Abstract

In a multispectral color imaging system, the spectral reflectance of the object being imaged always needs to be accurately reconstructed by employing the training samples on specific color charts. Considering that the workload is heavy when all those color samples are used in practical applications, it is important to select only a limited number of the most representative samples. This is possible as the color charts are usually designed to cover the range of commonly imaged colors, and the color samples are redundant for spectral image reconstruction. We propose an eigenvector-based method and a virtual-imaging-based method for representative color selection by minimizing the total reflectance root-mean-squares errors. The effectiveness of the proposed methods is confirmed by experimental results when compared with existing techniques.

© 2008 Optical Society of America

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References

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  1. Y. Murakami, T. Obi, M. Yamaguchi, N. Ohyama, and Y. Komiya, “Spectral reflectance estimation from multi-band image using color chart,” Opt. Commun. 188, 47-54 (2001).
    [CrossRef]
  2. N. Shimano, “Recovery of spectral reflectance of objects being imaged without prior knowledge,” IEEE Trans. Image Process. 15, 1848-1856 (2006).
    [CrossRef]
  3. H. L. Shen, P. Q. Cai, S. J. Shao, and J. H. Xin, “Reflectance reconstruction for multispectral imaging by adaptive Wiener estimation,” Opt. Express 15, 15545-15554 (2007).
    [CrossRef] [PubMed]
  4. J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches” (Universal Publishers, 2001), dissertation.com.
  5. J. Y. Hardeberg, F. Schmitt, and H. Brettel, “Multispectral color image capture using liquid crystal tunable filter,” Opt. Eng. 41, 2532-2548 (2002).
    [CrossRef]
  6. 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 22, 1231-1240 (2005).
    [CrossRef]
  7. J. P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318-322 (1989).
    [CrossRef]
  8. M. Mohammadi, M. Nezamabadi, R. S. Berns, and L. A. Taplin, “Spectral imaging target development based on hierarchical cluster analysis,” in Proceedings of Twelfth Color Imaging Conference: Color Science and Engineering, Systems, Technologies and Applications, (IS&T, 2004), pp. 59-64.
  9. V. Cheung and S. Westland, “Methods for optimal color selection,” J. Imaging Sci. Technol. 50, 481-488 (2006).
    [CrossRef]
  10. K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152-163 (2002).
    [CrossRef]
  11. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd Ed. (Cambridge University Press, 1992).
  12. L. Maloney, “Evaluation of linear models of surface spectral reflectance with small number of parameters,” J. Opt. Soc Am. A 3, 1673-1683 (1986).
    [CrossRef] [PubMed]
  13. M. J. Vrhel, R. Gershon, and L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4-9 (1994).
  14. M. G. A. Thomson and S. Westland, “Colour-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442-449 (2001).
    [CrossRef]
  15. M. L. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340-350 (2001).
    [CrossRef]

2007 (1)

2006 (2)

N. Shimano, “Recovery of spectral reflectance of objects being imaged without prior knowledge,” IEEE Trans. Image Process. 15, 1848-1856 (2006).
[CrossRef]

V. Cheung and S. Westland, “Methods for optimal color selection,” J. Imaging Sci. Technol. 50, 481-488 (2006).
[CrossRef]

2005 (1)

2004 (1)

M. Mohammadi, M. Nezamabadi, R. S. Berns, and L. A. Taplin, “Spectral imaging target development based on hierarchical cluster analysis,” in Proceedings of Twelfth Color Imaging Conference: Color Science and Engineering, Systems, Technologies and Applications, (IS&T, 2004), pp. 59-64.

2002 (2)

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

K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152-163 (2002).
[CrossRef]

2001 (4)

M. G. A. Thomson and S. Westland, “Colour-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442-449 (2001).
[CrossRef]

M. L. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

Y. Murakami, T. Obi, M. Yamaguchi, N. Ohyama, and Y. Komiya, “Spectral reflectance estimation from multi-band image using color chart,” Opt. Commun. 188, 47-54 (2001).
[CrossRef]

J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches” (Universal Publishers, 2001), dissertation.com.

1994 (1)

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

1992 (1)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd Ed. (Cambridge University Press, 1992).

1989 (1)

1986 (1)

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

Barnard, K.

K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152-163 (2002).
[CrossRef]

Berns, R. S.

