Abstract

In multispectral imaging, Wiener estimation is widely adopted for the reconstruction of spectral reflectance. We propose an improved reflectance reconstruction method by adaptively selecting training samples for the autocorrelation matrix calculation in Wiener estimation, without a prior knowledge of the spectral information of the samples being imaged. The performance of the proposed adaptive Wiener estimation and the traditional method are compared in the cases of different channel numbers and noise levels. Experimental results show that the proposed method outperforms the traditional method in terms of both spectral and colorimetric prediction errors when the imaging channel number is 7 or less. When the imaging system consists of 11 or more channels, the color accuracy of the proposed method is slightly better than or becomes close to that of the traditional method.

© 2007 Optical Society of America

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References

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  1. J. Y. Hardeberg, "Acquisition and reproduction of color images: colorimetric and multispectral approaches," Ph.D. dissertation (Ecole Nationale Superieure des Telecommunications, 1999).
  2. N. Shimano, "Recovery of spectral reflectances of objects being imaged without prior knowledge," IEEE Trans. Image Process. 15, 1848-1856 (2006).
    [CrossRef] [PubMed]
  3. 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]
  4. H. L. Shen, J. H. Xin, and S. J. Shao, "Improved reflectance reconstruction for multispectral imaging by combining different techniques," Opt. Express 15, 5531-5536 (2007).
    [CrossRef] [PubMed]
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    [PubMed]
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    [CrossRef]
  7. J. Y. Hardeberg, F. Schmitt, and H. Brettel, "Multispectral color image capture using liquid crystal tunable filter," Opt. Eng. 41, 2532-2548 (2002).
    [CrossRef]
  8. Y. Murakami, T. Obi, M. Yamaguchi, and N. Ohyama, "Nonlinear estimation of spectral reflectance based on Gaussian mixture distribution for color image reproduction," Appl. Opt. 41, 4840-4847 (2002).
    [CrossRef] [PubMed]
  9. H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, "System design for accurately estimating the spectral reflectance of art paintings," Appl. Opt. 39, 6621-6632 (2000).
    [CrossRef]
  10. N. Shimano, "Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise," Opt. Eng. 45, 013201 (2006).
    [CrossRef]
  11. 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]
  12. H. L. Shen and J. H. Xin, "Spectral characterization of a color scanner based on optimized adaptive estimation," J. Opt. Soc. Am. A 23, 1566-1569 (2006).
    [CrossRef]
  13. J. M. DiCarlo and B. A. Wandell, "Spectral estimation theory: beyond linear but before Bayesian," J. Opt. Soc. Am. A,  20, 1261-1270 (2003).
    [CrossRef]
  14. K. Barnard and B. Funt, "Camera characterization for color research," Color Res. Appl. 27, 152-163 (2002).
    [CrossRef]
  15. M. R. 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 (2)

2006 (3)

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

H. L. Shen and J. H. Xin, "Spectral characterization of a color scanner based on optimized adaptive estimation," J. Opt. Soc. Am. A 23, 1566-1569 (2006).
[CrossRef]

N. Shimano, "Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise," Opt. Eng. 45, 013201 (2006).
[CrossRef]

2005 (1)

2003 (1)

2002 (4)

2001 (2)

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]

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

2000 (1)

Barnard, K.

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

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]

Cheung, V.

Connah, D.

Cui, G.

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

DiCarlo, J. M.

Funt, B.

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

Haneishi, H.

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]

Hasegawa, T.

Hernández-Andrés, J.

Hosoi, A.

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.

López-Álvarez, M. A.

Luo, M. R.

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

Miyake, Y.

Murakami, Y.

Y. Murakami, T. Obi, M. Yamaguchi, and N. Ohyama, "Nonlinear estimation of spectral reflectance based on Gaussian mixture distribution for color image reproduction," Appl. Opt. 41, 4840-4847 (2002).
[CrossRef] [PubMed]

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]

Obi, T.

Y. Murakami, T. Obi, M. Yamaguchi, and N. Ohyama, "Nonlinear estimation of spectral reflectance based on Gaussian mixture distribution for color image reproduction," Appl. Opt. 41, 4840-4847 (2002).
[CrossRef] [PubMed]

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]

Oblefias, W.

Ohyama, N.

Y. Murakami, T. Obi, M. Yamaguchi, and N. Ohyama, "Nonlinear estimation of spectral reflectance based on Gaussian mixture distribution for color image reproduction," Appl. Opt. 41, 4840-4847 (2002).
[CrossRef] [PubMed]

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]

Rigg, B.

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

Saloma, C.

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, "Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise," Opt. Eng. 45, 013201 (2006).
[CrossRef]

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

Soriano, M.

Tsumura, N.

Valero, E. M.

Wandell, B. A.

Westland, S.

Xin, J. H.

Yamaguchi, M.

Y. Murakami, T. Obi, M. Yamaguchi, and N. Ohyama, "Nonlinear estimation of spectral reflectance based on Gaussian mixture distribution for color image reproduction," Appl. Opt. 41, 4840-4847 (2002).
[CrossRef] [PubMed]

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]

Yokoyama, Y.

Appl. Opt. (2)

Color Res. Appl. (2)

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

M. R. 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 reflectances of objects being imaged without prior knowledge," IEEE Trans. Image Process. 15, 1848-1856 (2006).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (4)

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. (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]

N. Shimano, "Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise," Opt. Eng. 45, 013201 (2006).
[CrossRef]

Opt. Express (2)

Other (1)

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 (5)

Fig. 1.
Fig. 1.

The spectral responsivities of the 31 channels of the multispectral imaging system.

Fig. 2.
Fig. 2.

Reflectances of the 1296 Munsell color chips.

Fig. 3.
Fig. 3.

The distribution of average reflectance rms error (left) and average color difference error (right) with respect to the training sample number L. Channel number C=6 and SNR=50.

Fig. 4.
Fig. 4.

Two typical examples of the training sets for the given candidate samples. Channel number C=6 and SNR=50.

Fig. 5.
Fig. 5.

Reflectance reconstruction of the proposed adaptive Wiener estimation and traditional Wiener estimation when using real data. Channel number C=7.

Tables (3)

Tables Icon

Table 2. The corresponding channel sequences of different channel number C

Tables Icon

Table 2. Comparison of the spectral and colorimetric errors of the proposed adaptive Wiener estimation (AWE), the traditional Wiener estimation (WE), and the optimized method (Opt.) [12] when using synthetic data.

Tables Icon

Table 3. Comparison of the spectral and colorimetric errors of the proposed adaptive Wiener estimation (AWE) and the traditional Wiener estimation (WE) when using real data.

Equations (16)

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

v c = l ( λ ) r ( λ ) f c ( λ ) S ( λ ) + b c + n c = m c ( λ ) r ( λ ) d λ + b c + n c ,
v = Mr + b + n ,
m ij 0
u = Mr + n .
r ̂ = Wu ,
W WE = 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 } ,
d i = α mean { r i r i r ̂ r ̂ } + ( 1 α ) max { r i r i r ̂ r ̂ } ,
Ω = { r 1 r 1 k 1 times , , r i r i k i times , , r L 1 times } ,
k i = ( d L d i ) γ + 0.5 ,
W AWE = K r , Ω M T ( MK r , Ω M T + K n ) 1 ,
rms = ( ( r r ̂ ) T ( r r ̂ ) N ) 1 2 .
u syn = Mr + n σ ,
SNR = 10   log ( Tr ( MK r M T ) σ 2 ) ,

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