Abstract

The apparent color of an object within a scene depends on the spectrum of the light illuminating the object. However, recording an object’s color independent of the illuminant spectrum is important in many machine vision applications. In this paper the performance of a blackbody-model-based color constancy algorithm that requires four sensors with different spectral responses is investigated under daylight illumination. In this investigation sensor noise was modeled as Gaussian noise, and the responses were quantized using different numbers of bits. A projection-based algorithm whose output is invariant to illuminant is investigated to improve the results that are obtained. The performance of both of these algorithms is then improved by optimizing the spectral sensitivities of the four sensors using freely available CIE standard daylight spectra and a set of lightness-normalized Munsell reflectance data. With the optimized sensors the performance of both algorithms is shown to be comparable to the human visual system. However, results obtained with measured daylight spectra show that the standard daylights may not be sufficiently representative of measured daylight for optimization with the standard daylight to lead to a reliable set of optimum sensor characteristics.

© 2010 Optical Society of America

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  1. S. Ratnasingam and S. Collins, “Study of the photodetector characteristics of a camera for color constancy in natural scene,” J. Opt. Soc. Am. A 27, 286–294 (2010).
    [CrossRef]
  2. J. A. Marchant. and C. M. Onyango, “Shadow-invariant classification for scenes illuminated by daylight,” J. Opt. Soc. Am. A 17, 1952–1961 (2000).
    [CrossRef]
  3. E. H. Land and J. J. McCann, “Lightness and retinex theory,” J. Opt. Soc. Am. 61, 1–11 (1971).
    [CrossRef] [PubMed]
  4. B. K. P. Horn, “Determining lightness from an image,” Comput. Graph. Image Process. 3, 277–299 (1974).
    [CrossRef]
  5. G. D. Finlayson and S. D. Hordley, “Color constancy at a pixel,” J. Opt. Soc. Am. A 18, 253–264 (2001).
    [CrossRef]
  6. M. Ebner, Color Constancy, Wiley Series in Imaging Science and Technology (Wiley, 2007).
  7. G. D. Finlayson and M. S. Drew, “4-sensor camera calibration for image representation invariant to shading, shadows, lighting, and specularities,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 473–480.
  8. J. Romero, J. Hernández-Andrés, J. L. Nieves, and E. M. Valero, “Spectral sensitivity of sensors for a color-image descriptor invariant to changes in daylight conditions,” Color Res. Appl. 31, 391–398 (2006).
    [CrossRef]
  9. S. Takada, M. Ihama, M. Inuiya, T. Komatsu, and T. Saito, “CMOS color image sensor with overlaid organic photoconductive layers having narrow absorption band,” Proc. SPIE 6502, 650207 (2007).
    [CrossRef]
  10. R. Jansen van Vuuren, K. D. Johnstone, S. Ratnasingam, H. Barcena, P. C. Deakin, A. K. Pandey, P. L. Burn, S. Collins, and I. D. W. Samuel, “Determining the absorption tolerance of single chromophore photodiodes for machine vision,” Appl. Phys. Lett. 96, 253303 (2010).
    [CrossRef]
  11. J. Hernández-Andrés, J. Romero, J. L. Nieves, and R. L. Lee, Jr, “Color and spectral analysis of daylight in southern Europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
    [CrossRef]
  12. S. T. Hendersons and D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125–133 (1963).
    [CrossRef]
  13. Munsell Color Science Laboratory, “Daylight spectra,” http://mcsl.rit.edu/.
  14. S. Tominaga and B. A. Wandell, “Natural scene-illuminant estimation using the sensor correlation,” in Proc. IEEE 90, 42–56 (2002).
    [CrossRef]
  15. Database—“Munnsell Colours Matt,” ftp://ftp.cs.joensuu.fi/pub/color/spectra/mspec/.
  16. R. Kawakami, J. Takamatsu, and K. Ikeuchi, “Color constancy from blackbody illumination,” J. Opt. Soc. Am. A 24, 1886–1893 (2007).
    [CrossRef]
  17. J. Yang, W. Lu, and A. Waibel, “Skin-color modeling and adaptation,” Lect. Notes Comput. Sci. 1352, 687–694(1997).
    [CrossRef]
  18. H. C. Lee, Introduction to Color Imaging Science (Cambridge University Press, 2005), pp. 46–47, 138–141, 450–459.
  19. A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci, “Art-works color calibration using the VASARI scanner,” in Proceedings of IS&T and SID’s 4th Color Imaging Conference: Color Science, Systems and Applications (IS&T, 1996), pp. 94–97.
  20. J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, 1999).
  21. B. Fowler, “High dynamic range image sensor architectures,” in High Dynamic Range Imaging Symposium and Workshop, Stanford University, California, 2009,http://scien.stanford.edu/HDR/HDR_files/Conference%20Materials/Presentation%20Slides/Fowler_WDR_sensor_architectures_9_8_2009.pdf.
  22. F. Xiao, J. E. Farrell, and B. Wandell, “Psychophysical thresholds and digital camera sensitivity: The thousand photon limit,” Proc. SPIE 5678, 75–84 (2005).
    [CrossRef]
  23. S. Winkler and S. Susstrunk, “Visibility of noise in natural images,” Proc. SPIE 5292, pages 121–129 (2004).
    [CrossRef]
  24. J. P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
    [CrossRef]
  25. S. E. J. Arnold, V. Savolainen, and L. Chittka , “FReD: The floral reflectance spectra database,” Nature, http://dx.doi.org/10.1038/npre.2008.1846.1.

