OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 27, Iss. 7 — Jul. 1, 2010
  • pp: 1620–1629

Upgrading color-difference formulas

Ingmar Lissner and Philipp Urban  »View Author Affiliations

JOSA A, Vol. 27, Issue 7, pp. 1620-1629 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (819 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We propose a method to improve the prediction performance of existing color-difference formulas with additional visual data. The formula is treated as the mean function of a Gaussian process, which is trained with experimentally determined color-discrimination data. Color-difference predictions are calculated using Gaussian process regression (GPR) considering the uncertainty of the visual data. The prediction accuracy of the CIE94 formula is significantly improved with the GPR approach for the Leeds and the Witt datasets. By upgrading CIE94 with GPR we achieve a significantly lower STRESS value of 26.58 compared with that for CIEDE2000 (27.49) on a combined dataset. The method could serve to improve the prediction performance of existing color-difference equations around particular color centers without changing the equations themselves.

© 2010 Optical Society of America

OCIS Codes
(330.0330) Vision, color, and visual optics : Vision, color, and visual optics
(330.1690) Vision, color, and visual optics : Color
(330.1730) Vision, color, and visual optics : Colorimetry

ToC Category:
Vision, Color, and Visual Optics

Original Manuscript: January 26, 2010
Revised Manuscript: April 15, 2010
Manuscript Accepted: April 19, 2010
Published: June 11, 2010

Virtual Issues
Vol. 5, Iss. 11 Virtual Journal for Biomedical Optics

Ingmar Lissner and Philipp Urban, "Upgrading color-difference formulas," J. Opt. Soc. Am. A 27, 1620-1629 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. Committee of the Society of Dyers and Colorists, “BS 6923: Method for calculation of small colour differences,” Tech. rep. (British Standards Institution, London, 1988).
  2. CIE Publication No. 116, “Industrial colour-difference evaluation,” Tech. rep. (Central Bureau of the CIE, Vienna, 1995).
  3. CIE Publication No. 142, “Improvement to industrial colour-difference evaluation,” Tech. rep. (Central Bureau of the CIE, Vienna, 2001).
  4. R. S. Berns, Billmeyer and Saltzman’s Principles of Color Technology, 3rd ed. (Wiley, 2000).
  5. M. R. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001). [CrossRef]
  6. M. Melgosa, R. Huertas, and R. S. Berns, “Relative significance of the terms in the CIEDE2000 and CIE94 color-difference formulas,” J. Opt. Soc. Am. A 21, 2269–2275 (2004). [CrossRef]
  7. R. G. Kuehni, “Variability in estimation of suprathreshold small color differences,” Color Res. Appl. 34, 367–374 (2009). [CrossRef]
  8. M. Melgosa, R. Huertas, and R. S. Berns, “Performance of recent advanced color-difference formulas using the standardized residual sum of squares index,” J. Opt. Soc. Am. A 25, 1828–1834 (2008). [CrossRef]
  9. S. Shen and R. S. Berns, “Evaluating color difference equation performance incorporating visual uncertainty,” Color Res. Appl. 34, 375–390 (2009). [CrossRef]
  10. R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991). [CrossRef]
  11. M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colours,” Color Res. Appl. 11, 25–42 (1986). [CrossRef]
  12. D. H. Kim and J. H. Nobbs, “New weighting functions for the weighted CIELAB colour difference formula,” in Proceedings of l'Association Internationale de la Couleur (AIC) (AIC, 1997), pp. 446–449.
  13. K. Witt, “Geometric relations between scales of small colour differences,” Color Res. Appl. 24, 78–92 (1999). [CrossRef]
  14. R. Kuehni, “Color difference formulas: An unsatisfactory state of affairs,” Color Res. Appl. 33, 324–326 (2008). [CrossRef]
  15. I. Lissner and P. Urban, “Improving color-difference formulas using visual data,” in Proceedings of the 5th European Conference on Colour in Graphics, Imaging, and Vision (CGIV) (IS&T, 2010).
  16. CIE Publication No. 101, “Parametric effects in colour-difference evaluation,” Tech. rep. (Central Bureau of the CIE, Vienna, 1993).
  17. C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (The MIT Press, 2006).
  18. L. Silberstein and D. L. MacAdam, “The distribution of color matchings around a color center,” J. Opt. Soc. Am. 35, 32–39 (1945). [CrossRef]
  19. W. R. J. Brown, “Statistics of color-matching data,” J. Opt. Soc. Am. 42, 252–256 (1952). [CrossRef]
  20. W. R. J. Brown, W. G. Howe, J. E. Jackson, and R. H. Morris, “Multivariate normality of the color-matching process,” J. Opt. Soc. Am. 46, 46–49 (1956). [CrossRef]
  21. K. V. Mardia and R. J. Marshall, “Maximum likelihood estimation of models for residual covariance in spatial regression,” Biometrika 71, 135–146 (1984). [CrossRef]
  22. M. Kuss, “Gaussian process models for robust regression, classification, and reinforcement learning,” Ph.D. thesis (Technische Universität Darmstadt, 2006).
  23. C. E. Rasmussen, “The Gaussian processes web site,” http://www.gaussianprocess.org.
  24. S.-S. Guan and M. R. Luo, “Investigation of parametric effects using small colour differences,” Color Res. Appl. 24, 331–343 (1999). [CrossRef]
  25. P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007). [CrossRef]
  26. S. Shen, “Color difference formula and uniform color space modeling and evaluation,” Master's thesis (Rochester Institute of Technology, 2009).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited