Abstract

In this paper, an algorithm is proposed to estimate the spectral power distribution of a light source at a pixel. The first step of the algorithm is forming a two-dimensional illuminant invariant chromaticity space. In estimating the illuminant spectrum, generalized inverse estimation and Wiener estimation methods were applied. The chromaticity space was divided into small grids and a weight matrix was used to estimate the illuminant spectrum illuminating the pixels that fall within a grid. The algorithm was tested using a different number of sensor responses to determine the optimum number of sensors for accurate colorimetric and spectral reproduction. To investigate the performance of the algorithm realistically, the responses were multiplied with Gaussian noise and then quantized to 10bits. The algorithm was tested with standard and measured data. Based on the results presented, the algorithm can be used with six sensors to obtain a colorimetrically good estimate of the illuminant spectrum at a pixel.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. D. Finlayson and S. D. Hordley, “Color constancy at a pixel,” J. Opt. Soc. Am. A 18, 253–264 (2001).
    [CrossRef]
  2. A. Mansouri, T. Sliwa, J. Y. Hardeberg, and Y. Voisin, “An adaptive-pca algorithm for reflectance estimation from color images,” in Proceedings of the 19th IEEE International Conference on Pattern Recognition (IEEE, 2008), pp. 1–4.
    [CrossRef]
  3. J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, 1999).
  4. 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, (Society of Multispectral Imaging of Japan, 1999), pp. 42–49.
  5. H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, “System design for accurately estimating the spectral reflectance of art paintings,” Appl. Opt. 39, 6621–6632(2000).
    [CrossRef]
  6. S. Ratnasingam, S. Collins, and J. Hernández-Andrés, “Extending “color constancy” outside the visible region,” J. Opt. Soc. Am. A 28, 541–547 (2011).
    [CrossRef]
  7. 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]
  8. 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]
  9. 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]
  10. L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with a small number of parameters,” J. Opt. Soc. Am. A 3, 1673–1683 (1986).
    [CrossRef] [PubMed]
  11. 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]
  12. M. J. Vhrel, R. Gershon, and L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9(1994).
  13. T. Harifi, S. H. Amirshahi, and F. Agahian., “Recovery of reflectance spectra from colorimetric data using principal component analysis embedded regression technique,” Opt. Rev. 15, 302–308(2008).
    [CrossRef]
  14. M. Shi and G. Healey, “Using reflectance models for color scanner calibration,” J. Opt. Soc. Am. A 19, 645–656 (2002).
    [CrossRef]
  15. 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]
  16. S. Ratnasingam and S. Collins, “Study of the photodetector characteristics of a camera for color constancy in natural scenes,” J. Opt. Soc. Am. A 27, 286–294 (2010).
    [CrossRef]
  17. 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]
  18. S. Ratnasingam, S. Collins, and J. Hernández-Andrés, “Optimum sensors for color constancy in scenes illuminated by daylight,” J. Opt. Soc. Am. A 27, 2198–2207 (2010).
    [CrossRef]
  19. Munsell Color Science Laboratory, “Daylight spectra,” http://www.cis.rit.edu/mcsl/
  20. “Munnsell Colors Matt database,” ftp://ftp. cs. joensuu. fi/pub/color/spectra/mspec/.
  21. 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]
  22. D. B. Judd, D. L. MacAdam, and G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. A 54, 1031–1040 (1964).
    [CrossRef]
  23. 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]
  24. S. E. J. Arnold, V. Savolainen, and L. Chittka, “FReD: the floral reflectance spectra database,” Nature Precedings (2008). http://dx.doi.org/10.1038/npre.2008.1846.1.
    [CrossRef]
  25. 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]
  26. M. Ebner, Color Constancy (Wiley, 2007).
  27. A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci. “Art-works color calibration using the VASARI scanner,” in Fourth Color Imaging Conference: Color Science, Systems, and Applications 4 (The Society for Imaging Science and Technology, 1996), pp. 94–97.
  28. G. Sharma and H. J. Trussell, “Digital color imaging,” IEEE Trans. Image Process. 6, 901–932 (1997).
    [CrossRef] [PubMed]
  29. S. Winkler and S. Susstrunk, “Visibility of noise in natural images,” Proc. SPIE 5292, 121–129 (2004).
    [CrossRef]