2010

R. Jansen van Vuuren, K. D. Johnstone, S. Ratnasingam, H. Barcena, P. C. Deakin, A. K. Pandey, P. L. Burn, S. Collins, and I. D. W. Samuel, “Determining the absorption tolerance of single chromophore photodiodes for machine vision,” Appl. Phys. Lett. 96, 253303 (2010).
[CrossRef]

S. Ratnasingam and S. Collins, “Study of the photodetector characteristics of a camera for color constancy in natural scene,” J. Opt. Soc. Am. A 27, 286–294 (2010).
[CrossRef]

2009

B. Fowler, “High dynamic range image sensor architectures,” in High Dynamic Range Imaging Symposium and Workshop, Stanford University, California, 2009,http://scien.stanford.edu/HDR/HDR_files/Conference%20Materials/Presentation%20Slides/Fowler_WDR_sensor_architectures_9_8_2009.pdf.

2007

M. Ebner, Color Constancy, Wiley Series in Imaging Science and Technology (Wiley, 2007).

S. Takada, M. Ihama, M. Inuiya, T. Komatsu, and T. Saito, “CMOS color image sensor with overlaid organic photoconductive layers having narrow absorption band,” Proc. SPIE 6502, 650207 (2007).
[CrossRef]

R. Kawakami, J. Takamatsu, and K. Ikeuchi, “Color constancy from blackbody illumination,” J. Opt. Soc. Am. A 24, 1886–1893 (2007).
[CrossRef]

2006

J. Romero, J. Hernández-Andrés, J. L. Nieves, and E. M. Valero, “Spectral sensitivity of sensors for a color-image descriptor invariant to changes in daylight conditions,” Color Res. Appl. 31, 391–398 (2006).
[CrossRef]

2005

H. C. Lee, Introduction to Color Imaging Science (Cambridge University Press, 2005), pp. 46–47, 138–141, 450–459.

F. Xiao, J. E. Farrell, and B. Wandell, “Psychophysical thresholds and digital camera sensitivity: The thousand photon limit,” Proc. SPIE 5678, 75–84 (2005).
[CrossRef]

2004

S. Winkler and S. Susstrunk, “Visibility of noise in natural images,” Proc. SPIE 5292, pages 121–129 (2004).
[CrossRef]

2002

S. Tominaga and B. A. Wandell, “Natural scene-illuminant estimation using the sensor correlation,” in Proc. IEEE 90, 42–56 (2002).
[CrossRef]

2001

2000

1999

J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, 1999).

1997

J. Yang, W. Lu, and A. Waibel, “Skin-color modeling and adaptation,” Lect. Notes Comput. Sci. 1352, 687–694(1997).
[CrossRef]

1996

A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci, “Art-works color calibration using the VASARI scanner,” in Proceedings of IS&T and SID’s 4th Color Imaging Conference: Color Science, Systems and Applications (IS&T, 1996), pp. 94–97.

