Abstract

This paper proposes an improved reflectance reconstruction method by adaptively selecting training samples. Modified Principal Component Analysis estimation was proposed by orthogonal regression considering the system noise; deriving the optimum number of training samples by BP-Adaboost neural network; and grouping the representative samples together by hierarchical cluster analysis from a large database of samples. Finally, the training samples were selected by colorimetric subspace tracking. Experimental results indicated that the proposed method significantly outperforms the traditional methods in terms of both spectral and colorimetric accuracy, and our reflectance modeling is a reasonable and convenient tool to generate adaptive training sets.

© 2017 Optical Society of America

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References

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  1. J. H. Yoo, D. C. Kim, H. G. Ha, and Y. H. Ha, “Adaptive spectral reflectance reconstruction method based on wiener estimation using a similar training set,” J. Imaging Sci. Technol. 60(2), 020503 (2016).
    [Crossref]
  2. Y. Murakami, M. Yamaguchi, and N. Ohyama, “Piecewise Wiener estimation for reconstruction of spectral reflectance image by multipoint spectral measurements,” Appl. Opt. 48(11), 2188–2202 (2009).
    [Crossref] [PubMed]
  3. X. Zhang and H. Xu, “Reconstructing spectral reflectance by dividing spectral space and extending the principal components in principal component analysis,” J. Opt. Soc. Am. A 25(2), 371–378 (2008).
    [Crossref] [PubMed]
  4. R. Shrestha, A. Mansouri, and J. Y. Hardeberg, “Multispectral imaging using a stereo camera: concept, design and assessment,” Eurasip. J. Adv. Sig. Pr 2011(1), 57 (2011).
    [Crossref]
  5. Z. Liu, X. X. Wan, X. G. Huang, Q. Liu, and C. Li, “The study on spectral reflectance reconstruction based on wideband multi-spectral acquisition system,” Guangpuxue Yu Guangpu Fenxi 33(4), 1076–1081 (2013).
    [PubMed]
  6. J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D dissertation (Ecole Nationale Superieure des Telecommunications, 1999).
  7. V. Cheung and S. Westland, “Methods for optimal color selection,” J. Imaging Sci. Technol. 50(5), 481–488 (2006).
    [Crossref]
  8. M. Mohammadi and M. Nezamabadi, “A Prototype Calibration Target for Spectral Imaging”, in 10th Congress of the International Colour Association (2005), pp. 387–390.
  9. 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(23), 15545–15554 (2007).
    [Crossref] [PubMed]
  10. H. L. Shen, H. G. Zhang, J. H. Xin, and S. J. Shao, “Optimal selection of representative colors for spectral reflectance reconstruction in a multispectral imaging system,” Appl. Opt. 47(13), 2494–2502 (2008).
    [Crossref] [PubMed]
  11. J. D. T. Kruschwitz, “Specialized Color Targets for Spectral Reflectance Reconstruction of Magnified Images,” Ph.D dissertation (Rochester Institute of Technology, 2015).
  12. T. Eckhard, E. M. Valero, J. Hernández-Andrés, and M. Schnitzlein, “Adaptive global training set selection for spectral estimation of printed inks using reflectance modeling,” Appl. Opt. 53(4), 709–719 (2014).
    [Crossref] [PubMed]
  13. M. D. Rahman and Y. Kai-Bor, “Total least squares approach for frequency estimation using linear prediction,” IEEE. T. Acoust. Spee. Signal. Proces 35(10), 1440–1454 (1987).
    [Crossref]

2016 (1)

J. H. Yoo, D. C. Kim, H. G. Ha, and Y. H. Ha, “Adaptive spectral reflectance reconstruction method based on wiener estimation using a similar training set,” J. Imaging Sci. Technol. 60(2), 020503 (2016).
[Crossref]

2014 (1)

2013 (1)

