Abstract

A linear interpolation method is applied for reconstruction of reflectance spectra of Munsell as well as ColorChecker SG color chips from the corresponding colorimetric values under a given set of viewing conditions. Hence, different types of lookup tables (LUTs) have been created to connect the colorimetric and spectrophotometeric data as the source and destination spaces in this approach. To optimize the algorithm, different color spaces and light sources have been used to build different types of LUTs. The effects of applied color datasets as well as employed color spaces are investigated. Results of recovery are evaluated by the mean and the maximum color difference values under other sets of standard light sources. The mean and the maximum values of root mean square (RMS) error between the reconstructed and the actual spectra are also calculated. Since the speed of reflectance reconstruction is a key point in the LUT algorithm, the processing time spent for interpolation of spectral data has also been measured for each model. Finally, the performance of the suggested interpolation technique is compared with that of the common principal component analysis method. According to the results, using the CIEXYZ tristimulus values as a source space shows priority over the CIELAB color space. Besides, the colorimetric position of a desired sample is a key point that indicates the success of the approach. In fact, because of the nature of the interpolation technique, the colorimetric position of the desired samples should be located inside the color gamut of available samples in the dataset. The resultant spectra that have been reconstructed by this technique show considerable improvement in terms of RMS error between the actual and the reconstructed reflectance spectra as well as CIELAB color differences under the other light source in comparison with those obtained from the standard PCA technique.

© 2009 Optical Society of America

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References

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  1. R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000).
  2. D. Dupont, “Study of the reconstruction of reflectance curves based on tristimulus values: comparison of methods of optimization,” Color Res. Appl. 27, 88-99 (2002).
    [CrossRef]
  3. N. Salamati and S. H. Amirshahi, “The comparison between PCA and simplex methods for reflectance recovery,” in Proceedings of AIC Interim Meeting on Color Science for Industry, Hangzhou, China (2007), pp. 149-152.
  4. S. Usui, S. Nakauchi, and M. Nakano, “Reconstruction of Munsell color space by a five-layer neural network,” J. Opt. Soc. Am. A 9, 516-520 (1992).
    [CrossRef]
  5. K. Ansari, S. H. Amirshahi, and S. Moradian, “Recovery of reflectance spectra from CIE tristimulus values using a progressive database selection technique,” J. Color. Technol. 122, 128-134 (2006).
    [CrossRef]
  6. C. J. Hawkyard, “Synthetic reflectance curves by subtractive color mixing,” J. Soc. Dyers Colour. 109, 246-251 (1993).
    [CrossRef]
  7. C. J. Hawkyard, “Synthetic reflectance curves by additive mixing,” J. Soc. Dyers Colour. 109, 323-329 (1993).
    [CrossRef]
  8. R. S. Berns and C. J. Hawkyard, “Synthetic reflectance curves,” J. Soc. Dyers Colour. 110, 386-389 (1994).
  9. G. Wang, C. Li, and M. R. Luo, “Improving the Hawkyard method for generating reflectance functions,” Color Res. Appl. 30, 283-287 (2005).
    [CrossRef]
  10. Y. Zhao and R. S. Berns, “Image-based spectral reflectance reconstruction using the matrix R method,” Color Res. Appl. 32, 343-351 (2007).
    [CrossRef]
  11. H. S. Fairman and M. H. Brill, “The principal components of reflectance,” Color Res. Appl. 29, 104-110 (2004).
    [CrossRef]
  12. F. Agahian, S. A. Amirshahi, and S. H. Amirshahi, “Reconstruction of reflectance spectra using weighted principal component analysis,” Color Res. Appl. 33, 369-371 (2008).
    [CrossRef]
  13. F. Ayala, J. F. Echávarri, P. Renet, and A. I. Negueruela, “Use of three tristimulus values from surface reflectance spectra to calculate the principal components for reconstructing these spectra by using only three eigenvectors,” J. Opt. Soc. Am. A 23, 2020-2026 (2006).
    [CrossRef]
  14. N. Attarchi and S. H. Amirshahi, “Reconstruction of reflectance data by modification of Berns' Gaussian method,” Color Res. Appl. 34, 26-32 (2009).
    [CrossRef]
  15. A. Shams-Nateri, “Effect of a standard colorimetric observer on the reconstruction of reflectance spectra of coloured fabrics,” Coloration Technology 124, 14-18 (2008).
    [CrossRef]
  16. S. Zuffi and R. Schettini, “Reflectance function estimation from tristimulus values,” Proc. SPIE 5293, 222-231 (2003).
    [CrossRef]
  17. 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]
  18. M. de Berg, M. van Krefeld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications, 2nd ed. (Springer, 2000).
  19. I. Amidror, “Scattered data interpolation methods for electronic imaging systems: A survey,” J. Electron. Imaging 11, 157-176 (2002).
    [CrossRef]
  20. P. Green and L. MacDonald, Color Engineering Achieving Device Independent Colour (Addison-Wesley, 2002).
  21. J. Kasson, W. Plouffe, and S. Nin, “A tetrahedral interpolation technique for color space conversion,” Proc. SPIE 1909, 127-138 (1993).
    [CrossRef]
  22. University of Joensuu Color Group, “Spectral Database,” http://spectral.joensuu.fi/.