1989

1974

B. K. P. Horn, “Determining lightness from an image,” Comput. Graph. Image Process. 3, 277–299 (1974).
[CrossRef]

1971

1963

S. T. Hendersons and D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125–133 (1963).
[CrossRef]

Abrardo, A.

A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci, “Art-works color calibration using the VASARI scanner,” in Proceedings of IS&T and SID’s 4th Color Imaging Conference: Color Science, Systems and Applications (IS&T, 1996), pp. 94–97.

Arnold, S. E. J.

S. E. J. Arnold, V. Savolainen, and L. Chittka , “FReD: The floral reflectance spectra database,” Nature, http://dx.doi.org/10.1038/npre.2008.1846.1.

Barcena, H.

R. Jansen van Vuuren, K. D. Johnstone, S. Ratnasingam, H. Barcena, P. C. Deakin, A. K. Pandey, P. L. Burn, S. Collins, and I. D. W. Samuel, “Determining the absorption tolerance of single chromophore photodiodes for machine vision,” Appl. Phys. Lett. 96, 253303 (2010).
[CrossRef]

Burn, P. L.

R. Jansen van Vuuren, K. D. Johnstone, S. Ratnasingam, H. Barcena, P. C. Deakin, A. K. Pandey, P. L. Burn, S. Collins, and I. D. W. Samuel, “Determining the absorption tolerance of single chromophore photodiodes for machine vision,” Appl. Phys. Lett. 96, 253303 (2010).
[CrossRef]

Cappellini, M.

A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci, “Art-works color calibration using the VASARI scanner,” in Proceedings of IS&T and SID’s 4th Color Imaging Conference: Color Science, Systems and Applications (IS&T, 1996), pp. 94–97.

Cappellini, V.

A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci, “Art-works color calibration using the VASARI scanner,” in Proceedings of IS&T and SID’s 4th Color Imaging Conference: Color Science, Systems and Applications (IS&T, 1996), pp. 94–97.

Collins, S.

S. Ratnasingam and S. Collins, “Study of the photodetector characteristics of a camera for color constancy in natural scene,” J. Opt. Soc. Am. A 27, 286–294 (2010).
[CrossRef]

R. Jansen van Vuuren, K. D. Johnstone, S. Ratnasingam, H. Barcena, P. C. Deakin, A. K. Pandey, P. L. Burn, S. Collins, and I. D. W. Samuel, “Determining the absorption tolerance of single chromophore photodiodes for machine vision,” Appl. Phys. Lett. 96, 253303 (2010).
[CrossRef]

Deakin, P. C.

R. Jansen van Vuuren, K. D. Johnstone, S. Ratnasingam, H. Barcena, P. C. Deakin, A. K. Pandey, P. L. Burn, S. Collins, and I. D. W. Samuel, “Determining the absorption tolerance of single chromophore photodiodes for machine vision,” Appl. Phys. Lett. 96, 253303 (2010).
[CrossRef]

Drew, M. S.

G. D. Finlayson and M. S. Drew, “4-sensor camera calibration for image representation invariant to shading, shadows, lighting, and specularities,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 473–480.

Ebner, M.

M. Ebner, Color Constancy, Wiley Series in Imaging Science and Technology (Wiley, 2007).

Farrell, J. E.

F. Xiao, J. E. Farrell, and B. Wandell, “Psychophysical thresholds and digital camera sensitivity: The thousand photon limit,” Proc. SPIE 5678, 75–84 (2005).
[CrossRef]

Finlayson, G. D.

G. D. Finlayson and S. D. Hordley, “Color constancy at a pixel,” J. Opt. Soc. Am. A 18, 253–264 (2001).
[CrossRef]

G. D. Finlayson and M. S. Drew, “4-sensor camera calibration for image representation invariant to shading, shadows, lighting, and specularities,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 473–480.

Fowler, B.

B. Fowler, “High dynamic range image sensor architectures,” in High Dynamic Range Imaging Symposium and Workshop, Stanford University, California, 2009,http://scien.stanford.edu/HDR/HDR_files/Conference%20Materials/Presentation%20Slides/Fowler_WDR_sensor_architectures_9_8_2009.pdf.