2011 (1)

2010 (2)

2008 (2)

T. Harifi, S. H. Amirshahi, and F. Agahian., “Recovery of reflectance spectra from colorimetric data using principal component analysis embedded regression technique,” Opt. Rev. 15, 302–308(2008).
[CrossRef]

S. E. J. Arnold, V. Savolainen, and L. Chittka, “FReD: the floral reflectance spectra database,” Nature Precedings (2008). http://dx.doi.org/10.1038/npre.2008.1846.1.
[CrossRef]

2007 (1)

2006 (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]

2004 (1)

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

2003 (1)

2002 (1)

2001 (3)

2000 (2)

1997 (2)

1994 (1)

M. J. Vhrel, R. Gershon, and L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9(1994).

1986 (2)

1976 (1)

1964 (1)

D. B. Judd, D. L. MacAdam, and G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. A 54, 1031–1040 (1964).
[CrossRef]

Abrardo, A.

A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci. “Art-works color calibration using the VASARI scanner,” in Fourth Color Imaging Conference: Color Science, Systems, and Applications 4 (The Society for Imaging Science and Technology, 1996), pp. 94–97.

Agahian., F.

T. Harifi, S. H. Amirshahi, and F. Agahian., “Recovery of reflectance spectra from colorimetric data using principal component analysis embedded regression technique,” Opt. Rev. 15, 302–308(2008).
[CrossRef]

Amirshahi, S. H.

T. Harifi, S. H. Amirshahi, and F. Agahian., “Recovery of reflectance spectra from colorimetric data using principal component analysis embedded regression technique,” Opt. Rev. 15, 302–308(2008).
[CrossRef]

Arnold, S. E. J.

S. E. J. Arnold, V. Savolainen, and L. Chittka, “FReD: the floral reflectance spectra database,” Nature Precedings (2008). http://dx.doi.org/10.1038/npre.2008.1846.1.
[CrossRef]

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, (Society of Multispectral Imaging of Japan, 1999), pp. 42–49.

Cappellini, M.

A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci. “Art-works color calibration using the VASARI scanner,” in Fourth Color Imaging Conference: Color Science, Systems, and Applications 4 (The Society for Imaging Science and Technology, 1996), pp. 94–97.

Cappellini, V.

A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci. “Art-works color calibration using the VASARI scanner,” in Fourth Color Imaging Conference: Color Science, Systems, and Applications 4 (The Society for Imaging Science and Technology, 1996), pp. 94–97.

Collins, S.

Dicarlo, J. M.

Ebner, M.

M. Ebner, Color Constancy (Wiley, 2007).

Finlayson, G. D.

García-Beltrán, A.

Gershon, R.

M. J. Vhrel, R. Gershon, and L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9(1994).

Haneishi, H.

Hardeberg, J. Y.

A. Mansouri, T. Sliwa, J. Y. Hardeberg, and Y. Voisin, “An adaptive-pca algorithm for reflectance estimation from color images,” in Proceedings of the 19th IEEE International Conference on Pattern Recognition (IEEE, 2008), pp. 1–4.
[CrossRef]

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

Harifi, T.

T. Harifi, S. H. Amirshahi, and F. Agahian., “Recovery of reflectance spectra from colorimetric data using principal component analysis embedded regression technique,” Opt. Rev. 15, 302–308(2008).
[CrossRef]

Hasegawa, T.

Healey, G.

Hernández-Andrés, J.

Hordley, S. D.

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, (Society of Multispectral Imaging of Japan, 1999), pp. 42–49.

Iwan, L. S.

M. J. Vhrel, R. Gershon, and L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9(1994).

Judd, D. B.

D. B. Judd, D. L. MacAdam, and G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. A 54, 1031–1040 (1964).
[CrossRef]

Lee, R. L.

López-Álvarez, M. A.

MacAdam, D. L.