Z. Liu, X. X. Wan, X. G. Huang, Q. Liu, and C. Li, “The study on spectral reflectance reconstruction based on wideband multi-spectral acquisition system,” Guangpuxue Yu Guangpu Fenxi 33(4), 1076–1081 (2013).
[PubMed]

2011 (1)

R. Shrestha, A. Mansouri, and J. Y. Hardeberg, “Multispectral imaging using a stereo camera: concept, design and assessment,” Eurasip. J. Adv. Sig. Pr 2011(1), 57 (2011).
[Crossref]

2009 (1)

2008 (2)

2007 (1)

2006 (1)

V. Cheung and S. Westland, “Methods for optimal color selection,” J. Imaging Sci. Technol. 50(5), 481–488 (2006).
[Crossref]

1987 (1)

M. D. Rahman and Y. Kai-Bor, “Total least squares approach for frequency estimation using linear prediction,” IEEE. T. Acoust. Spee. Signal. Proces 35(10), 1440–1454 (1987).
[Crossref]

Cai, P. Q.

Cheung, V.

V. Cheung and S. Westland, “Methods for optimal color selection,” J. Imaging Sci. Technol. 50(5), 481–488 (2006).
[Crossref]

Eckhard, T.

Ha, H. G.

J. H. Yoo, D. C. Kim, H. G. Ha, and Y. H. Ha, “Adaptive spectral reflectance reconstruction method based on wiener estimation using a similar training set,” J. Imaging Sci. Technol. 60(2), 020503 (2016).
[Crossref]

Ha, Y. H.

J. H. Yoo, D. C. Kim, H. G. Ha, and Y. H. Ha, “Adaptive spectral reflectance reconstruction method based on wiener estimation using a similar training set,” J. Imaging Sci. Technol. 60(2), 020503 (2016).
[Crossref]

Hardeberg, J. Y.

R. Shrestha, A. Mansouri, and J. Y. Hardeberg, “Multispectral imaging using a stereo camera: concept, design and assessment,” Eurasip. J. Adv. Sig. Pr 2011(1), 57 (2011).
[Crossref]

Hernández-Andrés, J.

Huang, X. G.

Z. Liu, X. X. Wan, X. G. Huang, Q. Liu, and C. Li, “The study on spectral reflectance reconstruction based on wideband multi-spectral acquisition system,” Guangpuxue Yu Guangpu Fenxi 33(4), 1076–1081 (2013).
[PubMed]

Kai-Bor, Y.

M. D. Rahman and Y. Kai-Bor, “Total least squares approach for frequency estimation using linear prediction,” IEEE. T. Acoust. Spee. Signal. Proces 35(10), 1440–1454 (1987).
[Crossref]

Kim, D. C.

J. H. Yoo, D. C. Kim, H. G. Ha, and Y. H. Ha, “Adaptive spectral reflectance reconstruction method based on wiener estimation using a similar training set,” J. Imaging Sci. Technol. 60(2), 020503 (2016).
[Crossref]

Li, C.

Z. Liu, X. X. Wan, X. G. Huang, Q. Liu, and C. Li, “The study on spectral reflectance reconstruction based on wideband multi-spectral acquisition system,” Guangpuxue Yu Guangpu Fenxi 33(4), 1076–1081 (2013).
[PubMed]

Liu, Q.

Z. Liu, X. X. Wan, X. G. Huang, Q. Liu, and C. Li, “The study on spectral reflectance reconstruction based on wideband multi-spectral acquisition system,” Guangpuxue Yu Guangpu Fenxi 33(4), 1076–1081 (2013).
[PubMed]

Liu, Z.

Z. Liu, X. X. Wan, X. G. Huang, Q. Liu, and C. Li, “The study on spectral reflectance reconstruction based on wideband multi-spectral acquisition system,” Guangpuxue Yu Guangpu Fenxi 33(4), 1076–1081 (2013).
[PubMed]

Mansouri, A.