Hallikainen, J.

Hardeberg, J. Y.

J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, 1999).

Hendersons, S. T.

S. T. Hendersons and D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125–133 (1963).
[CrossRef]

Hernández-Andrés, J.

J. Romero, J. Hernández-Andrés, J. L. Nieves, and E. M. Valero, “Spectral sensitivity of sensors for a color-image descriptor invariant to changes in daylight conditions,” Color Res. Appl. 31, 391–398 (2006).
[CrossRef]

J. Hernández-Andrés, J. Romero, J. L. Nieves, and R. L. Lee, Jr, “Color and spectral analysis of daylight in southern Europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
[CrossRef]

Hodgkiss, D.

S. T. Hendersons and D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125–133 (1963).
[CrossRef]

Hordley, S. D.

Horn, B. K. P.

B. K. P. Horn, “Determining lightness from an image,” Comput. Graph. Image Process. 3, 277–299 (1974).
[CrossRef]

Ihama, M.

S. Takada, M. Ihama, M. Inuiya, T. Komatsu, and T. Saito, “CMOS color image sensor with overlaid organic photoconductive layers having narrow absorption band,” Proc. SPIE 6502, 650207 (2007).
[CrossRef]

Ikeuchi, K.

Inuiya, M.

S. Takada, M. Ihama, M. Inuiya, T. Komatsu, and T. Saito, “CMOS color image sensor with overlaid organic photoconductive layers having narrow absorption band,” Proc. SPIE 6502, 650207 (2007).
[CrossRef]

Jaaskelainen, T.

Jansen van Vuuren, R.

R. Jansen van Vuuren, K. D. Johnstone, S. Ratnasingam, H. Barcena, P. C. Deakin, A. K. Pandey, P. L. Burn, S. Collins, and I. D. W. Samuel, “Determining the absorption tolerance of single chromophore photodiodes for machine vision,” Appl. Phys. Lett. 96, 253303 (2010).
[CrossRef]

Johnstone, K. D.

R. Jansen van Vuuren, K. D. Johnstone, S. Ratnasingam, H. Barcena, P. C. Deakin, A. K. Pandey, P. L. Burn, S. Collins, and I. D. W. Samuel, “Determining the absorption tolerance of single chromophore photodiodes for machine vision,” Appl. Phys. Lett. 96, 253303 (2010).
[CrossRef]

Kawakami, R.

Komatsu, T.

S. Takada, M. Ihama, M. Inuiya, T. Komatsu, and T. Saito, “CMOS color image sensor with overlaid organic photoconductive layers having narrow absorption band,” Proc. SPIE 6502, 650207 (2007).
[CrossRef]

Land, E. H.

Lee, H. C.

H. C. Lee, Introduction to Color Imaging Science (Cambridge University Press, 2005), pp. 46–47, 138–141, 450–459.

Lee, R. L.

Lu, W.

J. Yang, W. Lu, and A. Waibel, “Skin-color modeling and adaptation,” Lect. Notes Comput. Sci. 1352, 687–694(1997).
[CrossRef]

Marchant., J. A.

McCann, J. J.

Mecocci, A.

A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci, “Art-works color calibration using the VASARI scanner,” in Proceedings of IS&T and SID’s 4th Color Imaging Conference: Color Science, Systems and Applications (IS&T, 1996), pp. 94–97.

Nieves, J. L.

J. Romero, J. Hernández-Andrés, J. L. Nieves, and E. M. Valero, “Spectral sensitivity of sensors for a color-image descriptor invariant to changes in daylight conditions,” Color Res. Appl. 31, 391–398 (2006).
[CrossRef]

J. Hernández-Andrés, J. Romero, J. L. Nieves, and R. L. Lee, Jr, “Color and spectral analysis of daylight in southern Europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
[CrossRef]

Onyango, C. M.

Pandey, A. K.

R. Jansen van Vuuren, K. D. Johnstone, S. Ratnasingam, H. Barcena, P. C. Deakin, A. K. Pandey, P. L. Burn, S. Collins, and I. D. W. Samuel, “Determining the absorption tolerance of single chromophore photodiodes for machine vision,” Appl. Phys. Lett. 96, 253303 (2010).
[CrossRef]

Parkkinen, J. P. S.