D. B. Judd, D. L. MacAdam, and G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. A 54, 1031–1040 (1964).
[CrossRef]

Maloney, L. T.

Mancill, C. E.

Mansouri, A.

A. Mansouri, T. Sliwa, J. Y. Hardeberg, and Y. Voisin, “An adaptive-pca algorithm for reflectance estimation from color images,” in Proceedings of the 19th IEEE International Conference on Pattern Recognition (IEEE, 2008), pp. 1–4.
[CrossRef]

Marchant, J. A.

Mecocci, A.

A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci. “Art-works color calibration using the VASARI scanner,” in Fourth Color Imaging Conference: Color Science, Systems, and Applications 4 (The Society for Imaging Science and Technology, 1996), pp. 94–97.

Miyake, Y.

Nieves, J. L.

Onyango, C. M.

Pratt, W. K.

Ratnasingam, S.

Romero, J.

Savolainen, V.

S. E. J. Arnold, V. Savolainen, and L. Chittka, “FReD: the floral reflectance spectra database,” Nature Precedings (2008). http://dx.doi.org/10.1038/npre.2008.1846.1.
[CrossRef]

Sharma, G.

G. Sharma and H. J. Trussell, “Digital color imaging,” IEEE Trans. Image Process. 6, 901–932 (1997).
[CrossRef] [PubMed]

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. 45, 013201 (2006).
[CrossRef]

Sliwa, T.

A. Mansouri, T. Sliwa, J. Y. Hardeberg, and Y. Voisin, “An adaptive-pca algorithm for reflectance estimation from color images,” in Proceedings of the 19th IEEE International Conference on Pattern Recognition (IEEE, 2008), pp. 1–4.
[CrossRef]

Susstrunk, S.

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

Trussell, H. J.

G. Sharma and H. J. Trussell, “Digital color imaging,” IEEE Trans. Image Process. 6, 901–932 (1997).
[CrossRef] [PubMed]

Tsumura, N.

Valero, E. M.

Vhrel, M. J.

M. J. Vhrel, R. Gershon, and L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9(1994).

Voisin, Y.

A. Mansouri, T. Sliwa, J. Y. Hardeberg, and Y. Voisin, “An adaptive-pca algorithm for reflectance estimation from color images,” in Proceedings of the 19th IEEE International Conference on Pattern Recognition (IEEE, 2008), pp. 1–4.
[CrossRef]

Wandell, B. A.

Winkler, S.

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

Wyszecki, G.

D. B. Judd, D. L. MacAdam, and G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. A 54, 1031–1040 (1964).
[CrossRef]

Yokoyama, Y.

Appl. Opt. (2)

Color Res. Appl. (1)

M. J. Vhrel, R. Gershon, and L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9(1994).

IEEE Trans. Image Process. (1)

G. Sharma and H. J. Trussell, “Digital color imaging,” IEEE Trans. Image Process. 6, 901–932 (1997).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (14)

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]

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]

D. B. Judd, D. L. MacAdam, and G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. A 54, 1031–1040 (1964).
[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]

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]

L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with a small number of parameters,” J. Opt. Soc. Am. A 3, 1673–1683 (1986).
[CrossRef] [PubMed]

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]

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

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

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]

S. Ratnasingam, S. Collins, and J. Hernández-Andrés, “Optimum sensors for color constancy in scenes illuminated by daylight,” J. Opt. Soc. Am. A 27, 2198–2207 (2010).
[CrossRef]

S. Ratnasingam, S. Collins, and J. Hernández-Andrés, “Extending “color constancy” outside the visible region,” J. Opt. Soc. Am. A 28, 541–547 (2011).
[CrossRef]

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

Nature Precedings (1)

S. E. J. Arnold, V. Savolainen, and L. Chittka, “FReD: the floral reflectance spectra database,” Nature Precedings (2008). http://dx.doi.org/10.1038/npre.2008.1846.1.
[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]

Opt. Rev. (1)

T. Harifi, S. H. Amirshahi, and F. Agahian., “Recovery of reflectance spectra from colorimetric data using principal component analysis embedded regression technique,” Opt. Rev. 15, 302–308(2008).
[CrossRef]

Proc. SPIE (1)

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

Other (7)

M. Ebner, Color Constancy (Wiley, 2007).

A. Abrardo, V. Cappellini, M. Cappellini, and A. Mecocci. “Art-works color calibration using the VASARI scanner,” in Fourth Color Imaging Conference: Color Science, Systems, and Applications 4 (The Society for Imaging Science and Technology, 1996), pp. 94–97.