M. Mohammadi, M. Nezamabadi, R. S. Berns, and L. A. Taplin, “Spectral imaging target development based on hierarchical cluster analysis,” in Proceedings of Twelfth Color Imaging Conference: Color Science and Engineering, Systems, Technologies and Applications, (IS&T, 2004), pp. 59-64.

Brettel, H.

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

Cai, P. Q.

Cheung, V.

Connah, D.

Cui, G.

M. L. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd Ed. (Cambridge University Press, 1992).

Funt, B.

K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152-163 (2002).
[CrossRef]

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).

Hallikainen, J.

Hardeberg, J.

Hardeberg, J. Y.

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

J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches” (Universal Publishers, 2001), dissertation.com.

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).

Jaaskelainen, T.

Komiya, Y.

Y. Murakami, T. Obi, M. Yamaguchi, N. Ohyama, and Y. Komiya, “Spectral reflectance estimation from multi-band image using color chart,” Opt. Commun. 188, 47-54 (2001).
[CrossRef]

Li, C.

Luo, M. L.

M. L. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

Maloney, L.

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

Mohammadi, M.

M. Mohammadi, M. Nezamabadi, R. S. Berns, and L. A. Taplin, “Spectral imaging target development based on hierarchical cluster analysis,” in Proceedings of Twelfth Color Imaging Conference: Color Science and Engineering, Systems, Technologies and Applications, (IS&T, 2004), pp. 59-64.

Murakami, Y.

Y. Murakami, T. Obi, M. Yamaguchi, N. Ohyama, and Y. Komiya, “Spectral reflectance estimation from multi-band image using color chart,” Opt. Commun. 188, 47-54 (2001).
[CrossRef]

Nezamabadi, M.

M. Mohammadi, M. Nezamabadi, R. S. Berns, and L. A. Taplin, “Spectral imaging target development based on hierarchical cluster analysis,” in Proceedings of Twelfth Color Imaging Conference: Color Science and Engineering, Systems, Technologies and Applications, (IS&T, 2004), pp. 59-64.

Obi, T.

Y. Murakami, T. Obi, M. Yamaguchi, N. Ohyama, and Y. Komiya, “Spectral reflectance estimation from multi-band image using color chart,” Opt. Commun. 188, 47-54 (2001).
[CrossRef]

Ohyama, N.

Y. Murakami, T. Obi, M. Yamaguchi, N. Ohyama, and Y. Komiya, “Spectral reflectance estimation from multi-band image using color chart,” Opt. Commun. 188, 47-54 (2001).
[CrossRef]

Parkkinen, J. P. S.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd Ed. (Cambridge University Press, 1992).

Rigg, B.

M. L. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

Schmitt, F.

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

Shao, S. J.

Shen, H. L.

Shimano, N.

N. Shimano, “Recovery of spectral reflectance of objects being imaged without prior knowledge,” IEEE Trans. Image Process. 15, 1848-1856 (2006).
[CrossRef]

Taplin, L. A.

M. Mohammadi, M. Nezamabadi, R. S. Berns, and L. A. Taplin, “Spectral imaging target development based on hierarchical cluster analysis,” in Proceedings of Twelfth Color Imaging Conference: Color Science and Engineering, Systems, Technologies and Applications, (IS&T, 2004), pp. 59-64.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd Ed. (Cambridge University Press, 1992).

Thomson, M. G. A.

M. G. A. Thomson and S. Westland, “Colour-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442-449 (2001).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd Ed. (Cambridge University Press, 1992).

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).

Westland, S.

V. Cheung and S. Westland, “Methods for optimal color selection,” J. Imaging Sci. Technol. 50, 481-488 (2006).
[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 22, 1231-1240 (2005).
[CrossRef]

M. G. A. Thomson and S. Westland, “Colour-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442-449 (2001).
[CrossRef]

Xin, J. H.

Yamaguchi, M.

