Abstract

Estimation of the spectral reflectance of a scene is a critical problem in image processing and computer vision applications. Model-based multispectral imaging, one of the spectral reflectance estimation methods, can effectively reconstruct the full spectrum using a small number of camera shots. However, it is based on iterative optimization and, thus, is computationally too intensive. In this Letter, we modify the iterative optimization problem to a closed-form problem using nonnegative principal component analysis. The proposed method can substantially reduce the computational cost while maintaining the accuracy.

© 2012 Optical Society of America

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  1. M. Sambongi, M. Igarashi, T. Obi, M. Yamaguchi, N. Ohyama, M. Kobayashi, Y. Sano, S. Yoshida, and K. Gono, Opt. Rev. 9, 238 (2002).
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2010 (1)

2009 (1)

2007 (1)

2005 (3)

J. C. Noordam, W. van den Broek, and L. Buydens, J. Sci. Food Agric. 85, 2249 (2005).
[CrossRef]

L. Anderson, Y. Shimabukuro, R. Defries, and D. Morton, IEEE Geosci. Remote Sens. Lett. 2, 315 (2005).
[CrossRef]

D.-Y. Tzeng and R. S. Berns, Color Res. Appl. 30, 84 (2005).
[CrossRef]

2002 (2)

K. Barnard and B. Funt, Color Res. Appl. 27, 152 (2002).
[CrossRef]

M. Sambongi, M. Igarashi, T. Obi, M. Yamaguchi, N. Ohyama, M. Kobayashi, Y. Sano, S. Yoshida, and K. Gono, Opt. Rev. 9, 238 (2002).
[CrossRef]

2001 (1)

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, Biophys. J. 80, 986 (2001).
[CrossRef]

2000 (1)

1998 (1)

G. Sharma, J. Trussell, and M. J. Vrhel, IEEE Trans. Image Process. 7, 129 (1998).
[CrossRef]

1989 (1)

1986 (1)

1983 (1)

D. Goldfarb and A. Idnani, Math. Program. 27, 1 (1983).
[CrossRef]

Anderson, L.

L. Anderson, Y. Shimabukuro, R. Defries, and D. Morton, IEEE Geosci. Remote Sens. Lett. 2, 315 (2005).
[CrossRef]

Barnard, K.

K. Barnard and B. Funt, Color Res. Appl. 27, 152 (2002).
[CrossRef]

Berns, R. S.

D.-Y. Tzeng and R. S. Berns, Color Res. Appl. 30, 84 (2005).
[CrossRef]

Brady, D. J.

Buydens, L.

J. C. Noordam, W. van den Broek, and L. Buydens, J. Sci. Food Agric. 85, 2249 (2005).
[CrossRef]

Defries, R.

L. Anderson, Y. Shimabukuro, R. Defries, and D. Morton, IEEE Geosci. Remote Sens. Lett. 2, 315 (2005).
[CrossRef]

Descour, M. R.

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, Biophys. J. 80, 986 (2001).
[CrossRef]

Drew, M. S.

Finlayson, G. D.

Ford, B. K.

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, Biophys. J. 80, 986 (2001).
[CrossRef]

Funt, B.

K. Barnard and B. Funt, Color Res. Appl. 27, 152 (2002).
[CrossRef]

Gao, L.

Gehm, M. E.

Goldfarb, D.

D. Goldfarb and A. Idnani, Math. Program. 27, 1 (1983).
[CrossRef]

Gono, K.

M. Sambongi, M. Igarashi, T. Obi, M. Yamaguchi, N. Ohyama, M. Kobayashi, Y. Sano, S. Yoshida, and K. Gono, Opt. Rev. 9, 238 (2002).
[CrossRef]

Grossberg, M. D.

J. Park, M. Lee, M. D. Grossberg, and S. K. Nayar, in IEEE International Conference on Computer Vision (2007).

Hagen, N.

Hallikainen, J.

Idnani, A.