Ratnasingam, S.

R. Jansen van Vuuren, K. D. Johnstone, S. Ratnasingam, H. Barcena, P. C. Deakin, A. K. Pandey, P. L. Burn, S. Collins, and I. D. W. Samuel, “Determining the absorption tolerance of single chromophore photodiodes for machine vision,” Appl. Phys. Lett. 96, 253303 (2010).
[CrossRef]

S. Ratnasingam and S. Collins, “Study of the photodetector characteristics of a camera for color constancy in natural scene,” J. Opt. Soc. Am. A 27, 286–294 (2010).
[CrossRef]

Romero, J.

J. Romero, J. Hernández-Andrés, J. L. Nieves, and E. M. Valero, “Spectral sensitivity of sensors for a color-image descriptor invariant to changes in daylight conditions,” Color Res. Appl. 31, 391–398 (2006).
[CrossRef]

J. Hernández-Andrés, J. Romero, J. L. Nieves, and R. L. Lee, Jr, “Color and spectral analysis of daylight in southern Europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
[CrossRef]

Saito, T.

S. Takada, M. Ihama, M. Inuiya, T. Komatsu, and T. Saito, “CMOS color image sensor with overlaid organic photoconductive layers having narrow absorption band,” Proc. SPIE 6502, 650207 (2007).
[CrossRef]

Samuel, I. D. W.

R. Jansen van Vuuren, K. D. Johnstone, S. Ratnasingam, H. Barcena, P. C. Deakin, A. K. Pandey, P. L. Burn, S. Collins, and I. D. W. Samuel, “Determining the absorption tolerance of single chromophore photodiodes for machine vision,” Appl. Phys. Lett. 96, 253303 (2010).
[CrossRef]

Savolainen, V.

S. E. J. Arnold, V. Savolainen, and L. Chittka , “FReD: The floral reflectance spectra database,” Nature, http://dx.doi.org/10.1038/npre.2008.1846.1.

Susstrunk, S.

S. Winkler and S. Susstrunk, “Visibility of noise in natural images,” Proc. SPIE 5292, pages 121–129 (2004).
[CrossRef]

Takada, S.

S. Takada, M. Ihama, M. Inuiya, T. Komatsu, and T. Saito, “CMOS color image sensor with overlaid organic photoconductive layers having narrow absorption band,” Proc. SPIE 6502, 650207 (2007).
[CrossRef]

Takamatsu, J.

Tominaga, S.

S. Tominaga and B. A. Wandell, “Natural scene-illuminant estimation using the sensor correlation,” in Proc. IEEE 90, 42–56 (2002).
[CrossRef]

Valero, E. M.

J. Romero, J. Hernández-Andrés, J. L. Nieves, and E. M. Valero, “Spectral sensitivity of sensors for a color-image descriptor invariant to changes in daylight conditions,” Color Res. Appl. 31, 391–398 (2006).
[CrossRef]

Waibel, A.

J. Yang, W. Lu, and A. Waibel, “Skin-color modeling and adaptation,” Lect. Notes Comput. Sci. 1352, 687–694(1997).
[CrossRef]

Wandell, B.

F. Xiao, J. E. Farrell, and B. Wandell, “Psychophysical thresholds and digital camera sensitivity: The thousand photon limit,” Proc. SPIE 5678, 75–84 (2005).
[CrossRef]

Wandell, B. A.

S. Tominaga and B. A. Wandell, “Natural scene-illuminant estimation using the sensor correlation,” in Proc. IEEE 90, 42–56 (2002).
[CrossRef]

Winkler, S.

S. Winkler and S. Susstrunk, “Visibility of noise in natural images,” Proc. SPIE 5292, pages 121–129 (2004).
[CrossRef]

Xiao, F.

F. Xiao, J. E. Farrell, and B. Wandell, “Psychophysical thresholds and digital camera sensitivity: The thousand photon limit,” Proc. SPIE 5678, 75–84 (2005).
[CrossRef]

Yang, J.

J. Yang, W. Lu, and A. Waibel, “Skin-color modeling and adaptation,” Lect. Notes Comput. Sci. 1352, 687–694(1997).
[CrossRef]

Appl. Phys. Lett.

