Abstract

The aim of a multispectral system is to recover a spectral function at each image pixel, but when a scene is digitally imaged under a light of unknown spectral power distribution (SPD), the image pixels give incomplete information about the spectral reflectances of objects in the scene. We have analyzed how accurately the spectra of artificial fluorescent light sources can be recovered with a digital CCD camera. The red-green-blue (RGB) sensor outputs are modified by the use of successive cutoff color filters. Four algorithms for simplifying the spectra datasets are used: nonnegative matrix factorization (NMF), independent component analysis (ICA), a direct pseudoinverse method, and principal component analysis (PCA). The algorithms are tested using both simulated data and data from a real RGB digital camera. The methods are compared in terms of the minimum rank of factorization and the number of sensors required to derive acceptable spectral and colorimetric SPD estimations; the PCA results are also given for the sake of comparison. The results show that all the algorithms surpass the PCA when a reduced number of sensors is used. The experimental results suggest a significant loss of quality when more than one color filter is used, which agrees with the previous results for reflectances. Nevertheless, an RGB digital camera with or without a prefilter is found to provide good spectral and colorimetric recovery of indoor fluorescent lighting and can be used for color correction without the need of a telespectroradiometer.

© 2007 Optical Society of America

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2007 (1)

2005 (3)

2004 (1)

2002 (4)

J. Hardeberg, F. Schmitt, and H. Brettel, "Multispectral color image capture using a liquid crystal tunable filter," Opt. Eng. 41, 2532-2548 (2002).
[CrossRef]

S. M. C. Nascimento, F. P. Ferreira, and D. H. Foster, "Statistics of spatial cone-excitation ratios in natural scenes," J. Opt. Soc. Am. A 19, 1484-1490 (2002).
[CrossRef]

S. Tominaga, "Natural image database and its use for scene illuminant estimation," J. Electronic Imaging 11, 434-444 (2002).
[CrossRef]

K. Barnard, L. Martin, B. Funt, and A. Coath, "A data set for color research," Color Res. Appl. 27, 147-151 (2002).
[CrossRef]

2001 (4)

D. D. Lee and H. S. Seung, "Algorithms for non-negative matrix factorization," Adv. Neural Info. Proc. Syst. 13, 556-562 (2001).

G. D. Finlayson, S. D. Hordley, and P. M. Hubel, "Color by correlation: a simple, unifying framework for color constancy," IEEE Trans. Pattern Anal. Mach. Intell. 23, 1209-1221 (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]

S. Tominaga, S. Ebisui, and B. A. Wandell, "Scene illuminant classification: brighter is better," J. Opt. Soc. Am. A 1, 55-64 (2001).
[CrossRef]

2000 (2)

C.-C. Chiao, D. Osorio, M. Vorobyev, and T. W. Cronin, "Characterization of natural illuminants in forests and the use of digital video data to reconstruct illuminant spectra," J. Opt. Soc. Am. A 17, 1713-1721 (2000).
[CrossRef]

F. H. Imai, R. Berns, and D.-Y. Tzeng, "A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system," J. Imaging Sci. Technol. 44, 280-371 (2000).

1999 (1)

A. Hyvärinen, "Fast and robust fixed-point algorithms for independent component analysis," IEEE Trans. Neural Netw. 10, 626-634 (1999).
[CrossRef]

1998 (1)

1997 (1)

1995 (1)

A. J. Bell and T. J. Sejnowski, "An information-maximization approach to blind separation and blind deconvolution," Neural Comput. 7, 1129-1159 (1995).
[CrossRef] [PubMed]

1994 (2)

M. J. Vrhel, R. Gershon, and L. S. Iwan, "Measurement and analysis of object reflectance spectra," Color Res. Appl. 19, 4-9 (1994).

P. Paatero and U. Tapper, "Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values," Environmetrics 5, 111-126 (1994).
[CrossRef]

1993 (1)

1986 (1)

L. T. Maloney and B. A. Wandell, "Color constancy: a method for recovering surface spectral reflectance," J. Opt. Soc. Am. A 3, 23-33 (1986).
[CrossRef]

1975 (1)

W. K. Pratt and C. E. Mancill, "Spectral estimation techniques for the spectral calibration of a color image scanner," Appl. Opt. 14, 73-75 (1975).

Amano, K.

