Abstract

Alexander Logvinenko introduced an object-color atlas based on idealized reflectances called rectangular metamers in 2009. For a given color signal, the atlas specifies a unique reflectance that is metameric to it under the given illuminant. The atlas is complete and illuminant invariant, but not possible to implement in practice. He later introduced a parametric representation of the object-color atlas based on smoother “wraparound Gaussian” functions. In this paper, these wraparound Gaussians are used in predicting illuminant-induced color signal changes. The method proposed in this paper is based on computationally “relighting” that reflectance to determine what its color signal would be under any other illuminant. Since that reflectance is in the metamer set the prediction is also physically realizable, which cannot be guaranteed for predictions obtained via von Kries scaling. Testing on Munsell spectra and a multispectral image shows that the proposed method outperforms the predictions of both those based on von Kries scaling and those based on the Bradford transform.

© 2014 Optical Society of America

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References

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  1. A. D. Logvinenko, “Object-colour manifold,” Int. J. Comput. Vis. 101, 143–160 (2013).
    [CrossRef]
  2. M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. LUTCHI colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
    [CrossRef]
  3. M. D. Fairchild, “Spectral adaptation: a reason to use the wavenumber scale,” in Proceedings Fourteenth IS&T Color Imaging Conference (The Society for Imaging Science and Technology, 2006), pp. 314–319.
  4. A. Logvinenko, B. Funt, and C. Godau, “Metamer mismatching,” IEEE Trans. Image Process. 23, 34–43 (2014).
    [CrossRef]
  5. M. H. Brill and G. Finlayson, “Illuminant invariance from a single reflected light,” Color Res. Appl. 27, 45–48 (2002).
    [CrossRef]
  6. Y. Mizokami and M. Webster, “Are Gaussian spectra a viable perceptual assumption in color appearance?” J. Vis. 10(7):399 (2010).
  7. D. I. MacLeod and J. Golz, “A computational analysis of colour constancy,” in Colour Perception: Mind and the Physical World (Oxford University, 2003), pp. 205–242.
  8. G. Wyszecki and W. S. Stiles, Colour Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982).
  9. A. D. Logvinenko, “An object-colour space,” J. Vis. 9(11):5 (2009).
  10. P. Nikolaev, “A colour constancy model with continuous spectral functions,” Biophysics 30, 1–23 (1985).
  11. C. Godau and B. Funt, “XYZ to ADL: calculating Logvinenko’s object colour coordinates,” in Proceedings of Eighteenth IS&T Color Imaging Conference (2010).
  12. G. D. Finlayson, M. Mackiewicz, and A. Hurlbert, “Making the calculation of Logvinenko’s coordinates easy,” in Proceedings of Twentieth IS&T Color Imaging Conference (2012), pp. 264–269.
  13. J. von Kries, “Chromatic adaptation,” in Sources of Colour Vision, D. L. MacAdam, ed. (Massachusetts Institute of Technology, 1970), pp. 109–119.
  14. N. Moroney, M. Fairchild, R. Hunt, C. Li, M. Luo, and T. Newman, “The CIECAM02 colour appearance model,” in Proceedings of Tenth IS&T Color Imaging Conference, 2002.
  15. G. D. Finlayson, M. S. Drew, and B. V. Funt, “Spectral sharpening: sensor transformations for improved colour constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
    [CrossRef]
  16. University of Eastern Finland, “Joensuu spectral database,” 2012, http://www.uef.fi/fi/spectral/spectral-image-database .
  17. K. M. Lam, “Metamerism and colour constancy,” Ph.D. dissertation (University of Bradford, 1985).
  18. R. W. G. Hunt, The Reproduction of Colour, 6th ed. (Wiley, 2004).
  19. R. W. G. Hunt and M. R. Pointer, “A colour-appearance transform for the 1931 standard colorimetric observer,” Colour Res. Appl. 10, 165–179 (1985).
  20. A. D. Logvinenko and R. Tokunaga, “Colour constancy as measured by least dissimilar matching,” Seeing Perceiving 24, 407–452 (2011).
  21. R. V. Hogg and E. A. Tanis, Probability and Statistical Inference (Prentice-Hall, 2001).
  22. A. D. Logvinenko, B. Funt, and H. Mirzaei, “The extent of metamer mismatching,” in AIC 2013 (International Colour Association) Conference (International Colour Association, 2013), pp. 507–510.