R. Jansen van Vuuren, K. D. Johnstone, S. Ratnasingam, H. Barcena, P. C. Deakin, A. K. Pandey, P. L. Burn, S. Collins, and I. D. W. Samuel, “Determining the absorption tolerance of single chromophore photodiodes for machine vision,” Appl. Phys. Lett. 96, 253303 (2010).
[CrossRef]

Br. J. Appl. Phys.

S. T. Hendersons and D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125–133 (1963).
[CrossRef]

Color Res. Appl.

J. Romero, J. Hernández-Andrés, J. L. Nieves, and E. M. Valero, “Spectral sensitivity of sensors for a color-image descriptor invariant to changes in daylight conditions,” Color Res. Appl. 31, 391–398 (2006).
[CrossRef]

Comput. Graph. Image Process.

B. K. P. Horn, “Determining lightness from an image,” Comput. Graph. Image Process. 3, 277–299 (1974).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Lect. Notes Comput. Sci.

J. Yang, W. Lu, and A. Waibel, “Skin-color modeling and adaptation,” Lect. Notes Comput. Sci. 1352, 687–694(1997).
[CrossRef]

Proc. IEEE

S. Tominaga and B. A. Wandell, “Natural scene-illuminant estimation using the sensor correlation,” in Proc. IEEE 90, 42–56 (2002).
[CrossRef]

Proc. SPIE

S. Takada, M. Ihama, M. Inuiya, T. Komatsu, and T. Saito, “CMOS color image sensor with overlaid organic photoconductive layers having narrow absorption band,” Proc. SPIE 6502, 650207 (2007).
[CrossRef]

F. Xiao, J. E. Farrell, and B. Wandell, “Psychophysical thresholds and digital camera sensitivity: The thousand photon limit,” Proc. SPIE 5678, 75–84 (2005).
[CrossRef]

S. Winkler and S. Susstrunk, “Visibility of noise in natural images,” Proc. SPIE 5292, pages 121–129 (2004).
[CrossRef]

Other

Munsell Color Science Laboratory, “Daylight spectra,” http://mcsl.rit.edu/.

M. Ebner, Color Constancy, Wiley Series in Imaging Science and Technology (Wiley, 2007).

G. D. Finlayson and M. S. Drew, “4-sensor camera calibration for image representation invariant to shading, shadows, lighting, and specularities,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 473–480.

H. C. Lee, Introduction to Color Imaging Science (Cambridge University Press, 2005), pp. 46–47, 138–141, 450–459.

A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci, “Art-works color calibration using the VASARI scanner,” in Proceedings of IS&T and SID’s 4th Color Imaging Conference: Color Science, Systems and Applications (IS&T, 1996), pp. 94–97.

J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, 1999).

B. Fowler, “High dynamic range image sensor architectures,” in High Dynamic Range Imaging Symposium and Workshop, Stanford University, California, 2009,http://scien.stanford.edu/HDR/HDR_files/Conference%20Materials/Presentation%20Slides/Fowler_WDR_sensor_architectures_9_8_2009.pdf.

Database—“Munnsell Colours Matt,” ftp://ftp.cs.joensuu.fi/pub/color/spectra/mspec/.

S. E. J. Arnold, V. Savolainen, and L. Chittka , “FReD: The floral reflectance spectra database,” Nature, http://dx.doi.org/10.1038/npre.2008.1846.1.

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Figures (13)

Fig. 1
Fig. 1

Chromaticity space formed by the model-based algorithm with unquantized responses of evenly spread Gaussian sensors of FWHM of 80 nm . In this space 204 Munsell samples are projected when illuminated by 20 spectra of CIE standard test daylights.

Fig. 2
Fig. 2

Typical Mahalanobis distance boundaries for a pair of Munsell samples when illuminated with 20 spectra of CIE standard daylights. Noise was simulated by generating 100 values of random numbers that represent Gaussian noise of 40 dB .

Fig. 3
Fig. 3

Results of the model-based algorithm when testing with evenly spread sensor responses. Gaussian noise of 30 dB and 40 dB was applied to the sensor responses. The resulting linear responses were quantized to 10  bits . Munsell 3- and 6-units test sets were illuminated with the CIE standard test daylights.