E. M. Valero, J. L. Nieves, S. M. C. Nascimento, K. Amano, and D. H. Foster, "Recovering spectral data from natural scenes with an RGB digital camera," Color Res. Appl. (to be published).

Barnard, K.

K. Barnard, L. Martin, B. Funt, and A. Coath, "A data set for color research," Color Res. Appl. 27, 147-151 (2002).
[CrossRef]

Bell, A. J.

A. J. Bell and T. J. Sejnowski, "An information-maximization approach to blind separation and blind deconvolution," Neural Comput. 7, 1129-1159 (1995).
[CrossRef] [PubMed]

Bergner, S.

S. Bergner and M. S. Drew, "Spatiotemporal-chromatic structure of natural scenes," presented at the International Conference on Image Processing, Genova, Italy, 11-14 Sept. 2005.

Berns, R.

F. H. Imai, R. Berns, and D.-Y. Tzeng, "A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system," J. Imaging Sci. Technol. 44, 280-371 (2000).

Berns, R. S.

F. H. Imai and R. S. Berns, "Spectral estimation of oil paints using multi-filter trichromatic imaging," in Proceedings of the Ninth Congress of the International Colour Association (Rochester, 2001), pp. 504-507.

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

Brettel, H.

J. Hardeberg, F. Schmitt, and H. Brettel, "Multispectral color image capture using a liquid crystal tunable filter," Opt. Eng. 41, 2532-2548 (2002).
[CrossRef]

Cheung, V.

Chiao, C.-C.

Coath, A.

K. Barnard, L. Martin, B. Funt, and A. Coath, "A data set for color research," Color Res. Appl. 27, 147-151 (2002).
[CrossRef]

Connah, D.

Cronin, T. W.

D"Zmura, M.

Drew, M. S.

S. Bergner and M. S. Drew, "Spatiotemporal-chromatic structure of natural scenes," presented at the International Conference on Image Processing, Genova, Italy, 11-14 Sept. 2005.

Ebisui, S.

S. Tominaga, S. Ebisui, and B. A. Wandell, "Scene illuminant classification: brighter is better," J. Opt. Soc. Am. A 1, 55-64 (2001).
[CrossRef]

Ferreira, F. P.

Finlayson, G.

G. Finlayson, "Spectral sharpening: what is it and why is it important," in Proceedings of the First European Conference on Colour in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2002), pp. 230-235.

Finlayson, G. D.

G. D. Finlayson, S. D. Hordley, and P. M. Hubel, "Color by correlation: a simple, unifying framework for color constancy," IEEE Trans. Pattern Anal. Mach. Intell. 23, 1209-1221 (2001).
[CrossRef]

Foster, D. H.

S. M. C. Nascimento, F. P. Ferreira, and D. H. Foster, "Statistics of spatial cone-excitation ratios in natural scenes," J. Opt. Soc. Am. A 19, 1484-1490 (2002).
[CrossRef]

E. M. Valero, J. L. Nieves, S. M. C. Nascimento, K. Amano, and D. H. Foster, "Recovering spectral data from natural scenes with an RGB digital camera," Color Res. Appl. (to be published).

Funt, B.

K. Barnard, L. Martin, B. Funt, and A. Coath, "A data set for color research," Color Res. Appl. 27, 147-151 (2002).
[CrossRef]

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

García-Beltrán, A.

Gershon, R.

M. J. Vrhel, R. Gershon, and L. S. Iwan, "Measurement and analysis of object reflectance spectra," Color Res. Appl. 19, 4-9 (1994).

Haraguchi, H.

S. Tominaga and H. Haraguchi, "A spectral imaging method for classifying fluorescent scene illuminants," in Proceedings of the Tenth Congress of the International Colour Association (Granada, 2005), pp. 193-196.

Hardeberg, J.

V. Cheung, S. Westland, C. Li, J. Hardeberg, and D. Connah, "Characterization of trichromatic color cameras by using a new multispectral imaging technique," J. Opt. Soc. Am. A 7, 1231-1240 (2005).
[CrossRef]

J. Hardeberg, F. Schmitt, and H. Brettel, "Multispectral color image capture using a liquid crystal tunable filter," Opt. Eng. 41, 2532-2548 (2002).
[CrossRef]

Hernández-Andrés, J.

Hordley, S. D.

