Abstract

Principal component analysis (PCA) is widely used to reconstruct the spectral reflectance of surface colors. However, the estimated spectral accuracy is low when using only one set of three principal components for three-channel color-acquisition devices. In this study, the spectral space was first divided into 11 subgroups, and the principal components were calculated for individual subgroups. Then the principal components were further extended from three to nine through the residual spectral error of the reflectance in each subgroup. For each target sample, the extended principal components of the corresponding subgroup samples were used in the common PCA method to reconstruct the spectral reflectance. The results show that this proposed method is quite accurate and outperforms other related methods.

© 2008 Optical Society of America

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References

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2007 (4)

V. Bochko, "Spectral color imaging system for estimating spectral reflectance of paint," J. Imaging Sci. Technol. 51, 70-78 (2007).
[CrossRef]

Oh. Kwon, Ch. Lee, K. Park, and Y. Ha, "Surface reflectance estimation using the principal components of similar colors," J. Imaging Sci. Technol. 51, 166-174 (2007).
[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]

N. Shimano, K. Terai, and M. Hironaga, "Recovery of spectral reflectances of objects being imaged by multispectral cameras," J. Opt. Soc. Am. A 24, 3211-3219 (2007).
[CrossRef]

2006 (5)

P. Morovic and G. D. Finlayson, "Metamer-set-based approach to estimating surface reflectance from camera RGB," J. Opt. Soc. Am. A 23, 1814-1822 (2006).
[CrossRef]

F. Ayala, J. F. Echávarri, and P. Renet, "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]

D. Connah, A. Alsam, and J. Y. Hardeberg, "Multispectral imaging: how many sensors do we need?" J. Imaging Sci. Technol. 50, 45-52 (2006).
[CrossRef]

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

O. Kohonen, J. Parkkinen, and T. Jääskeläinen, "Databases for spectral color science," Color Res. Appl. 31, 381-388 (2006).
[CrossRef]

2005 (2)

D. Y. Tzeng and R. S. Berns, "A review of principal component analysis and its applications to color technology," Color Res. Appl. 30, 84-98 (2005).
[CrossRef]

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

2004 (3)

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

J. A. Worthey and M. H. Brill, "Principal components applied to modeling: dealing with the mean vectors," Color Res. Appl. 29, 261-266 (2004).
[CrossRef]

H. L. Shen and J. H. Xin, "Colorimetric and spectral characterization of a color scanner using local statistics," J. Imaging Sci. Technol. 48, 342-346 (2004).

2003 (1)

M. H. Brill, "A non-pc look at principal components," Color Res. Appl. 28, 69-71 (2003).
[CrossRef]

2002 (4)

G. Sharma and S. Wang, "Spectrum recovery from colorimetric data for color reproductions," Proc. SPIE 4663, 8-14 (2002).
[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]

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

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

2001 (1)

G. W. Hong, M. R. Luo, and P. A. Rhodes, "A study of digital camera colorimetric characterization based on polynomial modeling," Color Res. Appl. 26, 76-84 (2001).
[CrossRef]

2000 (1)

H. Laamanen, T. Jaaskelainen, and J. P. S. Parkkinen, "Comparison of PCA and ICA in color recognition," Proc. SPIE 4197, 367-377 (2000).
[CrossRef]

1996 (1)

H. J. Trusseli and M. S. Kulkarni, "Sampling and processing of color signals," IEEE Trans. Image Process. 5, 677-681 (1996).
[CrossRef] [PubMed]

1989 (1)

1986 (1)

1964 (1)

J. Cohen, "Dependency of the spectral reflectance curves of the Munsell color chips," Psychonomic Sci. 1, 369-370 (1964).

Color Res. Appl. (8)

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]

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

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

D. Y. Tzeng and R. S. Berns, "A review of principal component analysis and its applications to color technology," Color Res. Appl. 30, 84-98 (2005).
[CrossRef]

M. H. Brill, "A non-pc look at principal components," Color Res. Appl. 28, 69-71 (2003).
[CrossRef]

J. A. Worthey and M. H. Brill, "Principal components applied to modeling: dealing with the mean vectors," Color Res. Appl. 29, 261-266 (2004).
[CrossRef]

G. W. Hong, M. R. Luo, and P. A. Rhodes, "A study of digital camera colorimetric characterization based on polynomial modeling," Color Res. Appl. 26, 76-84 (2001).
[CrossRef]

O. Kohonen, J. Parkkinen, and T. Jääskeläinen, "Databases for spectral color science," Color Res. Appl. 31, 381-388 (2006).
[CrossRef]

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," Color. Technol. 122, 128-134 (2006).
[CrossRef]

IEEE Trans. Image Process. (1)

H. J. Trusseli and M. S. Kulkarni, "Sampling and processing of color signals," IEEE Trans. Image Process. 5, 677-681 (1996).
[CrossRef] [PubMed]

J. Imaging Sci. Technol. (4)

H. L. Shen and J. H. Xin, "Colorimetric and spectral characterization of a color scanner using local statistics," J. Imaging Sci. Technol. 48, 342-346 (2004).

