Abstract

It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., constant negative curvature) for the chromatic plane can significantly improve the performance of Euclidean colour metrics to the point where they are statistically significantly better than state-of-the-art non-Euclidean metrics on standard data sets. The resulting hyperbolic geometry nicely models both qualitatively and quantitatively the hue super-importance phenomenon observed in colour order systems.

© 2014 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Embedding non-Euclidean color spaces into Euclidean color spaces with minimal isometric disagreement

Philipp Urban, Mitchell R. Rosen, Roy S. Berns, and Dierk Schleicher
J. Opt. Soc. Am. A 24(6) 1516-1528 (2007)

A Metric for Colorspace*

Parry Moon and Domina Eberle Spencer
J. Opt. Soc. Am. 33(5) 260-269 (1943)

Euclidean color-difference formula for small-medium color differences in log-compressed OSA-UCS space

Claudio Oleari, Manuel Melgosa, and Rafael Huertas
J. Opt. Soc. Am. A 26(1) 121-134 (2009)

References

  • View by:
  • |
  • |
  • |

  1. S. M. Newhall, D. Nickerson, D. B. Judd, “Final report of the OSA subcommittee on the spacing of the Munsell colors,” J. Opt. Soc. Am. 33, 385–411 (1943).
    [Crossref]
  2. D. B. Judd, “Ideal color space – II. The super-importance of hue differences and its bearing on the geometry of color space,” Palette 30, 21–28 (1969).
  3. R. G. Kuehni, A. Schwarz, Color Ordered (Oxford University Press, 2008).
    [Crossref]
  4. L. Silberstein, “Investigations on the intrinsic properties of the color domain. II,” J. Opt. Soc. Am. 33, 1–9 (1943).
    [Crossref]
  5. D. L. MacAdam, “Visual sensitivities to color differences in daylight,” J. Opt. Soc. Am. 32, 247–274 (1942).
    [Crossref]
  6. D. L. MacAdam, “On the geometry of color space,” J. Franklin I. 238, 195–210 (1944).
    [Crossref]
  7. F. Clarke, R. McDonald, B. Rigg, “Modification to the JPC79 colour–difference formula,” J. Soc. Dyers Colour. 100, 128–132 (1984).
    [Crossref]
  8. R. McDonald, K. J. Smith, “CIE94 – A new colour-difference formula,” J. Soc. Dyers Colour. 111, 376–379 (1995).
    [Crossref]
  9. M. R. Luo, G. Cui, B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001).
    [Crossref]
  10. D. R. Pant, I. Farup, “Riemannian formulation and comparison of color difference formulas,” Color Res. Appl. 37, 429–440 (2012).
    [Crossref]
  11. M. Nölle, M. Suda, W. Boxleitner, I. Glendinning, “H2SI – a new perceptual colour space,” in “18th International Conference on Digital Signal Processing (DSP),” (IEEE, 2013), pp. 1–6.
    [Crossref]
  12. B. Riemann, “Ueber die Hypothesen, welche der Geometrie zu Grunde liegen, Abh,” Ge. Wiss. Gött 13, 133–152 (1868).
  13. H. v. Helmholtz, “Versuch einer erweiterten Anwendung des Fechnerschen Gesetzes im farbensystem,” Z. Psychol. Physiol. Sinnesorg. 2, 1–30 (1891).
  14. E. Schrödinger, “Grundlinien einer Theorie der Farbenmetrik im Tagessehen (III. Mitteilung),” Ann. Phys. 368, 481–520 (1920).
    [Crossref]
  15. W. S. Stiles, “A modified Helmholtz line-element in brightness-colour space,” P. Phys. Soc. 58, 41–65 (1946).
    [Crossref]
  16. A. Ashtekar, A. Corichi, M. Pierri, “Geometry in color perception,” in “Black Holes, Gravitational Radiation and the Universe,” (Springer, 1999), pp. 535–550.
    [Crossref]
  17. J. Chao, I. Osugi, M. Suzuki, “On definitions and construction of uniform color space,” in “CGIV 2004: The Second European Conference on Colour in Graphics, Imaging and Vision,” (2004), pp. 55–60.
  18. J. Chao, R. Lenz, D. Matsumoto, T. Nakamura, “Riemann geometry for color characterization and mapping,” in “Conference on Colour in Graphics, Imaging, and Vision,” (Society for Imaging Science and Technology, 2008), pp. 277–282.
  19. S. Ohshima, R. Mochizuki, J. Chao, R. Lenz, “Color reproduction using riemann normal coordinates,” in “Computational Color Imaging,” (Springer, 2009), pp. 140–149.
    [Crossref]
  20. D. R. Pant, I. Farup, “Geodesic calculation of color difference formulas and comparison with the Munsell color order system,” Color Res. Appl. 38, 259–266 (2013).
    [Crossref]
  21. H. L. Resnikoff, “Differential geometry and color perception,” J. Math. Biol. 1, 97–131 (1974).
    [Crossref]
  22. R. Lenz, T. H. Bui, J. Hernández-Andrés, “Group theoretical structure of spectral spaces,” J. Math. Imaging Vis. 23, 297–313 (2005).
    [Crossref]
  23. R. Lenz, P. Latorre Carmona, P. Meer, “The hyperbolic geometry of illumination-induced chromaticity changes,” in “Computer Vision and Pattern Recognition, 2007. CVPR’07. IEEE Conference on,” (IEEE, 2007), pp. 1–6.
    [Crossref]
  24. J. W. Anderson, Hyperbolic geometry (Springer, 2005), 2
  25. G. Cui, M. Luo, B. Rigg, G. Roesler, K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
    [Crossref]
  26. C. Oleari, M. Melgosa, R. Huertas, “Euclidean color-difference formula for small–medium color differences in log-compressed OSA-UCS space,” J. Opt. Soc. Am. A 26, 121–134 (2009).
    [Crossref]
  27. R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
    [Crossref]
  28. R. S. Berns, B. Hou, “RIT-DuPont supra-threshold color-tolerance individual color-difference pair dataset,” Color Res. Appl. 35, 274–283 (2010).
    [Crossref]
  29. P. A. García, R. Huertas, M. Melgosa, G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
    [Crossref]
  30. D. R. Pant, I. Farup, M. Melgosa, “Analysis of three Euclidean color-difference formulas for predicting the average RIT-DuPont color-difference ellipsoids,” in “Proceedings of AIC2013 – 12th International AIC Congress,” (2013), pp. 537–540.
  31. M. Luo, B. Rigg, “Chromaticity-discrimination ellipses for surface colours,” Color Res. Appl. 11, 25–42 (1986).
    [Crossref]
  32. G. Wyszecki, G. H. Fielder, “New color-matching ellipses,” J. Opt. Soc. Am. 61, 1135–1152 (1971).
    [Crossref] [PubMed]
  33. M. Melgosa, E. Hita, A. Poza, D. H. Alman, R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
    [Crossref]

