNR = 26 dB .

Fig. 3
Fig. 3

Plot of the transformation matrix versus wavelength at various noise levels. Matrix coefficients are given by the optimum sensors of the Imai–Berns[15] method for three sensors, three PCA basis vectors, and m = 1567 .

Fig. 4
Fig. 4

(a) Optimum three sensors, (b) four sensors, and (c) five sensors for Shi–Healey[16] method with m = 1567 training spectra. Here n = k + 2 PCA vectors are used. Solid curves denote SNR = 40 dB , and dashed curves denote SNR = 26 dB .

Fig. 5
Fig. 5

(a) Optimum three sensors, (b) four sensors, and (c) five sensors for the Wiener method[18] with m = 1567 training spectra. Solid curves denote SNR = 40 dB , and dashed curves denote SNR = 26 dB .

Fig. 6
Fig. 6

Skylight spectral radiance and the double of the corresponding spectral error curves for the 95th percentile of the CSCM metric and the Maloney–Wandell[6] method, which is recovered with the four methods studied (MW, Maloney–Wandell[6]; IB, Imai–Berns[15]; SH, Shi–Healey[16]; W, Wiener[17]). Five sensors are used with a SNR of 30 dB , 12 - bit quantization, and m = 156 . Five PCA basis vectors are used with the Maloney–Wandell[6] and Imai–Berns[15] methods, while six PCA vectors are used with the Shi–Healey[16] method.

Fig. 7
Fig. 7

Mean values for the CSCM metric when recovering the complete test set of skylight spectra with the optimum sensors found using m = 156 and different numbers of PCA basis vectors with three methods (MW, Maloney–Wandell;[6] IB, Imai–Berns;[15] SH, Shi–Healey[16]). Uniform 12 - bit quantization was used. (a) SNR = 40 dB , (b) SNR = 30 dB , (c) SNR = 26 dB . Note the different vertical axis scale in each case.

Fig. 8
Fig. 8

Optimum three sensors for (a) Maloney–Wandell,[6] (b) Imai–Berns,[15] and (c) Shi–Healey[16] methods with m = 156 training spectra at SNR = 30 dB and 12 - bit uniform quantization. In (a) and (b) the solid curves denote three PCA basis vectors and the dashed curves denote three NMF basis vectors. In (c) the solid curves denote five PCA basis vectors and the dashed curves denote five NMF basis vectors. Dotted curves denote nine ICA basis vectors in all the cases.

Fig. 9
Fig. 9

Relative comparison of the computation time with the four recovery methods as a function of the training-set size m. Three sensors are used with all the methods (MW, Maloney–Wandell[6]; IB, Imai–Berns[15]; SH, Shi–Healey[16]; W, Wiener[18]). Three basis vectors are used with the Maloney–Wandell[6] and Imai–Berns[15] methods, while five basis vectors are used with the Shi–Healey[16] method.

Tables (4)

Tables Icon

Table 1 Mean Values ± Standard Deviations for Various Metrics and Noise Situations When Recovering the Complete Test Set of 1567 Skylight Spectra Using the Optimum Sensors Found in Each Case with Various Sizes m of the Training Set of Spectra

Tables Icon

Table 2 Mean Values ± Standard Deviations for Various Metrics When Recovering the Complete Test Set of 1567 Skylight Spectra Using the Optimum Three Sensors Found in Each Case a

Tables Icon

Table 3 Differences and Similarities among the Four Spectral Estimation Methods

Tables Icon

Table 4 Mean Values ± Standard Deviations for Various Metrics When Recovering the Complete Test Set of 1567 Skylight Spectra Using the Optimum Three Sensors Found in Each Case at a SNR of 40 dB and Using m = 1567 Training Spectra

Equations (18)

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

ρ = R t E ,
ρ = ρ free + σ ,
E = V ϵ ,
ρ = R t V ϵ = Λ ϵ ,
E R = V Λ + ρ .
ϵ ts = G ρ ts .
G = ϵ ts ρ ts + .
E R = V G ρ .
ρ = R t ( V 1 ϵ 1 + V 2 ϵ 2 ) ,
ϵ 2 = ( R t V 2 ) 1 ( ρ R t V 1 ϵ 1 ) ,
E = V 1 ϵ 1 + V 2 ( R t V 2 ) 1 ( ρ R t V 1 ϵ 1 ) .
E * = V 1 ϵ 1 * + V 2 ( R t V 2 ) 1 ( ρ * R t V 1 ϵ 1 * ) ,
ϵ 1 * = ( V 1 V 2 ( R t V 2 ) 1 R t V 1 ) + ( E ts V 2 ( R t V 2 ) 1 ρ * ) ,
E R = E i * ,
E R = W ρ .
W = E ts ρ ts + .
CSCM = L n ( 1 + 1000 ( 1 GFC ) ) + Δ E * a b + IIE ( % ) ,
E = X ρ ,

Metrics