Abstract

An algorithm is described to extract two features that represent the chromaticity of a surface and that are independent of both the intensity and correlated color temperature of the daylight illuminating a scene. For mathematical convenience this algorithm is derived using the assumptions that each photodetector responds to a single wavelength and that the spectrum of the illumination source can be represented by a blackbody spectrum. Neither of these assumptions will be valid in a real application. A new method is proposed to determine the effect of violating these assumptions. The conclusion reached is that two features can be obtained that are effectively independent of the daylight illuminant if photodetectors with a spectral response whose full width at half maximum is 80 nm or less are used.

© 2010 Optical Society of America

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References

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  1. H. C. Lee, Introduction to Color Imaging Science (Cambridge Univ. Press, 2005), pp. 46-47, 450-459.
  2. S. D. Buluswar and B. A. Draper, “Color machine vision for autonomous vehicles,” Eng. Applic. Artif. Intell. 11, pp. 245-256 (1998).
    [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, (1974), pp. 277-299.
    [Crossref]
  5. M. Ebner, Color Constancy, Wiley Series in Imaging Science and Technology (Wiley, 2007).
  6. G. D. Finlayson and S. D. Hordley, “Color constancy at a pixel,” J. Opt. Soc. Am. A 18, 253-264 (2001).
    [Crossref]
  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. G. D. Finlayson, B. Schiele, and J. L. Crowley, “Comprehensive colour image normalization,” in H.Burkhard and B.Neumann, eds., Computer Vision--ECCV'98 (Springer, 1998), pp. 475-490.
  9. 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]
  10. Munsell Color Science Laborartory, “Daylight spectra,” http://mcsl.rit.edu/.
  11. V. D. P. Sastri and S. R. Das, “Spectral distribution and color of north sky at Delhi,” J. Opt. Soc. Am. 56, 829-830 (1966).
    [Crossref]
  12. Y. Nayatani and G. Wyszecki, “Color of daylight from north sky,” J. Opt. Soc. Am . 53, 626-629 (1963).
    [Crossref]
  13. T. Henderson and D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125-133 (1963).
    [Crossref]
  14. 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]
  15. Database--“Munnsell Colours Matt,” ftp://ftp.cs.joensuu.fi/pub/color/spectra/mspec/.
  16. L. T. Maloney, “Illuminant estimation as cue combination,” J. Vision 2, 493-504 (2002).
    [Crossref]
  17. G. D. Finlayson and M. S. Drew, “White-point preserving color correction,” in Proceedings of IS&T/SID 5th Color Imaging Conference (Society for Imaging Science and Technology, 1997), pp. 258-261.
  18. J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, 1999).
  19. A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci “Art-works colour calibration using the VASARI scanner,” in Proceedings of IS&T and SID's 4th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology,1996), pp. 94-97.
  20. S. Ratnasingam, S. Collins, and J. Hernández-Andrés, “A method for designing and assessing sensors for chromaticity constancy in high dynamic range scenes,” in Proceedings of Color Imaging Conference CIC17 (EEUU, 2009), pp 15-20.
  21. B. Fowler, “High dynamic range image sensor architectures,” 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. S. E. J. Arnold, V. Savolainen, and L. Chittka, “The floral reflectance spectra database,” Nature Proceedingshttp://dx.doi.org/10.1038/npre.2008.1846.1.

2002 (1)

L. T. Maloney, “Illuminant estimation as cue combination,” J. Vision 2, 493-504 (2002).
[Crossref]

2001 (2)

2000 (1)

1998 (1)

S. D. Buluswar and B. A. Draper, “Color machine vision for autonomous vehicles,” Eng. Applic. Artif. Intell. 11, pp. 245-256 (1998).
[Crossref]

1974 (1)

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

1971 (1)

1966 (1)

1963 (2)

Y. Nayatani and G. Wyszecki, “Color of daylight from north sky,” J. Opt. Soc. Am . 53, 626-629 (1963).
[Crossref]

T. Henderson 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 colour calibration using the VASARI scanner,” in Proceedings of IS&T and SID's 4th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology,1996), pp. 94-97.

Arnold, S. E. J.

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

Buluswar, S. D.

S. D. Buluswar and B. A. Draper, “Color machine vision for autonomous vehicles,” Eng. Applic. Artif. Intell. 11, pp. 245-256 (1998).
[Crossref]

Cappellini, M.

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

Cappellini, V.

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

Chittka, L.

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

Collins, S.

S. Ratnasingam, S. Collins, and J. Hernández-Andrés, “A method for designing and assessing sensors for chromaticity constancy in high dynamic range scenes,” in Proceedings of Color Imaging Conference CIC17 (EEUU, 2009), pp 15-20.