R. Shrestha, A. Mansouri, and J. Y. Hardeberg, “Multispectral imaging using a stereo camera: concept, design and assessment,” Eurasip. J. Adv. Sig. Pr 2011(1), 57 (2011).
[Crossref]

Mohammadi, M.

M. Mohammadi and M. Nezamabadi, “A Prototype Calibration Target for Spectral Imaging”, in 10th Congress of the International Colour Association (2005), pp. 387–390.

Murakami, Y.

Nezamabadi, M.

M. Mohammadi and M. Nezamabadi, “A Prototype Calibration Target for Spectral Imaging”, in 10th Congress of the International Colour Association (2005), pp. 387–390.

Ohyama, N.

Rahman, M. D.

M. D. Rahman and Y. Kai-Bor, “Total least squares approach for frequency estimation using linear prediction,” IEEE. T. Acoust. Spee. Signal. Proces 35(10), 1440–1454 (1987).
[Crossref]

Schnitzlein, M.

Shao, S. J.

Shen, H. L.

Shrestha, R.

R. Shrestha, A. Mansouri, and J. Y. Hardeberg, “Multispectral imaging using a stereo camera: concept, design and assessment,” Eurasip. J. Adv. Sig. Pr 2011(1), 57 (2011).
[Crossref]

Valero, E. M.

Wan, X. X.

Z. Liu, X. X. Wan, X. G. Huang, Q. Liu, and C. Li, “The study on spectral reflectance reconstruction based on wideband multi-spectral acquisition system,” Guangpuxue Yu Guangpu Fenxi 33(4), 1076–1081 (2013).
[PubMed]

Westland, S.

V. Cheung and S. Westland, “Methods for optimal color selection,” J. Imaging Sci. Technol. 50(5), 481–488 (2006).
[Crossref]

Xin, J. H.

Xu, H.

Yamaguchi, M.

Yoo, J. H.

J. H. Yoo, D. C. Kim, H. G. Ha, and Y. H. Ha, “Adaptive spectral reflectance reconstruction method based on wiener estimation using a similar training set,” J. Imaging Sci. Technol. 60(2), 020503 (2016).
[Crossref]

Zhang, H. G.

Zhang, X.

Appl. Opt. (3)

Eurasip. J. Adv. Sig. Pr (1)

R. Shrestha, A. Mansouri, and J. Y. Hardeberg, “Multispectral imaging using a stereo camera: concept, design and assessment,” Eurasip. J. Adv. Sig. Pr 2011(1), 57 (2011).
[Crossref]

Guangpuxue Yu Guangpu Fenxi (1)

Z. Liu, X. X. Wan, X. G. Huang, Q. Liu, and C. Li, “The study on spectral reflectance reconstruction based on wideband multi-spectral acquisition system,” Guangpuxue Yu Guangpu Fenxi 33(4), 1076–1081 (2013).
[PubMed]

IEEE. T. Acoust. Spee. Signal. Proces (1)

M. D. Rahman and Y. Kai-Bor, “Total least squares approach for frequency estimation using linear prediction,” IEEE. T. Acoust. Spee. Signal. Proces 35(10), 1440–1454 (1987).
[Crossref]

J. Imaging Sci. Technol. (2)

J. H. Yoo, D. C. Kim, H. G. Ha, and Y. H. Ha, “Adaptive spectral reflectance reconstruction method based on wiener estimation using a similar training set,” J. Imaging Sci. Technol. 60(2), 020503 (2016).
[Crossref]

V. Cheung and S. Westland, “Methods for optimal color selection,” J. Imaging Sci. Technol. 50(5), 481–488 (2006).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Other (3)

J. D. T. Kruschwitz, “Specialized Color Targets for Spectral Reflectance Reconstruction of Magnified Images,” Ph.D dissertation (Rochester Institute of Technology, 2015).

M. Mohammadi and M. Nezamabadi, “A Prototype Calibration Target for Spectral Imaging”, in 10th Congress of the International Colour Association (2005), pp. 387–390.