2014 (1)

A. Logvinenko, B. Funt, and C. Godau, “Metamer mismatching,” IEEE Trans. Image Process. 23, 34–43 (2014).
[CrossRef]

2013 (1)

A. D. Logvinenko, “Object-colour manifold,” Int. J. Comput. Vis. 101, 143–160 (2013).
[CrossRef]

2011 (1)

A. D. Logvinenko and R. Tokunaga, “Colour constancy as measured by least dissimilar matching,” Seeing Perceiving 24, 407–452 (2011).

2010 (1)

Y. Mizokami and M. Webster, “Are Gaussian spectra a viable perceptual assumption in color appearance?” J. Vis. 10(7):399 (2010).

2009 (1)

A. D. Logvinenko, “An object-colour space,” J. Vis. 9(11):5 (2009).

2002 (1)

M. H. Brill and G. Finlayson, “Illuminant invariance from a single reflected light,” Color Res. Appl. 27, 45–48 (2002).
[CrossRef]

1994 (1)

1991 (1)

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. LUTCHI colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

1985 (2)

P. Nikolaev, “A colour constancy model with continuous spectral functions,” Biophysics 30, 1–23 (1985).

R. W. G. Hunt and M. R. Pointer, “A colour-appearance transform for the 1931 standard colorimetric observer,” Colour Res. Appl. 10, 165–179 (1985).

Brill, M. H.

M. H. Brill and G. Finlayson, “Illuminant invariance from a single reflected light,” Color Res. Appl. 27, 45–48 (2002).
[CrossRef]

Clarke, A. A.

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. LUTCHI colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

Drew, M. S.

Fairchild, M.

N. Moroney, M. Fairchild, R. Hunt, C. Li, M. Luo, and T. Newman, “The CIECAM02 colour appearance model,” in Proceedings of Tenth IS&T Color Imaging Conference, 2002.

Fairchild, M. D.

M. D. Fairchild, “Spectral adaptation: a reason to use the wavenumber scale,” in Proceedings Fourteenth IS&T Color Imaging Conference (The Society for Imaging Science and Technology, 2006), pp. 314–319.

Finlayson, G.

M. H. Brill and G. Finlayson, “Illuminant invariance from a single reflected light,” Color Res. Appl. 27, 45–48 (2002).
[CrossRef]

Finlayson, G. D.

G. D. Finlayson, M. S. Drew, and B. V. Funt, “Spectral sharpening: sensor transformations for improved colour constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
[CrossRef]

G. D. Finlayson, M. Mackiewicz, and A. Hurlbert, “Making the calculation of Logvinenko’s coordinates easy,” in Proceedings of Twentieth IS&T Color Imaging Conference (2012), pp. 264–269.

Funt, B.

A. Logvinenko, B. Funt, and C. Godau, “Metamer mismatching,” IEEE Trans. Image Process. 23, 34–43 (2014).
[CrossRef]

A. D. Logvinenko, B. Funt, and H. Mirzaei, “The extent of metamer mismatching,” in AIC 2013 (International Colour Association) Conference (International Colour Association, 2013), pp. 507–510.

C. Godau and B. Funt, “XYZ to ADL: calculating Logvinenko’s object colour coordinates,” in Proceedings of Eighteenth IS&T Color Imaging Conference (2010).

Funt, B. V.

Godau, C.

A. Logvinenko, B. Funt, and C. Godau, “Metamer mismatching,” IEEE Trans. Image Process. 23, 34–43 (2014).
[CrossRef]

C. Godau and B. Funt, “XYZ to ADL: calculating Logvinenko’s object colour coordinates,” in Proceedings of Eighteenth IS&T Color Imaging Conference (2010).

Golz, J.

D. I. MacLeod and J. Golz, “A computational analysis of colour constancy,” in Colour Perception: Mind and the Physical World (Oxford University, 2003), pp. 205–242.

Hogg, R. V.

R. V. Hogg and E. A. Tanis, Probability and Statistical Inference (Prentice-Hall, 2001).

Hunt, R.

N. Moroney, M. Fairchild, R. Hunt, C. Li, M. Luo, and T. Newman, “The CIECAM02 colour appearance model,” in Proceedings of Tenth IS&T Color Imaging Conference, 2002.