2009 (1)

N. Attarchi and S. H. Amirshahi, “Reconstruction of reflectance data by modification of Berns' Gaussian method,” Color Res. Appl. 34, 26-32 (2009).
[CrossRef]

2008 (2)

A. Shams-Nateri, “Effect of a standard colorimetric observer on the reconstruction of reflectance spectra of coloured fabrics,” Coloration Technology 124, 14-18 (2008).
[CrossRef]

F. Agahian, S. A. Amirshahi, and S. H. Amirshahi, “Reconstruction of reflectance spectra using weighted principal component analysis,” Color Res. Appl. 33, 369-371 (2008).
[CrossRef]

2007 (2)

Y. Zhao and R. S. Berns, “Image-based spectral reflectance reconstruction using the matrix R method,” Color Res. Appl. 32, 343-351 (2007).
[CrossRef]

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]

2006 (2)

F. Ayala, J. F. Echávarri, P. Renet, and A. I. Negueruela, “Use of three tristimulus values from surface reflectance spectra to calculate the principal components for reconstructing these spectra by using only three eigenvectors,” J. Opt. Soc. Am. A 23, 2020-2026 (2006).
[CrossRef]

K. Ansari, S. H. Amirshahi, and S. Moradian, “Recovery of reflectance spectra from CIE tristimulus values using a progressive database selection technique,” J. Color. Technol. 122, 128-134 (2006).
[CrossRef]

2005 (1)

G. Wang, C. Li, and M. R. Luo, “Improving the Hawkyard method for generating reflectance functions,” Color Res. Appl. 30, 283-287 (2005).
[CrossRef]

2004 (1)

H. S. Fairman and M. H. Brill, “The principal components of reflectance,” Color Res. Appl. 29, 104-110 (2004).
[CrossRef]

2003 (1)

S. Zuffi and R. Schettini, “Reflectance function estimation from tristimulus values,” Proc. SPIE 5293, 222-231 (2003).
[CrossRef]

2002 (2)

D. Dupont, “Study of the reconstruction of reflectance curves based on tristimulus values: comparison of methods of optimization,” Color Res. Appl. 27, 88-99 (2002).
[CrossRef]

I. Amidror, “Scattered data interpolation methods for electronic imaging systems: A survey,” J. Electron. Imaging 11, 157-176 (2002).
[CrossRef]

1994 (1)

R. S. Berns and C. J. Hawkyard, “Synthetic reflectance curves,” J. Soc. Dyers Colour. 110, 386-389 (1994).

1993 (3)

C. J. Hawkyard, “Synthetic reflectance curves by subtractive color mixing,” J. Soc. Dyers Colour. 109, 246-251 (1993).
[CrossRef]

C. J. Hawkyard, “Synthetic reflectance curves by additive mixing,” J. Soc. Dyers Colour. 109, 323-329 (1993).
[CrossRef]

J. Kasson, W. Plouffe, and S. Nin, “A tetrahedral interpolation technique for color space conversion,” Proc. SPIE 1909, 127-138 (1993).
[CrossRef]

1992 (1)

Agahian, F.