G. D. Finlayson, S. D. Hordley, and P. M. Hubel, "Color by correlation: a simple, unifying framework for color constancy," IEEE Trans. Pattern Anal. Mach. Intell. 23, 1209-1221 (2001).
[CrossRef]

Hubel, P. M.

G. D. Finlayson, S. D. Hordley, and P. M. Hubel, "Color by correlation: a simple, unifying framework for color constancy," IEEE Trans. Pattern Anal. Mach. Intell. 23, 1209-1221 (2001).
[CrossRef]

Hyvärinen, A.

A. Hyvärinen, "Fast and robust fixed-point algorithms for independent component analysis," IEEE Trans. Neural Netw. 10, 626-634 (1999).
[CrossRef]

Imai, F. H.

F. H. Imai, R. Berns, and D.-Y. Tzeng, "A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system," J. Imaging Sci. Technol. 44, 280-371 (2000).

F. H. Imai and R. S. Berns, "Spectral estimation of oil paints using multi-filter trichromatic imaging," in Proceedings of the Ninth Congress of the International Colour Association (Rochester, 2001), pp. 504-507.

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

Iverson, G.

Iwan, L. S.

M. J. Vrhel, R. Gershon, and L. S. Iwan, "Measurement and analysis of object reflectance spectra," Color Res. Appl. 19, 4-9 (1994).

Lee, D. D.

D. D. Lee and H. S. Seung, "Algorithms for non-negative matrix factorization," Adv. Neural Info. Proc. Syst. 13, 556-562 (2001).

Lee, R. L.

Li, C.

Lopez-Alvarez, M. A.

López-Álvarez, M. A.

Maloney, L. T.

L. T. Maloney and B. A. Wandell, "Color constancy: a method for recovering surface spectral reflectance," J. Opt. Soc. Am. A 3, 23-33 (1986).
[CrossRef]

Mancill, C. E.

W. K. Pratt and C. E. Mancill, "Spectral estimation techniques for the spectral calibration of a color image scanner," Appl. Opt. 14, 73-75 (1975).

Martin, L.

K. Barnard, L. Martin, B. Funt, and A. Coath, "A data set for color research," Color Res. Appl. 27, 147-151 (2002).
[CrossRef]

Nascimento, S. M. C.

Nieves, J. L.

Osorio, D.

Paatero, P.

P. Paatero and U. Tapper, "Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values," Environmetrics 5, 111-126 (1994).
[CrossRef]

Pratt, W. K.

W. K. Pratt and C. E. Mancill, "Spectral estimation techniques for the spectral calibration of a color image scanner," Appl. Opt. 14, 73-75 (1975).

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 First European Conference on Colour in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2002), pp. 492-496.

Schmitt, F.

J. Hardeberg, F. Schmitt, and H. Brettel, "Multispectral color image capture using a liquid crystal tunable filter," Opt. Eng. 41, 2532-2548 (2002).
[CrossRef]

Sejnowski, T. J.

A. J. Bell and T. J. Sejnowski, "An information-maximization approach to blind separation and blind deconvolution," Neural Comput. 7, 1129-1159 (1995).
[CrossRef] [PubMed]

Seung, H. S.

D. D. Lee and H. S. Seung, "Algorithms for non-negative matrix factorization," Adv. Neural Info. Proc. Syst. 13, 556-562 (2001).

Tapper, U.

P. Paatero and U. Tapper, "Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values," Environmetrics 5, 111-126 (1994).
[CrossRef]

Tominaga, S.

S. Tominaga, "Natural image database and its use for scene illuminant estimation," J. Electronic Imaging 11, 434-444 (2002).
[CrossRef]

S. Tominaga, S. Ebisui, and B. A. Wandell, "Scene illuminant classification: brighter is better," J. Opt. Soc. Am. A 1, 55-64 (2001).
[CrossRef]

S. Tominaga and B. A. Wandell, "Natural scene-illuminant estimation using the sensor correlation," in Proceedings of IEEE 90 (IEEE, 2002), pp. 42-56.
[CrossRef]

S. Tominaga and H. Haraguchi, "A spectral imaging method for classifying fluorescent scene illuminants," in Proceedings of the Tenth Congress of the International Colour Association (Granada, 2005), pp. 193-196.

Tzeng, D.-Y.