Y. Murakami, T. Obi, M. Yamaguchi, N. Ohyama, and Y. Komiya, “Spectral reflectance estimation from multi-band image using color chart,” Opt. Commun. 188, 47-54 (2001).
[CrossRef]

Color Res. Appl. (4)

K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152-163 (2002).
[CrossRef]

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

M. G. A. Thomson and S. Westland, “Colour-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442-449 (2001).
[CrossRef]

M. L. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

IEEE Trans. Image Process. (1)

N. Shimano, “Recovery of spectral reflectance of objects being imaged without prior knowledge,” IEEE Trans. Image Process. 15, 1848-1856 (2006).
[CrossRef]

J. Imaging Sci. Technol. (1)

V. Cheung and S. Westland, “Methods for optimal color selection,” J. Imaging Sci. Technol. 50, 481-488 (2006).
[CrossRef]

J. Opt. Soc Am. A (1)

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

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

Y. Murakami, T. Obi, M. Yamaguchi, N. Ohyama, and Y. Komiya, “Spectral reflectance estimation from multi-band image using color chart,” Opt. Commun. 188, 47-54 (2001).
[CrossRef]

Opt. Eng. (1)

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

Opt. Express (1)

Other (3)

J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches” (Universal Publishers, 2001), dissertation.com.

M. Mohammadi, M. Nezamabadi, R. S. Berns, and L. A. Taplin, “Spectral imaging target development based on hierarchical cluster analysis,” in Proceedings of Twelfth Color Imaging Conference: Color Science and Engineering, Systems, Technologies and Applications, (IS&T, 2004), pp. 59-64.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd Ed. (Cambridge University Press, 1992).

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Figures (5)

Fig. 1
Fig. 1

Virtual spectral responsivity of (a) six channels and (b) 11 channels.

Fig. 2
Fig. 2

Relative spectral transmittance of the liquid-crystal tunable filter.

Fig. 3
Fig. 3

Distribution of mean spectral RMS error with respect to the number of representative colors in the combination of C = 6 and SNR = 50 .

Fig. 4
Fig. 4

(a) Mean spectral RMS errors and (b) mean Δ E 00 errors under D65 of different methods when applied on the synthetic dataset.

Fig. 5
Fig. 5

Reflectance reconstruction of different color selection methods.

Tables (3)

Tables Icon

Table 1 Interval Value Q and Filter Index q ( c ) for Different Channel Numbers C

Tables Icon

Table 2 Training and Testing Color Targets in the Synthetic and Real Datasets

Tables Icon

Table 3 Spectral RMS Errors and Colorimetric Errors of Different Color Selection Methods when Using Real Data of 198 Colors on the CDC Chart

Equations (30)

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

v = Mr + b + n ,
u = Mr + n .
r ^ = Wu ,
W = K r M T ( MK r M T + K n ) 1 ,
K r = E { rr T } ,
K n = diag { σ 1 2 , σ 2 2 , , σ C 2 } ,
σ c 2 = E { u c m c r 2 } ,
Ω 1 = { s 1 } ,
s 1 = arg max r j Θ r j .
s k = arg min r j Θ Ω ¯ k 1 J ,
Ω k = Ω k 1 { s k } .
J CN = d max [ Ω k 1 { r j } ] d min [ Ω k 1 { r j } ] , r j Θ Ω ¯ k 1
J MAXSUMS = i = 1 k 1 r j s i 1 / 2 , s i Ω k 1 , r j Θ Ω ¯ k 1 .
W s , L = K s , L M T ( MK s , L M T + K n ) 1 ,
K s , L = E { ss T } , s Ω L .
UDV T = [ Ω k 1 { r j } ] , r j Θ Ω ¯ k 1 ,
r = U p a ,
a = U p + r ,
r ^ EV = U p a = U p U p + r .
J EV = E { r ^ EV r } = E { ( U p U p + I ) r } ,
u VI = M VI r .
Q = N 1 C 1 ,
q ( c ) = 1 + Q ( c 1 ) .
M VI ( c , j ) = { 1 j [ max ( q ( c ) 1 , 1 ) , min ( q ( c ) + 1 , N ) ] 0 otherwise ,
K s , k = E { ss T } , s Ω k 1 { r j } ,
r ^ VI = K s , k M VI T ( M VI K s , k M VI T ) 1 u VI = K s , k M VI T ( M VI K s , k M VI T ) 1 M VI r .
J VI = E { r ^ VI r } = E { ( K s , k M VI T ( M VI K s , k M VI T ) 1 M VI I ) r } .
RMS = r ^ r .
u syn = Mr + n σ ,
SNR = 10 log ( Tr ( MK r M T ) σ 2 ) ,

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