F. Agahian, S. A. Amirshahi, and S. H. Amirshahi, “Reconstruction of reflectance spectra using weighted principal component analysis,” Color Res. Appl. 33, 369-371 (2008).
[CrossRef]

Amidror, I.

I. Amidror, “Scattered data interpolation methods for electronic imaging systems: A survey,” J. Electron. Imaging 11, 157-176 (2002).
[CrossRef]

Amirshahi, S. A.

F. Agahian, S. A. Amirshahi, and S. H. Amirshahi, “Reconstruction of reflectance spectra using weighted principal component analysis,” Color Res. Appl. 33, 369-371 (2008).
[CrossRef]

Amirshahi, S. H.

N. Attarchi and S. H. Amirshahi, “Reconstruction of reflectance data by modification of Berns' Gaussian method,” Color Res. Appl. 34, 26-32 (2009).
[CrossRef]

F. Agahian, S. A. Amirshahi, and S. H. Amirshahi, “Reconstruction of reflectance spectra using weighted principal component analysis,” Color Res. Appl. 33, 369-371 (2008).
[CrossRef]

K. Ansari, S. H. Amirshahi, and S. Moradian, “Recovery of reflectance spectra from CIE tristimulus values using a progressive database selection technique,” J. Color. Technol. 122, 128-134 (2006).
[CrossRef]

N. Salamati and S. H. Amirshahi, “The comparison between PCA and simplex methods for reflectance recovery,” in Proceedings of AIC Interim Meeting on Color Science for Industry, Hangzhou, China (2007), pp. 149-152.

Ansari, K.

K. Ansari, S. H. Amirshahi, and S. Moradian, “Recovery of reflectance spectra from CIE tristimulus values using a progressive database selection technique,” J. Color. Technol. 122, 128-134 (2006).
[CrossRef]

Attarchi, N.

N. Attarchi and S. H. Amirshahi, “Reconstruction of reflectance data by modification of Berns' Gaussian method,” Color Res. Appl. 34, 26-32 (2009).
[CrossRef]

Ayala, F.

Berns, R. S.

Y. Zhao and R. S. Berns, “Image-based spectral reflectance reconstruction using the matrix R method,” Color Res. Appl. 32, 343-351 (2007).
[CrossRef]

R. S. Berns and C. J. Hawkyard, “Synthetic reflectance curves,” J. Soc. Dyers Colour. 110, 386-389 (1994).

R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000).

Brill, M. H.

H. S. Fairman and M. H. Brill, “The principal components of reflectance,” Color Res. Appl. 29, 104-110 (2004).
[CrossRef]

Cai, P.-Q.

de Berg, M.

M. de Berg, M. van Krefeld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications, 2nd ed. (Springer, 2000).

Dupont, D.

D. Dupont, “Study of the reconstruction of reflectance curves based on tristimulus values: comparison of methods of optimization,” Color Res. Appl. 27, 88-99 (2002).
[CrossRef]

Echávarri, J. F.

Fairman, H. S.

H. S. Fairman and M. H. Brill, “The principal components of reflectance,” Color Res. Appl. 29, 104-110 (2004).
[CrossRef]

Green, P.

P. Green and L. MacDonald, Color Engineering Achieving Device Independent Colour (Addison-Wesley, 2002).

Hawkyard, C. J.