Crowley, J. L.

G. D. Finlayson, B. Schiele, and J. L. Crowley, “Comprehensive colour image normalization,” in H.Burkhard and B.Neumann, eds., Computer Vision--ECCV'98 (Springer, 1998), pp. 475-490.

Das, S. R.

Draper, B. A.

S. D. Buluswar and B. A. Draper, “Color machine vision for autonomous vehicles,” Eng. Applic. Artif. Intell. 11, pp. 245-256 (1998).
[Crossref]

Drew, M. S.

G. D. Finlayson and M. S. Drew, “White-point preserving color correction,” in Proceedings of IS&T/SID 5th Color Imaging Conference (Society for Imaging Science and Technology, 1997), pp. 258-261.

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).

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, “White-point preserving color correction,” in Proceedings of IS&T/SID 5th Color Imaging Conference (Society for Imaging Science and Technology, 1997), pp. 258-261.

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.

G. D. Finlayson, B. Schiele, and J. L. Crowley, “Comprehensive colour image normalization,” in H.Burkhard and B.Neumann, eds., Computer Vision--ECCV'98 (Springer, 1998), pp. 475-490.

Fowler, B.

B. Fowler, “High dynamic range image sensor architectures,” 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.

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).

Henderson, T.

T. Henderson and D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125-133 (1963).
[Crossref]

Hernández-Andrés, J.

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]

S. Ratnasingam, S. Collins, and J. Hernández-Andrés, “A method for designing and assessing sensors for chromaticity constancy in high dynamic range scenes,” in Proceedings of Color Imaging Conference CIC17 (EEUU, 2009), pp 15-20.

Hodgkiss, D.

T. Henderson 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, (1974), pp. 277-299.
[Crossref]

Land, E. H.

Lee, H. C.

H. C. Lee, Introduction to Color Imaging Science (Cambridge Univ. Press, 2005), pp. 46-47, 450-459.

Lee, R. L.

Maloney, L. T.

L. T. Maloney, “Illuminant estimation as cue combination,” J. Vision 2, 493-504 (2002).
[Crossref]

Marchant, J. A.

McCann, J. J.

Mecocci, A.

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

Nayatani, Y.

Y. Nayatani and G. Wyszecki, “Color of daylight from north sky,” J. Opt. Soc. Am . 53, 626-629 (1963).
[Crossref]

Nieves, J. L.

Onyango, C. M.

Ratnasingam, S.

S. Ratnasingam, S. Collins, and J. Hernández-Andrés, “A method for designing and assessing sensors for chromaticity constancy in high dynamic range scenes,” in Proceedings of Color Imaging Conference CIC17 (EEUU, 2009), pp 15-20.

Romero, J.

Sastri, V. D. P.

Savolainen, V.

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

Schiele, B.

G. D. Finlayson, B. Schiele, and J. L. Crowley, “Comprehensive colour image normalization,” in H.Burkhard and B.Neumann, eds., Computer Vision--ECCV'98 (Springer, 1998), pp. 475-490.

Wyszecki, G.

Y. Nayatani and G. Wyszecki, “Color of daylight from north sky,” J. Opt. Soc. Am . 53, 626-629 (1963).
[Crossref]

Br. J. Appl. Phys. (1)

T. Henderson and D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125-133 (1963).
[Crossref]

Comput. Graph. Image Process. (1)

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

Eng. Applic. Artif. Intell. (1)

S. D. Buluswar and B. A. Draper, “Color machine vision for autonomous vehicles,” Eng. Applic. Artif. Intell. 11, pp. 245-256 (1998).
[Crossref]

J. Opt. Soc. Am (1)

Y. Nayatani and G. Wyszecki, “Color of daylight from north sky,” J. Opt. Soc. Am . 53, 626-629 (1963).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

J. Vision (1)

L. T. Maloney, “Illuminant estimation as cue combination,” J. Vision 2, 493-504 (2002).
[Crossref]

Other (12)

G. D. Finlayson and M. S. Drew, “White-point preserving color correction,” in Proceedings of IS&T/SID 5th Color Imaging Conference (Society for Imaging Science and Technology, 1997), pp. 258-261.

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

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

S. Ratnasingam, S. Collins, and J. Hernández-Andrés, “A method for designing and assessing sensors for chromaticity constancy in high dynamic range scenes,” in Proceedings of Color Imaging Conference CIC17 (EEUU, 2009), pp 15-20.

B. Fowler, “High dynamic range image sensor architectures,” 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.

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

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.