2013 (1)

D. R. Pant, I. Farup, “Geodesic calculation of color difference formulas and comparison with the Munsell color order system,” Color Res. Appl. 38, 259–266 (2013).
[Crossref]

2012 (1)

D. R. Pant, I. Farup, “Riemannian formulation and comparison of color difference formulas,” Color Res. Appl. 37, 429–440 (2012).
[Crossref]

2010 (1)

R. S. Berns, B. Hou, “RIT-DuPont supra-threshold color-tolerance individual color-difference pair dataset,” Color Res. Appl. 35, 274–283 (2010).
[Crossref]

2009 (1)

2007 (1)

2005 (1)

R. Lenz, T. H. Bui, J. Hernández-Andrés, “Group theoretical structure of spectral spaces,” J. Math. Imaging Vis. 23, 297–313 (2005).
[Crossref]

2002 (1)

G. Cui, M. Luo, B. Rigg, G. Roesler, K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
[Crossref]

2001 (1)

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

1997 (1)

M. Melgosa, E. Hita, A. Poza, D. H. Alman, R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
[Crossref]

1995 (1)

R. McDonald, K. J. Smith, “CIE94 – A new colour-difference formula,” J. Soc. Dyers Colour. 111, 376–379 (1995).
[Crossref]

1991 (1)

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

1986 (1)

M. Luo, B. Rigg, “Chromaticity-discrimination ellipses for surface colours,” Color Res. Appl. 11, 25–42 (1986).
[Crossref]

1984 (1)

F. Clarke, R. McDonald, B. Rigg, “Modification to the JPC79 colour–difference formula,” J. Soc. Dyers Colour. 100, 128–132 (1984).
[Crossref]

1974 (1)

H. L. Resnikoff, “Differential geometry and color perception,” J. Math. Biol. 1, 97–131 (1974).
[Crossref]

1971 (1)

1969 (1)

D. B. Judd, “Ideal color space – II. The super-importance of hue differences and its bearing on the geometry of color space,” Palette 30, 21–28 (1969).