R. S. Berns and C. J. Hawkyard, “Synthetic reflectance curves,” J. Soc. Dyers Colour. 110, 386-389 (1994).

C. J. Hawkyard, “Synthetic reflectance curves by subtractive color mixing,” J. Soc. Dyers Colour. 109, 246-251 (1993).
[CrossRef]

C. J. Hawkyard, “Synthetic reflectance curves by additive mixing,” J. Soc. Dyers Colour. 109, 323-329 (1993).
[CrossRef]

Kasson, J.

J. Kasson, W. Plouffe, and S. Nin, “A tetrahedral interpolation technique for color space conversion,” Proc. SPIE 1909, 127-138 (1993).
[CrossRef]

Li, C.

G. Wang, C. Li, and M. R. Luo, “Improving the Hawkyard method for generating reflectance functions,” Color Res. Appl. 30, 283-287 (2005).
[CrossRef]

Luo, M. R.

G. Wang, C. Li, and M. R. Luo, “Improving the Hawkyard method for generating reflectance functions,” Color Res. Appl. 30, 283-287 (2005).
[CrossRef]

MacDonald, L.

P. Green and L. MacDonald, Color Engineering Achieving Device Independent Colour (Addison-Wesley, 2002).

Moradian, S.

K. Ansari, S. H. Amirshahi, and S. Moradian, “Recovery of reflectance spectra from CIE tristimulus values using a progressive database selection technique,” J. Color. Technol. 122, 128-134 (2006).
[CrossRef]

Nakano, M.

Nakauchi, S.

Negueruela, A. I.

Nin, S.

J. Kasson, W. Plouffe, and S. Nin, “A tetrahedral interpolation technique for color space conversion,” Proc. SPIE 1909, 127-138 (1993).
[CrossRef]

Overmars, M.

M. de Berg, M. van Krefeld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications, 2nd ed. (Springer, 2000).

Plouffe, W.

J. Kasson, W. Plouffe, and S. Nin, “A tetrahedral interpolation technique for color space conversion,” Proc. SPIE 1909, 127-138 (1993).
[CrossRef]

Renet, P.

Salamati, N.

N. Salamati and S. H. Amirshahi, “The comparison between PCA and simplex methods for reflectance recovery,” in Proceedings of AIC Interim Meeting on Color Science for Industry, Hangzhou, China (2007), pp. 149-152.

Schettini, R.

S. Zuffi and R. Schettini, “Reflectance function estimation from tristimulus values,” Proc. SPIE 5293, 222-231 (2003).
[CrossRef]

Schwarzkopf, O.

M. de Berg, M. van Krefeld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications, 2nd ed. (Springer, 2000).

Shams-Nateri, A.

A. Shams-Nateri, “Effect of a standard colorimetric observer on the reconstruction of reflectance spectra of coloured fabrics,” Coloration Technology 124, 14-18 (2008).
[CrossRef]

Shao, S.-J.

Shen, H.-L.

Usui, S.

van Krefeld, M.

M. de Berg, M. van Krefeld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications, 2nd ed. (Springer, 2000).

Wang, G.

G. Wang, C. Li, and M. R. Luo, “Improving the Hawkyard method for generating reflectance functions,” Color Res. Appl. 30, 283-287 (2005).
[CrossRef]

Xin, J. H.

Zhao, Y.

Y. Zhao and R. S. Berns, “Image-based spectral reflectance reconstruction using the matrix R method,” Color Res. Appl. 32, 343-351 (2007).
[CrossRef]

Zuffi, S.