V. Bochko, "Spectral color imaging system for estimating spectral reflectance of paint," J. Imaging Sci. Technol. 51, 70-78 (2007).
[CrossRef]

Oh. Kwon, Ch. Lee, K. Park, and Y. Ha, "Surface reflectance estimation using the principal components of similar colors," J. Imaging Sci. Technol. 51, 166-174 (2007).
[CrossRef]

D. Connah, A. Alsam, and J. Y. Hardeberg, "Multispectral imaging: how many sensors do we need?" J. Imaging Sci. Technol. 50, 45-52 (2006).
[CrossRef]

J. Opt. Soc. Am. A (7)

Opt. Eng. (1)

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

Proc. SPIE (2)

G. Sharma and S. Wang, "Spectrum recovery from colorimetric data for color reproductions," Proc. SPIE 4663, 8-14 (2002).
[CrossRef]

H. Laamanen, T. Jaaskelainen, and J. P. S. Parkkinen, "Comparison of PCA and ICA in color recognition," Proc. SPIE 4197, 367-377 (2000).
[CrossRef]

Psychonomic Sci. (1)

J. Cohen, "Dependency of the spectral reflectance curves of the Munsell color chips," Psychonomic Sci. 1, 369-370 (1964).

Other (5)

J. Y. Hardeberg, "Acquisition and reproduction of colour images: colorimetric and multispectral approaches," Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 21-22.

F. M. Abed, S. H. Amirshahi, S. Peyvandi, and M. R. M. Abed, "Reconstruction of the reflectance curves by using interpolation method," presented at the Midterm Meeting of the International Color Association, Hangzhou, China, July 12-14, 2007.

J. K. Eem, H. D. Shin, and S. O. Park, "Reconstruction of surface spectral reflectance using characteristic vectors of Munsell colors," in Recent Progress in Color Science, K.Braun and R.Eschbach, eds. (Academic, 1997), pp. 301-305.

Y. H. Zhao, L. A. Taplin, M. Nezamabadi, and R. S. Berns, "Methods of spectral reflectance reconstruction for a Sinarback 54 digital camera," http://art-si.org/.

G. W. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Academic, 1982).

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Figures (2)

Fig. 1
Fig. 1

Spectral reflectances of Munsell chips in the 11 subgroups from (a) to (k): R, YR, Y, GY, G, BG, B, PB, P, RP, and NGr subgroups, respectively.

Fig. 2
Fig. 2

Relationship between the numbers of extended principal components and the RMSE of Munsell chips.

Tables (7)

Tables Icon

Table 1 Comparisons of Performances among Methods pi, i, ii, and iii under the Condition of CIE Illuminant D65

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Table 2 ANOVA Results of RMSE among Methods pi, i, ii, and iii under the Condition of CIE Illuminant D65

Tables Icon

Table 3 Comparisons of Performances among Methods pi, i, ii, and iii under the Conditions of CIE Illuminant D65 with Odd Chips of NCS and Munsell Atlas As Training and Testing Samples, Respectively

Tables Icon

Table 4 Comparisons of Performances between Ayala Method[13] and Proposed Method iii

Tables Icon

Table 5 Comparisons of Performances among Methods pi, i, ii, and iii under the Conditions of Illuminants A and F11

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Table 6 ANOVA Results of RMSE between Method iii and Methods pi, i, and ii under the Conditions of Illuminants A and F11

Tables Icon

Table 7 ANOVA Results of RMSE for Methods pi, i, ii, and iii between Illuminants A and F11

Equations (11)

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

{ X = k E ( λ ) x ¯ ( λ ) r ( λ ) d λ Y = k E ( λ ) y ¯ ( λ ) r ( λ ) d λ Z = k E ( λ ) z ¯ ( λ ) r ( λ ) d λ } ,
k = 100 E ( λ ) y ¯ ( λ ) d λ ,
[ X Y Z ] = M r ,
r v ¯ + i = 1 l a i v i ,
[ X Y Z ] M v ¯ = M [ v 1 v 2 v 3 ] [ a 1 a 2 a 3 ] ,
[ a 1 a 2 a 3 ] = ( M [ v 1 v 2 v 3 ] ) 1 ( [ X Y Z ] M v ¯ ) .
Δ r i = r i , mea r i , com ( i = 1 , 2 , , N ) ,
Δ r i = j = 1 K b i , j ρ j ,
b i , j = ρ j T Δ r i ,
r i , pre = r i , com + Δ r i .
b j = c j , 0 + c j , 1 x + c j , 2 y + c j , 3 z + c j , 4 x y + c j , 5 x z + c j , 6 y z + c j , 7 x 2 + c j , 8 y 2 + c j , 9 z 2 + c j , 10 x y z ,

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