1946 (1)

W. S. Stiles, “A modified Helmholtz line-element in brightness-colour space,” P. Phys. Soc. 58, 41–65 (1946).
[Crossref]

1944 (1)

D. L. MacAdam, “On the geometry of color space,” J. Franklin I. 238, 195–210 (1944).
[Crossref]

1943 (2)

1942 (1)

1920 (1)

E. Schrödinger, “Grundlinien einer Theorie der Farbenmetrik im Tagessehen (III. Mitteilung),” Ann. Phys. 368, 481–520 (1920).
[Crossref]

1891 (1)

H. v. Helmholtz, “Versuch einer erweiterten Anwendung des Fechnerschen Gesetzes im farbensystem,” Z. Psychol. Physiol. Sinnesorg. 2, 1–30 (1891).

1868 (1)

B. Riemann, “Ueber die Hypothesen, welche der Geometrie zu Grunde liegen, Abh,” Ge. Wiss. Gött 13, 133–152 (1868).

Alman, D. H.

M. Melgosa, E. Hita, A. Poza, D. H. Alman, R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
[Crossref]

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

Anderson, J. W.

J. W. Anderson, Hyperbolic geometry (Springer, 2005), 2

Ashtekar, A.

A. Ashtekar, A. Corichi, M. Pierri, “Geometry in color perception,” in “Black Holes, Gravitational Radiation and the Universe,” (Springer, 1999), pp. 535–550.
[Crossref]

Balonon-Rosen, M. R.

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

Berns, R. S.

R. S. Berns, B. Hou, “RIT-DuPont supra-threshold color-tolerance individual color-difference pair dataset,” Color Res. Appl. 35, 274–283 (2010).
[Crossref]

M. Melgosa, E. Hita, A. Poza, D. H. Alman, R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
[Crossref]

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

Boxleitner, W.

M. Nölle, M. Suda, W. Boxleitner, I. Glendinning, “H2SI – a new perceptual colour space,” in “18th International Conference on Digital Signal Processing (DSP),” (IEEE, 2013), pp. 1–6.
[Crossref]

Bui, T. H.

R. Lenz, T. H. Bui, J. Hernández-Andrés, “Group theoretical structure of spectral spaces,” J. Math. Imaging Vis. 23, 297–313 (2005).
[Crossref]

Chao, J.

S. Ohshima, R. Mochizuki, J. Chao, R. Lenz, “Color reproduction using riemann normal coordinates,” in “Computational Color Imaging,” (Springer, 2009), pp. 140–149.
[Crossref]

J. Chao, R. Lenz, D. Matsumoto, T. Nakamura, “Riemann geometry for color characterization and mapping,” in “Conference on Colour in Graphics, Imaging, and Vision,” (Society for Imaging Science and Technology, 2008), pp. 277–282.

J. Chao, I. Osugi, M. Suzuki, “On definitions and construction of uniform color space,” in “CGIV 2004: The Second European Conference on Colour in Graphics, Imaging and Vision,” (2004), pp. 55–60.

Clarke, F.

F. Clarke, R. McDonald, B. Rigg, “Modification to the JPC79 colour–difference formula,” J. Soc. Dyers Colour. 100, 128–132 (1984).
[Crossref]

Corichi, A.

A. Ashtekar, A. Corichi, M. Pierri, “Geometry in color perception,” in “Black Holes, Gravitational Radiation and the Universe,” (Springer, 1999), pp. 535–550.
[Crossref]

Cui, G.

P. A. García, R. Huertas, M. Melgosa, G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
[Crossref]

G. Cui, M. Luo, B. Rigg, G. Roesler, K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
[Crossref]

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

Farup, I.

D. R. Pant, I. Farup, “Geodesic calculation of color difference formulas and comparison with the Munsell color order system,” Color Res. Appl. 38, 259–266 (2013).
[Crossref]

D. R. Pant, I. Farup, “Riemannian formulation and comparison of color difference formulas,” Color Res. Appl. 37, 429–440 (2012).
[Crossref]

D. R. Pant, I. Farup, M. Melgosa, “Analysis of three Euclidean color-difference formulas for predicting the average RIT-DuPont color-difference ellipsoids,” in “Proceedings of AIC2013 – 12th International AIC Congress,” (2013), pp. 537–540.