D. Goldfarb and A. Idnani, Math. Program. 27, 1 (1983).
[CrossRef]

Igarashi, M.

M. Sambongi, M. Igarashi, T. Obi, M. Yamaguchi, N. Ohyama, M. Kobayashi, Y. Sano, S. Yoshida, and K. Gono, Opt. Rev. 9, 238 (2002).
[CrossRef]

Jaaskelainen, T.

John, R.

Kester, R. T.

Kobayashi, M.

M. Sambongi, M. Igarashi, T. Obi, M. Yamaguchi, N. Ohyama, M. Kobayashi, Y. Sano, S. Yoshida, and K. Gono, Opt. Rev. 9, 238 (2002).
[CrossRef]

Lee, M.

J. Park, M. Lee, M. D. Grossberg, and S. K. Nayar, in IEEE International Conference on Computer Vision (2007).

Lynch, R. M.

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, Biophys. J. 80, 986 (2001).
[CrossRef]

Maloney, L. T.

Morton, D.

L. Anderson, Y. Shimabukuro, R. Defries, and D. Morton, IEEE Geosci. Remote Sens. Lett. 2, 315 (2005).
[CrossRef]

Murphy, S. M.

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, Biophys. J. 80, 986 (2001).
[CrossRef]

Nayar, S. K.

J. Park, M. Lee, M. D. Grossberg, and S. K. Nayar, in IEEE International Conference on Computer Vision (2007).

Noordam, J. C.

J. C. Noordam, W. van den Broek, and L. Buydens, J. Sci. Food Agric. 85, 2249 (2005).
[CrossRef]

Obi, T.

M. Sambongi, M. Igarashi, T. Obi, M. Yamaguchi, N. Ohyama, M. Kobayashi, Y. Sano, S. Yoshida, and K. Gono, Opt. Rev. 9, 238 (2002).
[CrossRef]

Ohyama, N.

M. Sambongi, M. Igarashi, T. Obi, M. Yamaguchi, N. Ohyama, M. Kobayashi, Y. Sano, S. Yoshida, and K. Gono, Opt. Rev. 9, 238 (2002).
[CrossRef]

Park, J.

J. Park, M. Lee, M. D. Grossberg, and S. K. Nayar, in IEEE International Conference on Computer Vision (2007).

Parkkinen, J.

Sambongi, M.

M. Sambongi, M. Igarashi, T. Obi, M. Yamaguchi, N. Ohyama, M. Kobayashi, Y. Sano, S. Yoshida, and K. Gono, Opt. Rev. 9, 238 (2002).
[CrossRef]

Sano, Y.

M. Sambongi, M. Igarashi, T. Obi, M. Yamaguchi, N. Ohyama, M. Kobayashi, Y. Sano, S. Yoshida, and K. Gono, Opt. Rev. 9, 238 (2002).
[CrossRef]

Schulz, T. J.

Sharma, G.

G. Sharma, J. Trussell, and M. J. Vrhel, IEEE Trans. Image Process. 7, 129 (1998).
[CrossRef]

Shashua, A.

R. Zass and A. Shashua, in Neural Information Processing Systems (2007).

Shimabukuro, Y.

L. Anderson, Y. Shimabukuro, R. Defries, and D. Morton, IEEE Geosci. Remote Sens. Lett. 2, 315 (2005).
[CrossRef]

Tkaczyk, T. S.

Trussell, J.

G. Sharma, J. Trussell, and M. J. Vrhel, IEEE Trans. Image Process. 7, 129 (1998).
[CrossRef]

Tzeng, D.-Y.

D.-Y. Tzeng and R. S. Berns, Color Res. Appl. 30, 84 (2005).
[CrossRef]

van den Broek, W.

J. C. Noordam, W. van den Broek, and L. Buydens, J. Sci. Food Agric. 85, 2249 (2005).
[CrossRef]

Volin, C. E.

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, Biophys. J. 80, 986 (2001).
[CrossRef]

Vrhel, M. J.