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

“Munnsell Colors Matt database,” ftp://ftp. cs. joensuu. fi/pub/color/spectra/mspec/.

A. Mansouri, T. Sliwa, J. Y. Hardeberg, and Y. Voisin, “An adaptive-pca algorithm for reflectance estimation from color images,” in Proceedings of the 19th IEEE International Conference on Pattern Recognition (IEEE, 2008), pp. 1–4.
[CrossRef]

J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, 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, (Society of Multispectral Imaging of Japan, 1999), pp. 42–49.

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 (5)

Fig. 1
Fig. 1

Typical chromaticity space formed by the model-based algorithm with unquantized responses of evenly spread Gaussian sensors of FWHM of 60 nm . In this space, 206 Munsell samples are projected when illuminated by 20 spectra of CIE standard daylights.

Fig. 2
Fig. 2

(a) Generalized inverse estimation, (b) Wiener estimation. Actual and estimated illuminant spectra when using three sensor responses. Both spectra are normalized at 550 nm . The CIELuv difference and GFC of the two spectra shown in (a) are 7.04 units and 0.9818 and 8.105 units and 0.9723 for that shown in (b), respectively.

Fig. 3
Fig. 3

(a) Generalized inverse estimation, (b) Wiener estimation. Actual and estimated illuminant spectra when using four sensor responses. Both spectra are normalized at 550 nm . The CIELuv difference and GFC of the two spectra shown in (a) are 2.35 units and 0.9946 and 6.926 units and 0.9862 for that shown in (b), respectively.

Fig. 4
Fig. 4

(a) Generalized inverse estimation, (b) Wiener estimation. Actual and estimated illuminant spectra when using six sensor responses. Both spectra are normalized at 550 nm . The CIELuv difference and GFC of the two spectra shown in (a) are 0.987 units and 0.9968 and 2.235 units and 0.9935 for that shown in (b), respectively.

Fig. 5
Fig. 5

(a) Generalized inverse estimation, (b) Wiener estimation. Actual and estimated illuminant spectra when using eight sensor responses. Both spectra are normalized at 550 nm . The CIELuv difference and GFC of the two spectra shown in (a) are 0.702 units and 0.9965 and 0.4749 units and 0.9961 for that shown in (b), respectively.

Tables (5)

Tables Icon

Table 1 Parameters of the Gaussian Sensitivity Functions

Tables Icon

Table 2 Test Results of the Algorithm Using Generalized Inverse Estimation When Applying Zero Noise and Unquantized Image Sensor Responses a

Tables Icon

Table 3 Test Results of the Algorithm Using Wiener Estimation When Applying Zero Noise and Unquantized Image Sensor Responses a

Tables Icon

Table 4 Test Results of the Algorithm Using Generalized Inverse Estimation When Applying Different Numbers of Image Sensor Responses a

Tables Icon

Table 5 Test Results of the Algorithm Using Wiener Estimation When Applying Different Numbers of Image Sensor Responses a

Equations (13)

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

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 ,
r x , E = a x . n x I x 400 nm 700 nm S x ( λ ) e ( λ ) c ( λ ) d λ ,
r x , E = a x . n x I x s x ( λ i ) e ( λ i ) .
log ( r x , E ) = log { g I x } + log { e ( λ i ) } + log { s x ( λ i ) } ,
F 1 = r 3 r 2 ,
F 2 = r 3 r 1 ,
r = i = 400 700 I g s i e i c i .
R = I g C S E ,
E ^ = W I 1 R = W I T ( W I W I T ) 1 R .
E ^ = E s s W w T ( W w E s s W w T ) 1 R ,

Metrics