Fielder, G. H.

García, P. A.

Glendinning, I.

M. Nölle, M. Suda, W. Boxleitner, I. Glendinning, “H2SI – a new perceptual colour space,” in “18th International Conference on Digital Signal Processing (DSP),” (IEEE, 2013), pp. 1–6.
[Crossref]

Helmholtz, H. v.

H. v. Helmholtz, “Versuch einer erweiterten Anwendung des Fechnerschen Gesetzes im farbensystem,” Z. Psychol. Physiol. Sinnesorg. 2, 1–30 (1891).

Hernández-Andrés, J.

R. Lenz, T. H. Bui, J. Hernández-Andrés, “Group theoretical structure of spectral spaces,” J. Math. Imaging Vis. 23, 297–313 (2005).
[Crossref]

Hita, E.

M. Melgosa, E. Hita, A. Poza, D. H. Alman, R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
[Crossref]

Hou, B.

R. S. Berns, B. Hou, “RIT-DuPont supra-threshold color-tolerance individual color-difference pair dataset,” Color Res. Appl. 35, 274–283 (2010).
[Crossref]

Huertas, R.

Judd, D. B.

D. B. Judd, “Ideal color space – II. The super-importance of hue differences and its bearing on the geometry of color space,” Palette 30, 21–28 (1969).

S. M. Newhall, D. Nickerson, D. B. Judd, “Final report of the OSA subcommittee on the spacing of the Munsell colors,” J. Opt. Soc. Am. 33, 385–411 (1943).
[Crossref]

Kuehni, R. G.

R. G. Kuehni, A. Schwarz, Color Ordered (Oxford University Press, 2008).
[Crossref]

Latorre Carmona, P.

R. Lenz, P. Latorre Carmona, P. Meer, “The hyperbolic geometry of illumination-induced chromaticity changes,” in “Computer Vision and Pattern Recognition, 2007. CVPR’07. IEEE Conference on,” (IEEE, 2007), pp. 1–6.
[Crossref]

Lenz, R.

R. Lenz, T. H. Bui, J. Hernández-Andrés, “Group theoretical structure of spectral spaces,” J. Math. Imaging Vis. 23, 297–313 (2005).
[Crossref]

R. Lenz, P. Latorre Carmona, P. Meer, “The hyperbolic geometry of illumination-induced chromaticity changes,” in “Computer Vision and Pattern Recognition, 2007. CVPR’07. IEEE Conference on,” (IEEE, 2007), pp. 1–6.
[Crossref]

S. Ohshima, R. Mochizuki, J. Chao, R. Lenz, “Color reproduction using riemann normal coordinates,” in “Computational Color Imaging,” (Springer, 2009), pp. 140–149.
[Crossref]

J. Chao, R. Lenz, D. Matsumoto, T. Nakamura, “Riemann geometry for color characterization and mapping,” in “Conference on Colour in Graphics, Imaging, and Vision,” (Society for Imaging Science and Technology, 2008), pp. 277–282.

Luo, M.

G. Cui, M. Luo, B. Rigg, G. Roesler, K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
[Crossref]

M. Luo, B. Rigg, “Chromaticity-discrimination ellipses for surface colours,” Color Res. Appl. 11, 25–42 (1986).
[Crossref]

Luo, M. R.

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

MacAdam, D. L.

D. L. MacAdam, “On the geometry of color space,” J. Franklin I. 238, 195–210 (1944).
[Crossref]

D. L. MacAdam, “Visual sensitivities to color differences in daylight,” J. Opt. Soc. Am. 32, 247–274 (1942).
[Crossref]

Matsumoto, D.

J. Chao, R. Lenz, D. Matsumoto, T. Nakamura, “Riemann geometry for color characterization and mapping,” in “Conference on Colour in Graphics, Imaging, and Vision,” (Society for Imaging Science and Technology, 2008), pp. 277–282.

McDonald, R.

R. McDonald, K. J. Smith, “CIE94 – A new colour-difference formula,” J. Soc. Dyers Colour. 111, 376–379 (1995).
[Crossref]

F. Clarke, R. McDonald, B. Rigg, “Modification to the JPC79 colour–difference formula,” J. Soc. Dyers Colour. 100, 128–132 (1984).
[Crossref]

Meer, P.