G. Sharma, J. Trussell, and M. J. Vrhel, IEEE Trans. Image Process. 7, 129 (1998).
[CrossRef]

Willett, R. M.

Yamaguchi, M.

M. Sambongi, M. Igarashi, T. Obi, M. Yamaguchi, N. Ohyama, M. Kobayashi, Y. Sano, S. Yoshida, and K. Gono, Opt. Rev. 9, 238 (2002).
[CrossRef]

Yoshida, S.

M. Sambongi, M. Igarashi, T. Obi, M. Yamaguchi, N. Ohyama, M. Kobayashi, Y. Sano, S. Yoshida, and K. Gono, Opt. Rev. 9, 238 (2002).
[CrossRef]

Zass, R.

R. Zass and A. Shashua, in Neural Information Processing Systems (2007).

Biophys. J. (1)

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, Biophys. J. 80, 986 (2001).
[CrossRef]

Color Res. Appl. (2)

D.-Y. Tzeng and R. S. Berns, Color Res. Appl. 30, 84 (2005).
[CrossRef]

K. Barnard and B. Funt, Color Res. Appl. 27, 152 (2002).
[CrossRef]

IEEE Geosci. Remote Sens. Lett. (1)

L. Anderson, Y. Shimabukuro, R. Defries, and D. Morton, IEEE Geosci. Remote Sens. Lett. 2, 315 (2005).
[CrossRef]

IEEE Trans. Image Process. (1)

G. Sharma, J. Trussell, and M. J. Vrhel, IEEE Trans. Image Process. 7, 129 (1998).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Sci. Food Agric. (1)

J. C. Noordam, W. van den Broek, and L. Buydens, J. Sci. Food Agric. 85, 2249 (2005).
[CrossRef]

Math. Program. (1)

D. Goldfarb and A. Idnani, Math. Program. 27, 1 (1983).
[CrossRef]

Opt. Express (3)

Opt. Rev. (1)

M. Sambongi, M. Igarashi, T. Obi, M. Yamaguchi, N. Ohyama, M. Kobayashi, Y. Sano, S. Yoshida, and K. Gono, Opt. Rev. 9, 238 (2002).
[CrossRef]

Other (2)

R. Zass and A. Shashua, in Neural Information Processing Systems (2007).

J. Park, M. Lee, M. D. Grossberg, and S. K. Nayar, in IEEE International Conference on Computer Vision (2007).

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Figures (5)

Fig. 1.
Fig. 1.

Illustration of our active multispectral imaging system. The scene is lit with a set of distinct illuminations and a synchronized RGB camera captures the corresponding images.

Fig. 2.
Fig. 2.

First eight basis functions using PCA (Parkkinen’s [16]) and NNPCA.

Fig. 3.
Fig. 3.

Left: a Macbeth color chart image captured using the camera having the spectral reflectance of the right graph under illuminations A and B. The illuminations are combinations of commercial LEDs (A, red and green; B, white, amber, and blue). Right: the spectra of illuminations and a camera used for our experiments.

Fig. 4.
Fig. 4.

Spectral reflectances of color chips on the Macbeth chart. The spectra reconstructed using PCA and NNPCA basis functions are shown as green and red curves and the true spectra (ground truth) are shown as black curves.

Fig. 5.
Fig. 5.

Reconstruction errors of PCA basis functions and NNPCA basis functions for the Macbeth chart.

Equations (10)

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

Imn=s(λ)cm(λ)pn(λ)dλ,
s(λ)=k=1Ksσkbk(λ),
Imn=k=1Ksσkbk(λ)cm(λ)pn(λ)dλ,
Fσ=I.
s(λ)=k=1Ksσkbk(λ)0,for allλ.
σ+=argminσ|FσI|2,subject toAσ0,
minσ[|FσI|2+α|2s(λ)λ2|2],
σ+=argminσ|F˜σI˜|2,subject toAσ0,
σ+=argminσ|F˜σI˜|2.
σ+=(F˜TF˜)1F˜TI˜.

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