G. D. Finlayson, B. Schiele, and J. L. Crowley, “Comprehensive colour image normalization,” in H.Burkhard and B.Neumann, eds., Computer Vision--ECCV'98 (Springer, 1998), pp. 475-490.

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

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

H. C. Lee, Introduction to Color Imaging Science (Cambridge Univ. Press, 2005), pp. 46-47, 450-459.

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Figures (9)

Fig. 1
Fig. 1 Reflectance spectra of four different Munsell colors, with the wavelengths of the four different photodetector responses indicated by P1, P2, P3, and P4.

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Fig. 2
Fig. 2 Two-dimensional feature space formed with 80   nm FWHM equal weight photodetectors when applying 202 Munsell surfaces and 14 CIE standard daylights. Each cross is the color of the relevant Munsell color.

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Fig. 3
Fig. 3 Pair of clusters of responses in the feature space and the boundary of equal Mahalanobis distance metric of both clusters when they touch each other.

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Fig. 4
Fig. 4 Test results when applying Mahalanobis distance as the metric in finding the residual dependency of the features extracted from test data set. Munsell test samples separated by between 4.6 to 6.0 CIELab units. 14 CIE daylight spectra were applied in this test.

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Fig. 5
Fig. 5 Expected SNR of two types of pixel models using parameters and method described by Fowler [21]. The dashed curve represents the expected SNR of a low cost cell phone camera, while the solid curve represents the expected SNR of a CMOS camera. If the CMOS cameras output is represented using 10  bits then the lowest photocurrents that can be detected are approximately three orders of magnitude less than the maximum detected photocurrent.

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Fig. 6
Fig. 6 Test results for the uniform spread and equal weight sensor set. Munsell samples were illuminated with 14 CIE standard daylight spectra with CCT varying between 5000   K and 9000   K and Mahalanobis distance was applied as the test metric.

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Fig. 7
Fig. 7 Sensitivity of the three models of Gaussian, Lorentzian, and parabola at 80   nm FWHM.

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Fig. 8
Fig. 8 Test results of the algorithm when applying different sensor models. The sensor responses were generated with sensors positions listed in Table 1 and different FWHM varying between 20   nm and 200   nm . Munsell test set separated by between 4.6 to 6.0 CIELab units and 14 CIE standard daylight spectra ( 5000   K to 9000   K ) were applied in this test.

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Fig. 9
Fig. 9 Test results of the algorithm when applying Munsell and floral data set to equal weight sensor responses. Mahalanobis distance metric was applied as the metric with 14 spectra of CIE standard daylights.

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Tables (2)

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Table 1 Parameters of the First Set of Photodetectors

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Table 2 Parameters of a Second Set of Photodetectors

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Equations (15)

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

R x , E = a ̱ x ⋅ n ̱ x I ∫ ω S x ( λ ) E ( λ ) F ( λ ) d λ ,
R x , E = a ̱ x ⋅ n ̱ x I S x ( λ i ) E ( λ i ) .
log ( R x , E ) = log { G I } + log { E ( λ i ) } + log { S x ( λ i ) } ,
L ( λ , T ) = 2 h c 2 λ 5 1 ( e h c ∕ k B T λ − 1 ) ,
E ( λ , T ) = c 1 λ − 5 e − C 2 ∕ T λ ,
log ( R i ) = log ( G I ) + log ( c 1 λ i − 5 S i ) − c 2 T λ i ,
F 1 = log ( R 2 ) − { α log ( R 1 ) + ( 1 − α ) log ( R 3 ) } .
F 1 = log ( c 1 λ 2 − 5 S 2 ) − { α log ( c 1 λ 1 − 5 S 1 ) + ( 1 − α ) log ( c 1 λ 3 − 5 S 3 ) } + c 2 T λ 2 − { α c 2 T λ 1 + ( 1 − α ) c 2 T λ 3 } .
c 2 T λ 2 − { α c 2 T λ 1 + ( 1 − α ) c 2 T λ 3 } = 0 ,
1 λ 2 = α λ 1 + 1 − α λ 3 .
F 2 = log ( R 3 ) − { γ log ( R 2 ) + ( 1 − γ ) log ( R 4 ) } .
1 λ 3 = γ λ 2 + 1 − γ λ 4 .
F 1 = log ( S 2 ) − 1 2 { log ( S 1 ) + log ( S 3 ) } + K 1 ,
F 2 = log ( S 3 ) − 1 2 { log ( S 2 ) + log ( S 4 ) } + K 2 ,
D M 2 = ( P − C ) ′ Σ − 1 ( P − C ) ,

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