Fig. 4
Fig. 4

Test results of model-based algorithm and Finlayson and Drew’s [7] algorithm with evenly spread sensors. Gaussian noise of 40 dB was applied to the sensor responses and the resulting linear responses were quantized to 10  bits . Munsell data (3 and 6 units) were illuminated by the CIE standard test daylights.

Fig. 5
Fig. 5

Initial and optimized performance of the model-based and projection-based algorithm. Gaussian sensors were optimized with Munsell data (1 unit) and the CIE standard training daylights. Munsell data (3 and 6 units) and the CIE standard test daylights are applied in testing both algorithms. Gaussian noise of 40 dB was applied to the sensor responses and the resulting linear responses were quantized to 10  bits . (a) Model-based algorithm. (b) Projection-based algorithm.

Fig. 6
Fig. 6

Sensitivity functions of optimized Gaussian sensors for (a) model-based algorithm and (b) projection-based algorithm. In optimizing the Gaussian sensors Munsell data (1 unit) and the CIE standard training daylights are applied.

Fig. 7
Fig. 7

Performance of model-based and projection-based algorithms with evenly spread sensors. In this test floral reflectances were illuminated by the CIE standard test daylights. Gaussian noise of 40 dB was applied to the sensor responses and the resulting linear responses were quantized to 10  bits . (a) Model-based algorithm. (b) Projection-based algorithm.

Fig. 8
Fig. 8

Initial and optimized performance of the model-based and projection-based algorithms. In optimizing the Gaussian sensors Munsell data (1 unit) and the CIE standard training daylights are applied. Floral data (3 and 6 units) and the CIE standard test daylights are applied in testing both algorithms. Gaussian noise of 40 dB was applied to the sensor responses. The resulting linear responses were quantized to 10  bits .

Fig. 9
Fig. 9

Test results of the projection-based algorithm with optimized sensor responses. Gaussian sensors were optimized with Munsell data (1 unit) and the CIE standard training daylights. The CIE standard test daylights were applied in illuminating the reflectances. Gaussian noise of 40 dB was applied to the sensor responses and the resulting linear responses were quantized to 10  bits .

Fig. 10
Fig. 10

Spectra of CIE ( 6500 K ) and measured daylight with correlated color temperature 6508 K , 6481 K , and 6519 K .

Fig. 11
Fig. 11

Test results of model-based and projection-based algorithms when testing with responses generated by evenly spread sensor responses. Gaussian noise of 40 dB was applied to the sensor responses and the resulting linear responses were quantized to 10  bits . Munsell reflectances were illuminated by measured daylight.

Fig. 12
Fig. 12

Initial and optimized performance of (a) model-based and (b) projection-based algorithm with Munsell and measured daylight spectra. Gaussian sensors were optimized with Munsell data (1 unit) and the CIE standard training daylights. Both the algorithms were tested with Munsell reflectance data (3, 6 units) and 146 spectra of measured daylight. Gaussian noise of 40 dB was applied to the sensor responses and the resulting linear responses were quantized to 10  bits .

Fig. 13
Fig. 13

Test results of the projection-based algorithm with optimized sensors when illuminating the Munsell reflectance samples with the CIE standard test daylight spectra and measured daylight spectra. Gaussian noise of 40 dB was applied to the sensor responses and the resulting linear responses were quantized to 10  bits .

Tables (2)

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Table 1 Optimized Parameters of the Model-Based Algorithm

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Table 2 Optimized Parameters of the Projection-Based Algorithm When Normalizing the Sensor Responses by the Response of Sensor 3

Equations (7)

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F 1 = log ( R 2 ) { α log ( R 1 ) + ( 1 α ) log ( R 3 ) } ,
F 2 = log ( R 3 ) { γ log ( R 2 ) + ( 1 γ ) log ( R 4 ) } ,
1 λ 2 = α λ 1 + 1 α λ 3 ,
1 λ 3 = γ λ 2 + 1 γ λ 4 .
D M 2 = ( P C ) Σ 1 ( P C ) ,
R = N ( 1 , σ 2 ) 400 nm 700 nm S ( λ ) E ( λ ) F ( λ ) d λ ,
p n + 1 = p n ε G ( p n ) ,

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