R. Lenz, P. Latorre Carmona, P. Meer, “The hyperbolic geometry of illumination-induced chromaticity changes,” in “Computer Vision and Pattern Recognition, 2007. CVPR’07. IEEE Conference on,” (IEEE, 2007), pp. 1–6.
[Crossref]

Melgosa, M.

C. Oleari, M. Melgosa, R. Huertas, “Euclidean color-difference formula for small–medium color differences in log-compressed OSA-UCS space,” J. Opt. Soc. Am. A 26, 121–134 (2009).
[Crossref]

P. A. García, R. Huertas, M. Melgosa, G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
[Crossref]

M. Melgosa, E. Hita, A. Poza, D. H. Alman, R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
[Crossref]

D. R. Pant, I. Farup, M. Melgosa, “Analysis of three Euclidean color-difference formulas for predicting the average RIT-DuPont color-difference ellipsoids,” in “Proceedings of AIC2013 – 12th International AIC Congress,” (2013), pp. 537–540.

Mochizuki, R.

S. Ohshima, R. Mochizuki, J. Chao, R. Lenz, “Color reproduction using riemann normal coordinates,” in “Computational Color Imaging,” (Springer, 2009), pp. 140–149.
[Crossref]

Nakamura, T.

J. Chao, R. Lenz, D. Matsumoto, T. Nakamura, “Riemann geometry for color characterization and mapping,” in “Conference on Colour in Graphics, Imaging, and Vision,” (Society for Imaging Science and Technology, 2008), pp. 277–282.

Newhall, S. M.

Nickerson, D.

Nölle, M.

M. Nölle, M. Suda, W. Boxleitner, I. Glendinning, “H2SI – a new perceptual colour space,” in “18th International Conference on Digital Signal Processing (DSP),” (IEEE, 2013), pp. 1–6.
[Crossref]

Ohshima, S.

S. Ohshima, R. Mochizuki, J. Chao, R. Lenz, “Color reproduction using riemann normal coordinates,” in “Computational Color Imaging,” (Springer, 2009), pp. 140–149.
[Crossref]

Oleari, C.

Osugi, I.

J. Chao, I. Osugi, M. Suzuki, “On definitions and construction of uniform color space,” in “CGIV 2004: The Second European Conference on Colour in Graphics, Imaging and Vision,” (2004), pp. 55–60.

Pant, D. R.

D. R. Pant, I. Farup, “Geodesic calculation of color difference formulas and comparison with the Munsell color order system,” Color Res. Appl. 38, 259–266 (2013).
[Crossref]

D. R. Pant, I. Farup, “Riemannian formulation and comparison of color difference formulas,” Color Res. Appl. 37, 429–440 (2012).
[Crossref]

D. R. Pant, I. Farup, M. Melgosa, “Analysis of three Euclidean color-difference formulas for predicting the average RIT-DuPont color-difference ellipsoids,” in “Proceedings of AIC2013 – 12th International AIC Congress,” (2013), pp. 537–540.

Pierri, M.

A. Ashtekar, A. Corichi, M. Pierri, “Geometry in color perception,” in “Black Holes, Gravitational Radiation and the Universe,” (Springer, 1999), pp. 535–550.
[Crossref]

Poza, A.

M. Melgosa, E. Hita, A. Poza, D. H. Alman, R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
[Crossref]

Reniff, L.

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

Resnikoff, H. L.

H. L. Resnikoff, “Differential geometry and color perception,” J. Math. Biol. 1, 97–131 (1974).
[Crossref]

Riemann, B.

B. Riemann, “Ueber die Hypothesen, welche der Geometrie zu Grunde liegen, Abh,” Ge. Wiss. Gött 13, 133–152 (1868).

Rigg, B.

G. Cui, M. Luo, B. Rigg, G. Roesler, K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
[Crossref]

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

M. Luo, B. Rigg, “Chromaticity-discrimination ellipses for surface colours,” Color Res. Appl. 11, 25–42 (1986).
[Crossref]

F. Clarke, R. McDonald, B. Rigg, “Modification to the JPC79 colour–difference formula,” J. Soc. Dyers Colour. 100, 128–132 (1984).
[Crossref]

Roesler, G.