F. H. Imai, R. Berns, and D.-Y. Tzeng, "A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system," J. Imaging Sci. Technol. 44, 280-371 (2000).

Valero, E.

Valero, E. M.

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]

E. M. Valero, J. L. Nieves, S. M. C. Nascimento, K. Amano, and D. H. Foster, "Recovering spectral data from natural scenes with an RGB digital camera," Color Res. Appl. (to be published).

Vorobyev, M.

Vrhel, M. J.

M. J. Vrhel, R. Gershon, and L. S. Iwan, "Measurement and analysis of object reflectance spectra," Color Res. Appl. 19, 4-9 (1994).

Wandell, B. A.

S. Tominaga, S. Ebisui, and B. A. Wandell, "Scene illuminant classification: brighter is better," J. Opt. Soc. Am. A 1, 55-64 (2001).
[CrossRef]

L. T. Maloney and B. A. Wandell, "Color constancy: a method for recovering surface spectral reflectance," J. Opt. Soc. Am. A 3, 23-33 (1986).
[CrossRef]

S. Tominaga and B. A. Wandell, "Natural scene-illuminant estimation using the sensor correlation," in Proceedings of IEEE 90 (IEEE, 2002), pp. 42-56.
[CrossRef]

Westland, S.

Wild, S.

S. Wild, "Seeding non-negative matrix factorizations with the spherical K-Means clustering," M.Sc. thesis (University of Colorado, 2003).

Xiong, W.

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

Adv. Neural Info. Proc. Syst. (1)

D. D. Lee and H. S. Seung, "Algorithms for non-negative matrix factorization," Adv. Neural Info. Proc. Syst. 13, 556-562 (2001).

Appl. Opt. (4)

Color Res. Appl. (3)

M. J. Vrhel, R. Gershon, and L. S. Iwan, "Measurement and analysis of object reflectance spectra," Color Res. Appl. 19, 4-9 (1994).

E. M. Valero, J. L. Nieves, S. M. C. Nascimento, K. Amano, and D. H. Foster, "Recovering spectral data from natural scenes with an RGB digital camera," Color Res. Appl. (to be published).

K. Barnard, L. Martin, B. Funt, and A. Coath, "A data set for color research," Color Res. Appl. 27, 147-151 (2002).
[CrossRef]

Environmetrics (1)

P. Paatero and U. Tapper, "Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values," Environmetrics 5, 111-126 (1994).
[CrossRef]

IEEE Trans. Neural Netw. (1)

A. Hyvärinen, "Fast and robust fixed-point algorithms for independent component analysis," IEEE Trans. Neural Netw. 10, 626-634 (1999).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

G. D. Finlayson, S. D. Hordley, and P. M. Hubel, "Color by correlation: a simple, unifying framework for color constancy," IEEE Trans. Pattern Anal. Mach. Intell. 23, 1209-1221 (2001).
[CrossRef]

J. Electronic Imaging (1)

S. Tominaga, "Natural image database and its use for scene illuminant estimation," J. Electronic Imaging 11, 434-444 (2002).
[CrossRef]

J. Imaging Sci. Technol. (1)

F. H. Imai, R. Berns, and D.-Y. Tzeng, "A comparative analysis of spectral reflectance estimated in various spaces using a trichromatic camera system," J. Imaging Sci. Technol. 44, 280-371 (2000).

J. Opt. Soc. Am. A (10)

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]

C.-C. Chiao, D. Osorio, M. Vorobyev, and T. W. Cronin, "Characterization of natural illuminants in forests and the use of digital video data to reconstruct illuminant spectra," J. Opt. Soc. Am. A 17, 1713-1721 (2000).
[CrossRef]

S. M. C. Nascimento, F. P. Ferreira, and D. H. Foster, "Statistics of spatial cone-excitation ratios in natural scenes," J. Opt. Soc. Am. A 19, 1484-1490 (2002).
[CrossRef]

J. Romero, A. García-Beltrán, and J. Hernández-Andrés, "Linear bases for representation of natural and artificial iluminants," J. Opt. Soc. Am. A 14, 1007-1014 (1997).
[CrossRef]

J. Hernández-Andrés, J. L. Nieves, E. Valero, and J. Romero, "Spectral-daylight recovery by use of only a few sensors," J. Opt. Soc. Am. A 21, 13-23 (2004).
[CrossRef]