Hunt, R. W. G.

R. W. G. Hunt and M. R. Pointer, “A colour-appearance transform for the 1931 standard colorimetric observer,” Colour Res. Appl. 10, 165–179 (1985).

R. W. G. Hunt, The Reproduction of Colour, 6th ed. (Wiley, 2004).

Hurlbert, A.

G. D. Finlayson, M. Mackiewicz, and A. Hurlbert, “Making the calculation of Logvinenko’s coordinates easy,” in Proceedings of Twentieth IS&T Color Imaging Conference (2012), pp. 264–269.

Lam, K. M.

K. M. Lam, “Metamerism and colour constancy,” Ph.D. dissertation (University of Bradford, 1985).

Li, C.

N. Moroney, M. Fairchild, R. Hunt, C. Li, M. Luo, and T. Newman, “The CIECAM02 colour appearance model,” in Proceedings of Tenth IS&T Color Imaging Conference, 2002.

Logvinenko, A.

A. Logvinenko, B. Funt, and C. Godau, “Metamer mismatching,” IEEE Trans. Image Process. 23, 34–43 (2014).
[CrossRef]

Logvinenko, A. D.

A. D. Logvinenko, “Object-colour manifold,” Int. J. Comput. Vis. 101, 143–160 (2013).
[CrossRef]

A. D. Logvinenko and R. Tokunaga, “Colour constancy as measured by least dissimilar matching,” Seeing Perceiving 24, 407–452 (2011).

A. D. Logvinenko, “An object-colour space,” J. Vis. 9(11):5 (2009).

A. D. Logvinenko, B. Funt, and H. Mirzaei, “The extent of metamer mismatching,” in AIC 2013 (International Colour Association) Conference (International Colour Association, 2013), pp. 507–510.

Luo, M.

N. Moroney, M. Fairchild, R. Hunt, C. Li, M. Luo, and T. Newman, “The CIECAM02 colour appearance model,” in Proceedings of Tenth IS&T Color Imaging Conference, 2002.

Luo, M. R.

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. LUTCHI colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

Mackiewicz, M.

G. D. Finlayson, M. Mackiewicz, and A. Hurlbert, “Making the calculation of Logvinenko’s coordinates easy,” in Proceedings of Twentieth IS&T Color Imaging Conference (2012), pp. 264–269.

MacLeod, D. I.

D. I. MacLeod and J. Golz, “A computational analysis of colour constancy,” in Colour Perception: Mind and the Physical World (Oxford University, 2003), pp. 205–242.

Mirzaei, H.

A. D. Logvinenko, B. Funt, and H. Mirzaei, “The extent of metamer mismatching,” in AIC 2013 (International Colour Association) Conference (International Colour Association, 2013), pp. 507–510.

Mizokami, Y.

Y. Mizokami and M. Webster, “Are Gaussian spectra a viable perceptual assumption in color appearance?” J. Vis. 10(7):399 (2010).

Moroney, N.

N. Moroney, M. Fairchild, R. Hunt, C. Li, M. Luo, and T. Newman, “The CIECAM02 colour appearance model,” in Proceedings of Tenth IS&T Color Imaging Conference, 2002.

Newman, T.

N. Moroney, M. Fairchild, R. Hunt, C. Li, M. Luo, and T. Newman, “The CIECAM02 colour appearance model,” in Proceedings of Tenth IS&T Color Imaging Conference, 2002.

Nikolaev, P.

P. Nikolaev, “A colour constancy model with continuous spectral functions,” Biophysics 30, 1–23 (1985).

Pointer, M. R.

R. W. G. Hunt and M. R. Pointer, “A colour-appearance transform for the 1931 standard colorimetric observer,” Colour Res. Appl. 10, 165–179 (1985).

Rhodes, P. A.

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. LUTCHI colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

Schappo, A.

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. LUTCHI colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

Scrivener, S. A.

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. LUTCHI colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Colour Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982).

Tait, C. J.

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. LUTCHI colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

Tanis, E. A.

R. V. Hogg and E. A. Tanis, Probability and Statistical Inference (Prentice-Hall, 2001).

Tokunaga, R.

A. D. Logvinenko and R. Tokunaga, “Colour constancy as measured by least dissimilar matching,” Seeing Perceiving 24, 407–452 (2011).

von Kries, J.