G. Cui, M. Luo, B. Rigg, G. Roesler, K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
[Crossref]

Schrödinger, E.

E. Schrödinger, “Grundlinien einer Theorie der Farbenmetrik im Tagessehen (III. Mitteilung),” Ann. Phys. 368, 481–520 (1920).
[Crossref]

Schwarz, A.

R. G. Kuehni, A. Schwarz, Color Ordered (Oxford University Press, 2008).
[Crossref]

Silberstein, L.

Smith, K. J.

R. McDonald, K. J. Smith, “CIE94 – A new colour-difference formula,” J. Soc. Dyers Colour. 111, 376–379 (1995).
[Crossref]

Snyder, G. D.

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

Stiles, W. S.

W. S. Stiles, “A modified Helmholtz line-element in brightness-colour space,” P. Phys. Soc. 58, 41–65 (1946).
[Crossref]

Suda, M.

M. Nölle, M. Suda, W. Boxleitner, I. Glendinning, “H2SI – a new perceptual colour space,” in “18th International Conference on Digital Signal Processing (DSP),” (IEEE, 2013), pp. 1–6.
[Crossref]

Suzuki, M.

J. Chao, I. Osugi, M. Suzuki, “On definitions and construction of uniform color space,” in “CGIV 2004: The Second European Conference on Colour in Graphics, Imaging and Vision,” (2004), pp. 55–60.

Witt, K.

G. Cui, M. Luo, B. Rigg, G. Roesler, K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
[Crossref]

Wyszecki, G.

Ann. Phys. (1)

E. Schrödinger, “Grundlinien einer Theorie der Farbenmetrik im Tagessehen (III. Mitteilung),” Ann. Phys. 368, 481–520 (1920).
[Crossref]

Color Res. Appl. (8)

D. R. Pant, I. Farup, “Geodesic calculation of color difference formulas and comparison with the Munsell color order system,” Color Res. Appl. 38, 259–266 (2013).
[Crossref]

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

D. R. Pant, I. Farup, “Riemannian formulation and comparison of color difference formulas,” Color Res. Appl. 37, 429–440 (2012).
[Crossref]

G. Cui, M. Luo, B. Rigg, G. Roesler, K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
[Crossref]

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

R. S. Berns, B. Hou, “RIT-DuPont supra-threshold color-tolerance individual color-difference pair dataset,” Color Res. Appl. 35, 274–283 (2010).
[Crossref]

M. Luo, B. Rigg, “Chromaticity-discrimination ellipses for surface colours,” Color Res. Appl. 11, 25–42 (1986).
[Crossref]

M. Melgosa, E. Hita, A. Poza, D. H. Alman, R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
[Crossref]

Ge. Wiss. Gött (1)

B. Riemann, “Ueber die Hypothesen, welche der Geometrie zu Grunde liegen, Abh,” Ge. Wiss. Gött 13, 133–152 (1868).

J. Franklin I. (1)

D. L. MacAdam, “On the geometry of color space,” J. Franklin I. 238, 195–210 (1944).
[Crossref]

J. Math. Biol. (1)

H. L. Resnikoff, “Differential geometry and color perception,” J. Math. Biol. 1, 97–131 (1974).
[Crossref]

J. Math. Imaging Vis. (1)

R. Lenz, T. H. Bui, J. Hernández-Andrés, “Group theoretical structure of spectral spaces,” J. Math. Imaging Vis. 23, 297–313 (2005).
[Crossref]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (2)

J. Soc. Dyers Colour. (2)

F. Clarke, R. McDonald, B. Rigg, “Modification to the JPC79 colour–difference formula,” J. Soc. Dyers Colour. 100, 128–132 (1984).
[Crossref]

R. McDonald, K. J. Smith, “CIE94 – A new colour-difference formula,” J. Soc. Dyers Colour. 111, 376–379 (1995).
[Crossref]

P. Phys. Soc. (1)

W. S. Stiles, “A modified Helmholtz line-element in brightness-colour space,” P. Phys. Soc. 58, 41–65 (1946).
[Crossref]

Palette (1)

D. B. Judd, “Ideal color space – II. The super-importance of hue differences and its bearing on the geometry of color space,” Palette 30, 21–28 (1969).

