Abstract

Nonnegative color analysis filters are obtained by using an invertible linear transformation of characteristic spectra, which are orthogonal vectors from a principal component analysis (PCA) of a representative ensemble of color spectra. These filters maintain the optimal compression properties of the PCA scheme. Linearly constrained nonlinear programming is used to find a transformation that minimizes the noise sensitivity of the filter set. The method is illustrated by computing analysis and synthesis filters for an ensemble of measured Munsell color spectra.

© 2002 Optical Society of America

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References

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  1. B. A. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 2–13 (1987).
    [CrossRef]
  2. T. Jaaskelainen, J. Parkkinen, S. Toyooka, “Vector-subspace model for color representation,” J. Opt. Soc. Am. A 7, 725–730 (1990).
    [CrossRef]
  3. T. Jaaskelainen, S. Toyooka, S. Izawa, H. Kadono, “Color classification by vector subspace method and its optical implementation using liquid crystal spatial light modulator,” Opt. Commun. 89, 23–29 (1992).
    [CrossRef]
  4. M. J. Vrhel, H. J. Trussel, “Filter Considerations in Color Correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
    [CrossRef] [PubMed]
  5. G. Sharma, H. J. Trussel, M. J. Vrhel, “Optimal nonne-gative color scanning filters,” IEEE Trans. Image Process. 7, 129–133 (1998).
    [CrossRef]
  6. M. Hauta-Kasari, W. Wang, S. Toyooka, J. Parkkinen, R. Lenz, “Unsupervised filtering of Munsell spectral,” in Proceedings of the 3rd Asian Conference on Computer Vision ACCV98, R. Chin, T.-C. Pong, eds. (Springer, New York, 1998), pp. 248–255.
  7. R. A. Horn, C. R. Johnson, Matrix Analysis (Cambridge U. Press, Cambridge, UK, 1985).
  8. J. P. S. Parkkinen, J. Hallikainen, T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
    [CrossRef]
  9. J. Hiltunen, Department of Computer Science, University of Joensuu, Reflectance spectra of 1269 matte Munsell color chips, http://cs.joensuu.fi/spectral/databases/download/munsell_spec_matt.htm .

1998

G. Sharma, H. J. Trussel, M. J. Vrhel, “Optimal nonne-gative color scanning filters,” IEEE Trans. Image Process. 7, 129–133 (1998).
[CrossRef]

1994

M. J. Vrhel, H. J. Trussel, “Filter Considerations in Color Correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
[CrossRef] [PubMed]

1992

T. Jaaskelainen, S. Toyooka, S. Izawa, H. Kadono, “Color classification by vector subspace method and its optical implementation using liquid crystal spatial light modulator,” Opt. Commun. 89, 23–29 (1992).
[CrossRef]

1990

1989

1987

B. A. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

Hallikainen, J.

Hauta-Kasari, M.

M. Hauta-Kasari, W. Wang, S. Toyooka, J. Parkkinen, R. Lenz, “Unsupervised filtering of Munsell spectral,” in Proceedings of the 3rd Asian Conference on Computer Vision ACCV98, R. Chin, T.-C. Pong, eds. (Springer, New York, 1998), pp. 248–255.

Horn, R. A.

R. A. Horn, C. R. Johnson, Matrix Analysis (Cambridge U. Press, Cambridge, UK, 1985).

Izawa, S.

T. Jaaskelainen, S. Toyooka, S. Izawa, H. Kadono, “Color classification by vector subspace method and its optical implementation using liquid crystal spatial light modulator,” Opt. Commun. 89, 23–29 (1992).
[CrossRef]

Jaaskelainen, T.

T. Jaaskelainen, S. Toyooka, S. Izawa, H. Kadono, “Color classification by vector subspace method and its optical implementation using liquid crystal spatial light modulator,” Opt. Commun. 89, 23–29 (1992).
[CrossRef]

T. Jaaskelainen, J. Parkkinen, S. Toyooka, “Vector-subspace model for color representation,” J. Opt. Soc. Am. A 7, 725–730 (1990).
[CrossRef]

J. P. S. Parkkinen, J. Hallikainen, T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
[CrossRef]

Johnson, C. R.

R. A. Horn, C. R. Johnson, Matrix Analysis (Cambridge U. Press, Cambridge, UK, 1985).

Kadono, H.

T. Jaaskelainen, S. Toyooka, S. Izawa, H. Kadono, “Color classification by vector subspace method and its optical implementation using liquid crystal spatial light modulator,” Opt. Commun. 89, 23–29 (1992).
[CrossRef]

Lenz, R.

M. Hauta-Kasari, W. Wang, S. Toyooka, J. Parkkinen, R. Lenz, “Unsupervised filtering of Munsell spectral,” in Proceedings of the 3rd Asian Conference on Computer Vision ACCV98, R. Chin, T.-C. Pong, eds. (Springer, New York, 1998), pp. 248–255.

Parkkinen, J.

T. Jaaskelainen, J. Parkkinen, S. Toyooka, “Vector-subspace model for color representation,” J. Opt. Soc. Am. A 7, 725–730 (1990).
[CrossRef]

M. Hauta-Kasari, W. Wang, S. Toyooka, J. Parkkinen, R. Lenz, “Unsupervised filtering of Munsell spectral,” in Proceedings of the 3rd Asian Conference on Computer Vision ACCV98, R. Chin, T.-C. Pong, eds. (Springer, New York, 1998), pp. 248–255.