S. Zuffi and R. Schettini, “Reflectance function estimation from tristimulus values,” Proc. SPIE 5293, 222-231 (2003).
[CrossRef]

Color Res. Appl. (6)

G. Wang, C. Li, and M. R. Luo, “Improving the Hawkyard method for generating reflectance functions,” Color Res. Appl. 30, 283-287 (2005).
[CrossRef]

Y. Zhao and R. S. Berns, “Image-based spectral reflectance reconstruction using the matrix R method,” Color Res. Appl. 32, 343-351 (2007).
[CrossRef]

H. S. Fairman and M. H. Brill, “The principal components of reflectance,” Color Res. Appl. 29, 104-110 (2004).
[CrossRef]

F. Agahian, S. A. Amirshahi, and S. H. Amirshahi, “Reconstruction of reflectance spectra using weighted principal component analysis,” Color Res. Appl. 33, 369-371 (2008).
[CrossRef]

N. Attarchi and S. H. Amirshahi, “Reconstruction of reflectance data by modification of Berns' Gaussian method,” Color Res. Appl. 34, 26-32 (2009).
[CrossRef]

D. Dupont, “Study of the reconstruction of reflectance curves based on tristimulus values: comparison of methods of optimization,” Color Res. Appl. 27, 88-99 (2002).
[CrossRef]

Coloration Technology (1)

A. Shams-Nateri, “Effect of a standard colorimetric observer on the reconstruction of reflectance spectra of coloured fabrics,” Coloration Technology 124, 14-18 (2008).
[CrossRef]

J. Color. Technol. (1)

K. Ansari, S. H. Amirshahi, and S. Moradian, “Recovery of reflectance spectra from CIE tristimulus values using a progressive database selection technique,” J. Color. Technol. 122, 128-134 (2006).
[CrossRef]

J. Electron. Imaging (1)

I. Amidror, “Scattered data interpolation methods for electronic imaging systems: A survey,” J. Electron. Imaging 11, 157-176 (2002).
[CrossRef]

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

J. Soc. Dyers Colour. (3)

C. J. Hawkyard, “Synthetic reflectance curves by subtractive color mixing,” J. Soc. Dyers Colour. 109, 246-251 (1993).
[CrossRef]

C. J. Hawkyard, “Synthetic reflectance curves by additive mixing,” J. Soc. Dyers Colour. 109, 323-329 (1993).
[CrossRef]

R. S. Berns and C. J. Hawkyard, “Synthetic reflectance curves,” J. Soc. Dyers Colour. 110, 386-389 (1994).

Opt. Express (1)

Proc. SPIE (2)

J. Kasson, W. Plouffe, and S. Nin, “A tetrahedral interpolation technique for color space conversion,” Proc. SPIE 1909, 127-138 (1993).
[CrossRef]

S. Zuffi and R. Schettini, “Reflectance function estimation from tristimulus values,” Proc. SPIE 5293, 222-231 (2003).
[CrossRef]

Other (5)

M. de Berg, M. van Krefeld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications, 2nd ed. (Springer, 2000).

P. Green and L. MacDonald, Color Engineering Achieving Device Independent Colour (Addison-Wesley, 2002).

N. Salamati and S. H. Amirshahi, “The comparison between PCA and simplex methods for reflectance recovery,” in Proceedings of AIC Interim Meeting on Color Science for Industry, Hangzhou, China (2007), pp. 149-152.

R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000).

University of Joensuu Color Group, “Spectral Database,” http://spectral.joensuu.fi/.

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Figures (8)

Fig. 1
Fig. 1

Voronoi and Delaunay partitioning for scattered points in a plane. Solid lines indicate the Delaunay triangles associated with the Voronoi tessellation, and the dotted lines inside it show the Voronoi tiles of the scattered point set [19].

Fig. 2
Fig. 2

Tristimulus values of 1269 Matt Munsell color chips in CIEXYZ space under D65 illumination and 10° observer.

Fig. 3
Fig. 3

The 1269 Munsell color points in CIEXYZ tetrahedrized by the Delaunay method.

Fig. 4
Fig. 4

Distribution of 200 chosen samples and 1069 Munsell color points in CIELAB space using D65 illuminant and 1964 standard observer. 200 Munsell samples are shown by solid circles.