J. von Kries, “Chromatic adaptation,” in Sources of Colour Vision, D. L. MacAdam, ed. (Massachusetts Institute of Technology, 1970), pp. 109–119.

Webster, M.

Y. Mizokami and M. Webster, “Are Gaussian spectra a viable perceptual assumption in color appearance?” J. Vis. 10(7):399 (2010).

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Colour Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982).

Biophysics (1)

P. Nikolaev, “A colour constancy model with continuous spectral functions,” Biophysics 30, 1–23 (1985).

Color Res. Appl. (2)

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. LUTCHI colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

M. H. Brill and G. Finlayson, “Illuminant invariance from a single reflected light,” Color Res. Appl. 27, 45–48 (2002).
[CrossRef]

Colour Res. Appl. (1)

R. W. G. Hunt and M. R. Pointer, “A colour-appearance transform for the 1931 standard colorimetric observer,” Colour Res. Appl. 10, 165–179 (1985).

IEEE Trans. Image Process. (1)

A. Logvinenko, B. Funt, and C. Godau, “Metamer mismatching,” IEEE Trans. Image Process. 23, 34–43 (2014).
[CrossRef]

Int. J. Comput. Vis. (1)

A. D. Logvinenko, “Object-colour manifold,” Int. J. Comput. Vis. 101, 143–160 (2013).
[CrossRef]

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

J. Vis. (2)

Y. Mizokami and M. Webster, “Are Gaussian spectra a viable perceptual assumption in color appearance?” J. Vis. 10(7):399 (2010).

A. D. Logvinenko, “An object-colour space,” J. Vis. 9(11):5 (2009).

Seeing Perceiving (1)

A. D. Logvinenko and R. Tokunaga, “Colour constancy as measured by least dissimilar matching,” Seeing Perceiving 24, 407–452 (2011).

Other (12)

R. V. Hogg and E. A. Tanis, Probability and Statistical Inference (Prentice-Hall, 2001).

A. D. Logvinenko, B. Funt, and H. Mirzaei, “The extent of metamer mismatching,” in AIC 2013 (International Colour Association) Conference (International Colour Association, 2013), pp. 507–510.

D. I. MacLeod and J. Golz, “A computational analysis of colour constancy,” in Colour Perception: Mind and the Physical World (Oxford University, 2003), pp. 205–242.

G. Wyszecki and W. S. Stiles, Colour Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982).

M. D. Fairchild, “Spectral adaptation: a reason to use the wavenumber scale,” in Proceedings Fourteenth IS&T Color Imaging Conference (The Society for Imaging Science and Technology, 2006), pp. 314–319.

University of Eastern Finland, “Joensuu spectral database,” 2012, http://www.uef.fi/fi/spectral/spectral-image-database .

K. M. Lam, “Metamerism and colour constancy,” Ph.D. dissertation (University of Bradford, 1985).

R. W. G. Hunt, The Reproduction of Colour, 6th ed. (Wiley, 2004).

C. Godau and B. Funt, “XYZ to ADL: calculating Logvinenko’s object colour coordinates,” in Proceedings of Eighteenth IS&T Color Imaging Conference (2010).

G. D. Finlayson, M. Mackiewicz, and A. Hurlbert, “Making the calculation of Logvinenko’s coordinates easy,” in Proceedings of Twentieth IS&T Color Imaging Conference (2012), pp. 264–269.

J. von Kries, “Chromatic adaptation,” in Sources of Colour Vision, D. L. MacAdam, ed. (Massachusetts Institute of Technology, 1970), pp. 109–119.

N. Moroney, M. Fairchild, R. Hunt, C. Li, M. Luo, and T. Newman, “The CIECAM02 colour appearance model,” in Proceedings of Tenth IS&T Color Imaging Conference, 2002.

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Figures (9)

Fig. 1.
Fig. 1.

Spectral reflectance of Munsell 7.5 PB 5/8 (dashed black) illuminated by D65 and metameric inverse Gaussian (solid cyan), subtractive Gaussian (dashed green), rectangular (dashed blue), and wraparound Gaussian (solid red) spectra.

Fig. 2.
Fig. 2.