V. Cheung, S. Westland, C. Li, J. Hardeberg, and D. Connah, "Characterization of trichromatic color cameras by using a new multispectral imaging technique," J. Opt. Soc. Am. A 7, 1231-1240 (2005).
[CrossRef]

S. Tominaga, S. Ebisui, and B. A. Wandell, "Scene illuminant classification: brighter is better," J. Opt. Soc. Am. A 1, 55-64 (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]

L. T. Maloney and B. A. Wandell, "Color constancy: a method for recovering surface spectral reflectance," J. Opt. Soc. Am. A 3, 23-33 (1986).
[CrossRef]

M. D"Zmura and G. Iverson, "Color constancy. I. Basic theory of two-stage linear recovery of spectral descriptions for lights and surfaces," J. Opt. Soc. Am. A 10, 2148-2165 (1993).
[CrossRef]

Neural Comput. (1)

A. J. Bell and T. J. Sejnowski, "An information-maximization approach to blind separation and blind deconvolution," Neural Comput. 7, 1129-1159 (1995).
[CrossRef] [PubMed]

Opt. Eng. (1)

J. Hardeberg, F. Schmitt, and H. Brettel, "Multispectral color image capture using a liquid crystal tunable filter," Opt. Eng. 41, 2532-2548 (2002).
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[CrossRef]

S. Tominaga and H. Haraguchi, "A spectral imaging method for classifying fluorescent scene illuminants," in Proceedings of the Tenth Congress of the International Colour Association (Granada, 2005), pp. 193-196.

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Figures (6)

Fig. 1
Fig. 1

Spectral sensitivities of the 3-, 6-, 9-, and 12-band spectral camera. Dashed and solid curves represent the unmodified and modified bands of the RGB digital camera sensors, respectively. The successive cutoff filters were the OG550, RG630, and BG12 colored-glass filters from OWIS GmbH.

Fig. 2
Fig. 2

The CIELab a*b* color distributions obtained for chip 19 of the MacBeth ColorChecker under each of the training and test illuminants.

Fig. 3
Fig. 3

CIELab color differences derived from the algorithms tested using different numbers of sensors and factorization rank. The results are mean values for the training set of fluorescent illuminants.

Fig. 4
Fig. 4

Cumulative distribution function for the GFC (upper plot) and color difference (lower plot) data derived from the direct pseudoinverse method. The results are for the test set of fluorescent illuminants and different numbers of sensors.

Fig. 5
Fig. 5

Examples of SPD recoveries from the computational results and different algorithms, with different numbers, k, of sensors. Original (Ȕ) and recovered (o) spectra are shown.

Fig. 6
Fig. 6

Examples of experimental SPD recoveries using a real RGB digital camera coupled with different numbers, k, of color filters; the results are for the direct pseudoinverse method. Original (Ȕ) and recovered (o) spectra are shown.

Tables (4)

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Table 1 Mean and Sample Standard Deviation of GFC and ΔE*ab Values Obtained for the Training Spectra a

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Table 2 Mean and Sample Standard Deviation of GFC and ΔE*ab Values Obtained for the Test Spectra a

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Table 3 Average Spectral and Colorimetric Performance of the Experimental Results for the NMF Euclidean (Using the Maximum Rank of Factorization) and Direct Pseudoinverse Methods with Different Numbers of Sensors

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Table 4 Average Spectral and Colorimetric Quality Classification of Test Illuminants Using the Direct Pseudoinverse Method with Different Numbers of Sensors a

Equations (10)

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

ρ k x = λ = 400 700 E x ( λ ) r x ( λ ) Q k ( λ ) Δ λ ,
ρ = C E ,
E = W H .
H = [ H o ( ρ o T ρ o ) 1 ρ o T ] ρ = ( H o ρ o + ) ρ ,
E = F ρ .
F = E o [ ( ρ o T ρ o ) 1 ρ o T ] = E o ρ o + ,
G = ε ρ T [ ρ ρ T ] 1 ,
E e = V ( G ρ ) .
GFC = | j f ( λ j ) f r ( λ j ) | [ | j [ f ( λ j ) ] 2 | | j [ f r ( λ j ) ] 2 | ] 1 / 2 .
min [ i = 1 k ( ρ i P i ) 2 ] 1 / 2 ; ( k = 3 , 6 , 9 , 12 ) ,

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