Parkkinen, J. P. S.

Sharma, G.

G. Sharma, H. J. Trussel, M. J. Vrhel, “Optimal nonne-gative color scanning filters,” IEEE Trans. Image Process. 7, 129–133 (1998).
[CrossRef]

Toyooka, S.

T. Jaaskelainen, S. Toyooka, S. Izawa, H. Kadono, “Color classification by vector subspace method and its optical implementation using liquid crystal spatial light modulator,” Opt. Commun. 89, 23–29 (1992).
[CrossRef]

T. Jaaskelainen, J. Parkkinen, S. Toyooka, “Vector-subspace model for color representation,” J. Opt. Soc. Am. A 7, 725–730 (1990).
[CrossRef]

M. Hauta-Kasari, W. Wang, S. Toyooka, J. Parkkinen, R. Lenz, “Unsupervised filtering of Munsell spectral,” in Proceedings of the 3rd Asian Conference on Computer Vision ACCV98, R. Chin, T.-C. Pong, eds. (Springer, New York, 1998), pp. 248–255.

Trussel, H. J.

G. Sharma, H. J. Trussel, M. J. Vrhel, “Optimal nonne-gative color scanning filters,” IEEE Trans. Image Process. 7, 129–133 (1998).
[CrossRef]

M. J. Vrhel, H. J. Trussel, “Filter Considerations in Color Correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
[CrossRef] [PubMed]

Vrhel, M. J.

G. Sharma, H. J. Trussel, M. J. Vrhel, “Optimal nonne-gative color scanning filters,” IEEE Trans. Image Process. 7, 129–133 (1998).
[CrossRef]

M. J. Vrhel, H. J. Trussel, “Filter Considerations in Color Correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
[CrossRef] [PubMed]

Wandell, B. A.

B. A. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

Wang, W.

M. Hauta-Kasari, W. Wang, S. Toyooka, J. Parkkinen, R. Lenz, “Unsupervised filtering of Munsell spectral,” in Proceedings of the 3rd Asian Conference on Computer Vision ACCV98, R. Chin, T.-C. Pong, eds. (Springer, New York, 1998), pp. 248–255.

IEEE Trans. Image Process.

M. J. Vrhel, H. J. Trussel, “Filter Considerations in Color Correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
[CrossRef] [PubMed]

G. Sharma, H. J. Trussel, M. J. Vrhel, “Optimal nonne-gative color scanning filters,” IEEE Trans. Image Process. 7, 129–133 (1998).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

B. A. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

T. Jaaskelainen, S. Toyooka, S. Izawa, H. Kadono, “Color classification by vector subspace method and its optical implementation using liquid crystal spatial light modulator,” Opt. Commun. 89, 23–29 (1992).
[CrossRef]

Other

J. Hiltunen, Department of Computer Science, University of Joensuu, Reflectance spectra of 1269 matte Munsell color chips, http://cs.joensuu.fi/spectral/databases/download/munsell_spec_matt.htm .

M. Hauta-Kasari, W. Wang, S. Toyooka, J. Parkkinen, R. Lenz, “Unsupervised filtering of Munsell spectral,” in Proceedings of the 3rd Asian Conference on Computer Vision ACCV98, R. Chin, T.-C. Pong, eds. (Springer, New York, 1998), pp. 248–255.

R. A. Horn, C. R. Johnson, Matrix Analysis (Cambridge U. Press, Cambridge, UK, 1985).

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Figures (3)

Fig. 1
Fig. 1

First six characteristic spectra computed from measured Munsell color spectral data.

Fig. 2
Fig. 2

Set of three nonnegative analysis filters obtained as linear combinations of the first three characteristic spectra, and the corresponding synthesis filters.

Fig. 3
Fig. 3

Set of six nonnegative analysis filters obtained as linear combinations of the first six characteristic spectra, and the corresponding synthesis filters.

Tables (1)

Tables Icon

Table 1 Relative Ensemble Approximation Error p and Noise Amplification Factor W¯2 for Munsell Spectral Data Compressed with p Nonnegative Analysis Filters

Equations (16)

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p=S-RFSF,
s-r2=Sb-Rb2S-RFb2=pSFb2.
R˜-RF=VWTNS+VNCFV2(W2NSF+NCF).
S=PΣQT=[P1P2]Σ100Σ2Q1TQ2T=P1Σ1Q1T+P2Σ2Q2T,
S-R=S-VWTS=(I-P1P1T)(P1Σ1Q1T+P2Σ2Q2T)=P2Σ2Q2T.
p=S-RFSF=P2Σ2Q2TFPΣQTF
=Σ2FΣF=Σi=p+1nσi21/2Σi=1nσi2)1/2.
V¯W¯¯T=(VX-T)(WX)T=VX-TXTWT=VWT.
κF(X)X=XX-1FXF-1-X-TX-1X-TXFX-1F-1.
W¯i=wi+γiw1(2ip).
minimizeγsubjecttowi+γw10
X=1γ2:pT0I.
R¯-SFR¯-RF+R-SFpSF+V2(W2NSF+NCF).
R¯-SF0.044SF+1.4NCF.
R¯-SF0.082SF+NCF.
NCFSF0.082-0.0441.4-1=0.095.

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