Gamut of chromaticities obtained using only true reflectance functions (i.e., all values in [0,1] across the visible spectrum) for (a) all subtractive Gaussian reflectance functions forming either peaks (blue) or troughs (red), (b) all inverse Gaussian reflectance functions with positive curvature (blue) or negative curvature (red), and (c) all wraparound Gaussian reflectance functions.

Fig. 3.
Fig. 3.

Gamut of XYZ under D65 for the wraparound Gaussian reflectances plotted inside the gamut of the two-transition (rectangular) reflectances.

Fig. 4.
Fig. 4.

KSM color descriptor (k, σ, μ) maps for the Fruits and Flowers scene under D65. (a) sRGB rendering, (b) map of k values, (c) map of log(σ) values, and (d) map of μ values. Panel (d) illustrates the correspondence between μ and hue.

Fig. 5.
Fig. 5.

Reflectance and illuminant pair example for which von Kries fails. Black curve is the reflectance of Munsell chip 7.5 R 5/16. Blue curve is the corresponding wraparound Gaussian metamer for that Munsell chip. The dashed red curve and the gray curve are the relative spectral power distributions of the first (R2) and second (N) illuminants.

Fig. 6.
Fig. 6.

Spectral power distributions of the green (G), blue (B), neutral (N), yellow (Y), first red (R1), and second red (R2) illuminants used in Logvinenko and Tokunaga’s experiments [20]. The plotted colors identify the associated spectrum along with gray indicating N. Solid red indicates R1, and dashed red indicates R2.

Fig. 7.
Fig. 7.

Color signal prediction for the 20 Munsell papers when the illuminant is changed from G (green) to N (neutral). Left GM, center von Kries, and right Bradford. Plot is of CIE xy chromaticities. An arrow tail indicates the actual chromaticity of the paper under the neutral illuminant and the corresponding arrow head its predicted chromaticity. The red curve simply links the arrow tails for clarity and is the same in all three panels.

Fig. 8.
Fig. 8.

Maps of the difference in CIEDE2000 error of the color signals predicted by GM versus Bradford for an illuminant change from CIE D65 to CIE A (left) and to CIE F11 (right). White indicates that the GM error is at least 2 ΔE less than Bradford, gray indicates the absolute error difference between them is less than 2 ΔE, and black indicates a Bradford error at least 2 ΔE less than that of GM. Results for von Kries are qualitatively similar to those of Bradford and are not shown here.

Fig. 9.
Fig. 9.

Reflectance and illuminant pair for which GM prediction yields a poor result. Black curve is the spectral reflectance of (Munsell 2.5 R 4/14). Green curve is the relative spectral power distribution of G, the first illuminant. Dashed red curve is the second illuminant, R2. Blue curve is the wraparound Gaussian metamer to the reflectance under G.

Tables (3)

Tables Icon

Table 1. Comparison of Color Signal Prediction Accuracy for the 1600 Munsell Reflectance Spectra Using the Proposed GM Method, von Kries Scaling, and the Bradford Transform in Terms of CIEDE2000 for a Change in Illuminant from CIE D65 to CIE A and CIE F11

Tables Icon

Table 2. Comparison of the Color Signal Predictions Made by the GM, Bradford, and von Kries Methods in Terms of the CIEDE2000 Error Statistics for the 20 Chromatic Stimulus Papers Used in Logvinenko’s Color Matching Experiment [20] when the Illuminant Changes from G to N

Tables Icon

Table 3. CIEDE2000 Color Difference Statistics Taken over all Munsell Reflectances and 30 Illuminant Pairs

Equations (9)

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

gm(λ;km,θm,μm)=kmexp[θm(λμm)2].
gm(λ;km,θm,μm)=kmexp[θm(λμmΛ)2],
gm(λ;km,θm,μm)=kmexp[θm(λμmΛ)2].
gm(λ;km,θm,μm)=kmexp[θm(λμm)2].
λminλmaxr(λ;α,δ,λ¯)p(λ)si(λ)dλ=λminλmaxgm(λ;km,θm,μm)p(λ)si(λ)dλ
P(λ)=γ.eC(λT)2,
S(λ)={αe0.5(λpeakσ)2forα01+αe0.5(λpeakσ)2forα<0.
E(k,σ,μ)=arccosφ0·φ(k,σ,μ)|φ0||φ(k,σ,μ)|
k=|φ0||φ(1,σ,μ)|

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