Fig. 5
Fig. 5

Reconstruction of reflectance data in 3D XYZ space. Asterisk (red online) and solid (blue online) curves show the standard and predicted reflectance curves, respectively, while dashed–dotted curves show the reflectance data of neighboring points that were used for the reconstruction process.

Fig. 6
Fig. 6

Results of spectral recovery of eight randomly selected samples of Matt Munsell chips from their tristimulus values by using LUT and PCA methods.

Fig. 7
Fig. 7

Distribution of 137 samples of ColorChecker chart and 200 Munsell color samples in L * a * b * color space.

Fig. 8
Fig. 8

Distribution of 137 samples of ColorChecker chart and 1269 Munsell color samples in L * a * b * color space.

Tables (6)

Tables Icon

Table 1 Spectral and Colorimetric Accuracy of Spectral Estimation by LUT and PCA Methods

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Table 2 Hypothesis Tests for RMS Errors and Color Difference Values for PCA and Interpolation Methods a

Tables Icon

Table 3 Spectral and Colorimetric Accuracy of Spectral Estimation by LUT Method Using Different Color Spaces

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Table 4 Spectral and Colorimetric Accuracy of Spectral Estimation by LUT and PCA Methods Using Different Color Coordinates

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Table 5 Processing Time of Reflectance Recovery by LUT Method for Different Input Spaces

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Table 6 RMS and Color Difference Errors of Recovery Process Using LUT and PCA Methods and Different Databases

Equations (22)

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

T i = { x R 2 d ( x , x j ) d ( x , x j ) j = 1 n } ,
P = a P 1 + b P 2 + c P 3 + d P 4 .
a x 1 + b x 2 + c x 3 + d x 4 = x ,
a y 1 + b y 2 + c y 3 + d y 4 = y ,
a z 1 + b z 2 + c z 3 + d z 4 = z ,
a + b + c + d = 1 .
R j = a R j P 1 + b R j P 2 + c R j P 3 + d R j P 4 ,
( a b c d ) = [ x 1 x 2 x 3 x 4 y 1 y 2 y 3 y 4 z 1 z 2 z 3 z 4 1 1 1 1 ] 1 ( x y z 1 ) .
R j = a R j P 1 + b R j P 2 + c R j P 3 + d R j P 4 + e R j P 5 ,
( a b c d e ) = [ x 1 x 2 x 3 x 4 x 5 y 1 y 2 y 3 y 4 y 5 z 1 z 2 z 3 z 4 z 5 t 1 t 2 t 3 t 4 t 5 1 1 1 1 1 ] 1 ( x y z t 1 ) .
R j = a R j P 1 + b R j P 2 + c R j P 3 + d R j P 4 + + n R j P n ,
( a b c d m p ) = [ x 1 x 2 x 3 x 4 x n x n + 1 y 1 y 2 y 3 y 4 y n y n + 1 z 1 z 2 z 3 z 4 z n z n + 1 t 1 t 2 t 3 t 4 t n t n + 1 m 1 m 2 m 3 m 4 m n m n + 1 1 1 1 1 1 1 1 ] 1 ( x y z t m 1 ) .
T j = 400 700 S λ r λ q j , λ d λ ,
T = A T r ,
r v 0 + j = 1 k c j v j ,
r v 0 + V c ,
T = A T v 0 + A T V c ,
T = T V 0 + T V c .
c = T V 1 ( T T V 0 ) .
X t = i = 1 n + 1 a i X i ,
R ̂ λ = i = 1 n + 1 a i R i ,
X ̑ t = λ = 400 700 R ̂ λ E λ x ¯ λ = λ = 400 700 ( i = 1 n + 1 a i R i ) E λ x ¯ λ = λ = 400 700 i = 1 n + 1 ( a i R i , λ E λ x ¯ λ ) = i = 1 n + 1 λ = 400 700 ( a i R i , λ E λ x ¯ λ ) = i = 1 n + 1 a i λ = 400 700 ( R i , λ E λ x ¯ λ ) = i = 1 n + 1 a i X i = X t .

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