Abstract

A fast, accurate model for computing Logvinenko’s optimal metamers is introduced. The spectral reflectance of an optimal metamer is uniquely determined from a class of metamers with common tristimulus values. A set of optimal metamers is useful for evaluating the color reproduction and gamut of object colors under different illuminants. In conventional methods, optimal metamers are calculated by interpolating the coordinates of precomputed optimal colors. This model optimizes the spectral reflectance parameters efficiently without switching between bandpass (Type I) and bandstop (Type II) optimal metamers, or requiring any stored optimal-color datasets. Some optimal metamer loci computed using MATLAB are presented.

© 2013 Optical Society of America

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References

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  1. A. D. Logvinenko, J. Vis. 9(11):5 (2009).
  2. W. Ostwald, Phys. Z. 17, 322 (1916).
  3. E. Schrödinger, Ann. Phys. 367, 603 (1920).
    [CrossRef]
  4. C. Godau and B. Funt, in Proceedings of IS&T/SID 18th Color and Imaging Conference (IS&T, 2010), pp. 334–339.
  5. G. D. Finlayson, M. Mackiewicz, and A. Hurlbert, in Proceedings of IS&T/SID 20th Color and Imaging Conference (IS&T, 2012), pp. 264–269.
  6. K. Masaoka, Opt. Lett. 35, 2031 (2010).
    [CrossRef]
  7. University of Eastern Finland, Spectral Database, http://www.uef.fi/spectral/spectral-database .

2010 (1)

2009 (1)

A. D. Logvinenko, J. Vis. 9(11):5 (2009).

1920 (1)

E. Schrödinger, Ann. Phys. 367, 603 (1920).
[CrossRef]

1916 (1)

W. Ostwald, Phys. Z. 17, 322 (1916).

Finlayson, G. D.

G. D. Finlayson, M. Mackiewicz, and A. Hurlbert, in Proceedings of IS&T/SID 20th Color and Imaging Conference (IS&T, 2012), pp. 264–269.

Funt, B.

C. Godau and B. Funt, in Proceedings of IS&T/SID 18th Color and Imaging Conference (IS&T, 2010), pp. 334–339.

Godau, C.

C. Godau and B. Funt, in Proceedings of IS&T/SID 18th Color and Imaging Conference (IS&T, 2010), pp. 334–339.

Hurlbert, A.

G. D. Finlayson, M. Mackiewicz, and A. Hurlbert, in Proceedings of IS&T/SID 20th Color and Imaging Conference (IS&T, 2012), pp. 264–269.

Logvinenko, A. D.

A. D. Logvinenko, J. Vis. 9(11):5 (2009).

Mackiewicz, M.

G. D. Finlayson, M. Mackiewicz, and A. Hurlbert, in Proceedings of IS&T/SID 20th Color and Imaging Conference (IS&T, 2012), pp. 264–269.

Masaoka, K.

Ostwald, W.

W. Ostwald, Phys. Z. 17, 322 (1916).

Schrödinger, E.

E. Schrödinger, Ann. Phys. 367, 603 (1920).
[CrossRef]

Ann. Phys. (1)

E. Schrödinger, Ann. Phys. 367, 603 (1920).
[CrossRef]

J. Vis. (1)

A. D. Logvinenko, J. Vis. 9(11):5 (2009).

Opt. Lett. (1)

Phys. Z. (1)

W. Ostwald, Phys. Z. 17, 322 (1916).

Other (3)

C. Godau and B. Funt, in Proceedings of IS&T/SID 18th Color and Imaging Conference (IS&T, 2010), pp. 334–339.

G. D. Finlayson, M. Mackiewicz, and A. Hurlbert, in Proceedings of IS&T/SID 20th Color and Imaging Conference (IS&T, 2012), pp. 264–269.

University of Eastern Finland, Spectral Database, http://www.uef.fi/spectral/spectral-database .

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Figures (5)

Fig. 1.
Fig. 1.

Spectral reflectances of a Type I optimal metamer (top) and a Type II optimal metamer (bottom).

Fig. 2.
Fig. 2.

Concatenated three copies of the color-matching functions and the illuminant spectrum (top) and the spectral reflectance of a Type II optimal metamer R(l) with central wavelength l¯ and half-bandwidth h on the concatenated wavelength scale l (bottom).

Fig. 3.
Fig. 3.

Diagram of trapezoidal integration of RoptC(l)T(l).

Fig. 4.
Fig. 4.

MATLAB code for computing an optimal metamer.

Fig. 5.
Fig. 5.

Optimal metamer loci at constant luminance factors with α=0.25, 0.5, 0.75, and 1 at intervals of the luminance factor Y of 2.5.

Equations (7)

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(1α)x0.5(λ)+αxoptC(λ),
δ=λcut-offλcut-on,
λ¯=(λcut-on+λcut-off)/2,
δ=(λmaxλmin)(λcut-on+λcut-off),
λ¯={λcut-on+δ/2,ifλcut-on+δ/2<λmaxλcut-offδ/2,otherwise,
[XMYMZM]=1α2[XWYWZW]+α[XoptCYoptCZoptC],
XoptC=RoptC(l)Tx(l)dl=lcut-onlcut-offTx(l)dl=k=l¯hl¯+hTx(k)(1+2{l¯h}{l¯h}2)Tx(l¯h)/2{l¯h}2Tx(l¯h+1)/2(12{l¯+h}+{l¯+h}2)Tx(l¯+h)/2+{l¯+h}2Tx(l¯+h+1)/2.

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