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

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Figures (8)

Fig. 1
Fig. 1 Structural diagram of the neural networks.
Fig. 2
Fig. 2 (a) Boxplot of CIE DE2000 color difference, and (b) spectral root-mean-square error
Fig. 3
Fig. 3 Distribution of training samples in principal component space, for six randomly selected samples ((a)188, (b)90, (c)202, (d)143, (e)227, (f)132) among 240 reconstructed samples. The yellow circles are selected targets based on the Mohammadi clustering method; the purple squares are selected based on our method. The cyan diamonds are a distribution of all the training samples. The red star is a reconstructed sample.
Fig. 4
Fig. 4 Distribution of training samples in multidimensional scaling space, for six randomly selected samples ((a)188, (b)90, (c)202, (d)143, (e)227, (f)132).
Fig. 5
Fig. 5 Distribution of training samples in xyY chromaticity space, for six randomly selected samples ((a) 188, (b) 90, (c) 202, (d) 143, (e) 227, (f)132) among 240 reconstructed samples.
Fig. 6
Fig. 6 Distribution of training samples in lab chromaticity space, for six randomly selected samples ((a) 188, (b) 90, (c) 202, (d) 143, (e) 227, (f)132) among 240 reconstructed samples.
Fig. 7
Fig. 7 (a) Histograms of training sample numbers predicted by neural network; (b) Measured reflectance of 240 test samples.
Fig. 8
Fig. 8 Reflectance reconstruction of the proposed method and traditional estimation, for six randomly selected samples ((a)188, (b)90, (c)202, (d)132, (e)227, (f)143) .

Tables (3)

Tables Icon

Table 1 CIEDE2000 errors of Wiener, PCA, Mohammdi, and Our Methods.

Tables Icon

Table 2 Spectral GFC and rms errors of Wiener, PCA, Mohammdi, and Our Methods.

Tables Icon

Table 3 Comparison of a different number of training samples on spectral and colorimetric errors.

Equations (17)

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

r= i=1 p e i a i = Fa
c=Mr=MFa
M F 0 a= c 0 [ MFΔMF ]a=cε
( [c,MF]+[ε,ΔMF] )[ 1 a ]=0
min B,a B F = min B,a [ε,ΔMF] F =min{ ( i=1 m j=1 n b ij 2 ) 1/2 }= min B,a ( trace( B H B) )
a ˜ = [ (MF) H MF σ min 2 I ] ( MF ) H c
r ^ =F a ˜ =F [ (MF) H MF σ min 2 I ] 1 ( MF ) H c
d(r,s)= 2 n r n s ( n r + n s ) x r ¯ x s ¯ 2
t c = λ=380 780 P n (λ) V n (λ) r n (λ)
t c = Θ H r
Θ=U V H =[ U 1 , U 2 ][ 1 O (m3)×n ] V H = U 1 V H
P Θ =[ U 1 , U 2 ][ I 3 0 3×(m3) 0 (m3)×3 0 (m3)×(m3) ][ U 1 H U 2 H ]= U 1 U 1 H =Θ ( Θ H Θ ) 1 Θ H
r * = P Θ r=Θ ( Θ H Θ ) 1 Θ H r=Θ ( Θ H Θ ) 1 t c
d s,t =1 ( r s r s ¯ )( r t r t ¯ )' ( r s r s ¯ )( r s r s ¯ )' ( r t r t ¯ )( r t r t ¯ )' r s ¯ = 1 n j r sj = (n+1) 2 , r t ¯ = 1 n j r tj = (n+1) 2
Ω={ x i,j | x i,j min( d s,t ( r i,j , r t )) }
r ^ = F Ω a ˜ = F Ω [ (M F Ω ) H M F Ω σ min 2 I ] 1 ( M F Ω ) H c
GFC= i=1 n r i r ^ i i=1 n r i 2 i=1 n r ^ i 2 , rms= 1 n i=1 n [ r i r ^ i ] 2

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