Z. Psychol. Physiol. Sinnesorg. (1)

H. v. Helmholtz, “Versuch einer erweiterten Anwendung des Fechnerschen Gesetzes im farbensystem,” Z. Psychol. Physiol. Sinnesorg. 2, 1–30 (1891).

Other (9)

D. R. Pant, I. Farup, M. Melgosa, “Analysis of three Euclidean color-difference formulas for predicting the average RIT-DuPont color-difference ellipsoids,” in “Proceedings of AIC2013 – 12th International AIC Congress,” (2013), pp. 537–540.

R. G. Kuehni, A. Schwarz, Color Ordered (Oxford University Press, 2008).
[Crossref]

M. Nölle, M. Suda, W. Boxleitner, I. Glendinning, “H2SI – a new perceptual colour space,” in “18th International Conference on Digital Signal Processing (DSP),” (IEEE, 2013), pp. 1–6.
[Crossref]

A. Ashtekar, A. Corichi, M. Pierri, “Geometry in color perception,” in “Black Holes, Gravitational Radiation and the Universe,” (Springer, 1999), pp. 535–550.
[Crossref]

J. Chao, I. Osugi, M. Suzuki, “On definitions and construction of uniform color space,” in “CGIV 2004: The Second European Conference on Colour in Graphics, Imaging and Vision,” (2004), pp. 55–60.

J. Chao, R. Lenz, D. Matsumoto, T. Nakamura, “Riemann geometry for color characterization and mapping,” in “Conference on Colour in Graphics, Imaging, and Vision,” (Society for Imaging Science and Technology, 2008), pp. 277–282.

S. Ohshima, R. Mochizuki, J. Chao, R. Lenz, “Color reproduction using riemann normal coordinates,” in “Computational Color Imaging,” (Springer, 2009), pp. 140–149.
[Crossref]

R. Lenz, P. Latorre Carmona, P. Meer, “The hyperbolic geometry of illumination-induced chromaticity changes,” in “Computer Vision and Pattern Recognition, 2007. CVPR’07. IEEE Conference on,” (IEEE, 2007), pp. 1–6.
[Crossref]

J. W. Anderson, Hyperbolic geometry (Springer, 2005), 2

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 Equi-distant circles of radius r = 0.1 in the Poincaré disk model of hyperbolic geometry with R = 1.
Fig. 2
Fig. 2 Equi-distant ellipses in the Euclidean plane according to the Poincaré disk metric dr for various radii of curvature. Left to right: R = ∞ (Euclidean), R = 1, and R = 0.5.
Fig. 3
Fig. 3 STRESS values for the prediction of the RIT-DuPont T50 data set for the hyperbolic metrics derived from the given Euclidean metrics as a function of the radius of curvature, R. The dashed lines show the STRESS values for the corresponding Euclidean metric.
Fig. 4
Fig. 4 WSTRESS values for the prediction of the full RIT-DuPont data set for the hyperbolic metrics derived from the given Euclidean metrics as a function of the radius of curvature, R. The dashed lines show the WSTRESS values for the corresponding Euclidean metric.
Fig. 5
Fig. 5 Various cross sections in the CIELAB space of Melgosa’s fitted ellipsoids for the RIT-DuPont data set (grey) and computed ellipsiod cross sections (black) for the standard DIN99 metric (left) and the hyperbolic version of the DIN99 metric (right).

Tables (2)

Tables Icon

Table 1 p-values for two-sided paired t-tests for the full and T50 versions of the RIT-DuPont data set for the difference between the standard Euclidean and the suggested hyperbolic improvement of the metric.

Tables Icon

Table 2 p-values for two-sided paired t-tests for the full and T50 versions of the RIT-DuPont data set for the difference between the suggested hyperbolic improvement of the metric and DE2000.

Equations (5)

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

d 𝔻 ( z 1 , z 2 ) = 2 artanh | z 1 z 2 1 z 1 z ¯ 2 | ,
d s 𝔻 2 = 4 | d z | 2 ( 1 | z | 2 ) 2 ,
r ˜ = tanh ( r / 2 R ) ,
d R ( z ˜ 1 , z ˜ 2 ) = R d 𝔻 ( z ˜ 1 , z ˜ 2 ) ,
d ( ( L 1 , x 1 , y 1 ) , ( L 2 , x 2 , y 2 ) ) 2 = ( L 1 L 2 ) 2 + ( d R ( z ˜ 1 , z ˜ 2 ) ) 2 ,

Metrics