OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 6 — Jun. 1, 2002
  • pp: 1084–1095

Psychophysical model of chromatic perceptual transparency based on substractive color mixture

Franz Faul and Vebjørn Ekroll  »View Author Affiliations

JOSA A, Vol. 19, Issue 6, pp. 1084-1095 (2002)

View Full Text Article

Acrobat PDF (375 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Variants of Metelli’s episcotister model, which are based on additive color mixture, have been found to describe the luminance conditions for perceptual transparency very accurately. However, the findings in the chromatic domain are not that clear-cut, since there exist chromatic stimuli that conform to the additive model but do <i>not</i> appear transparent. We present evidence that such failures are of a systematic nature, and we propose an alternative psychophysical model based on subtractive color mixture. Results of a computer simulation revealed that this model approximately describes color changes that occur when a surface is covered by a filter. We present the results of two psychophysical experiments with chromatic stimuli, in which we directly compared the predictions of the additive model and the predictions of the new model. These results show that the color relations leading to the perception of a homogeneous transparent layer conform very closely to the predictions of the new model and deviate systematically from the predictions of the additive model.

© 2002 Optical Society of America

OCIS Codes
(330.1690) Vision, color, and visual optics : Color
(330.1710) Vision, color, and visual optics : Color, measurement
(330.1720) Vision, color, and visual optics : Color vision
(330.7310) Vision, color, and visual optics : Vision

Franz Faul and Vebjørn Ekroll, "Psychophysical model of chromatic perceptual transparency based on substractive color mixture," J. Opt. Soc. Am. A 19, 1084-1095 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. F. Metelli, “An algebraic development of the theory of perceptual transparency,” Ergonomics 13, 59–66 (1970).
  2. F. Metelli, “The perception of transparency,” Sci. Am. 230, 90–98 (1974).
  3. O. Da Pos, Trasparenze (Icone, Società a Responsabilità Limitata, Padova, Italy, 1989).
  4. F. Faul, “Chromatic scission in perceptual transparency,” Perception 25 (Suppl.), 105 (1996).
  5. F. Faul, “Theoretische und experimentelle Untersuchung chromatischer Determinanten perzeptueller Transparenz,” Ph.D dissertation (Christian-Albrechts-Universität zu Kiel, Kiel, Germany, 1997).
  6. M. D’Zmura, P. Colantoni, K. Knoblauch, and B. Laget, “Color transparency,” Perception 26, 471–492 (1997).
  7. W. Gerbino, C. I. F. H. J. Stultiens, J. M. Troost, and C. M. M. De Weert, “Transparent layer constancy,” J. Exp. Psychol. Hum. Percept. Perform. 16, 3–20 (1990).
  8. J. Beck and R. Ivry, “On the role of figural organization in perceptual transparency,” Percept. Psychophys. 44, 585–594 (1988).
  9. J. Beck, K. Prazdny, and R. Ivry, “The perception of transparency with achromatic colors,” Percept. Psychophys. 35, 407–422 (1984).
  10. S. Nakauchi, P. Silfsten, J. Parkinnen, and S. Usui, “Computational theory of color transparency: recovery of spectral properties for overlapping surfaces,” J. Opt. Soc. Am. A 16, 2612–2624 (1999).
  11. S. Westland and C. Ripamonti, “Invariant cone-excitation ratios may predict transparency,” J. Opt. Soc. Am. A 17, 255–264 (2000).
  12. R. Kasrai and F. A. A. Kingdom, “Precision, accuracy, and range of perceived achromatic transparency,” J. Opt. Soc. Am. A 18, 1–11 (2001).
  13. V. J. Chen and M. D’Zmura, “Test of a convergence model for color transparency,” Perception 27, 595–608 (1998).
  14. J. Hagedorn and M. D’Zmura, “Color appearance of surfaces viewed through fog,” Perception 29, 1169–1184 (2000).
  15. M. D’Zmura, O. Rinner, and K. R. Gegenfurtner, “The colors seen behind transparent filters,” Perception 29, 911–926 (2000).
  16. J. Foley, A. van Dam, S. Feiner, and J. Hughes, Computer Graphics. Principles and Practice (Addision-Wesley, New York, 1990).
  17. M. Singh and B. L. Anderson, “Toward a perceptual theory of transparency,” Psychol. Rev. (to be published).
  18. E. Allen, “Colorant formulation and shading,” in Optical Radiation Measurements. Vol 2: Color Measurement, F. Grum and C. J. Bartelson, eds. (Academic, New York, 1980).
  19. M. Brill, “Physical and informational constraints on the perception of transparency and translucency,” Vision Graph. Image Process. 28, 356–362 (1984).
  20. A minor drawback of this formulation is that Eq. (11) may be undefined for some i. This problem is easily solved: Choose i such that Ai ≠Bi (this is always possible, since at an X junction we have A ≠B) and calculate κ for this coordinate using Eq. (12). Then βi =Pi /(Ai +Wi), with Wi =κ(Ai +Bi)/2.
  21. S. M. C. Nascimento and D. H. Foster, “Detecting natural changes of cone-excitation ratios in simple and complex coloured images,” Proc. R. Soc. London Ser. B 264, 1395–1402 (1997).
  22. M. D’Zmura, G. Iverson, and B. Singer, “Probabilistic color constancy,” in Geometric Representations of Perceptual Phenomena, R. Luce, M. D’Zmura, D. Hoffman, G. Iverson, and R. Kimball, eds. (Erlbaum, Mahwah, N.J., 1995), Chap. 11, pp. 187–202.
  23. W. S. Stiles, G. Wyszecki, and N. Ohta, “Counting metameric object-color stimuli using frequency-limited spectral reflectance functions,” J. Opt. Soc. Am. 67, 779–784 (1977).
  24. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).
  25. L. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. A 3, 1673–1683 (1986).
  26. A. Stockman and L. T. Sharpe, “Cone spectral sensitivities and color matching,” in Color Vision. From Genes to Perception, K. R. Gegenfurtner and L. T. Sharpe, eds. (Cambridge U. Press, Cambridge, UK, 2000), Chap. 2, pp. 53–101.
  27. D. Brainard, “Calibration of a computer controlled monitor,” Color Res. Appl. 14, 23–34 (1989).
  28. J. Parkkinen, J. Hallikainen, and T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
  29. J. Golz and D. I. A. MacLeod, “Colorimetry for CRT displays: almost-valid measures from invalid color matching functions and invalid assumptions,” manuscript available from the authors (golz@psychologie.uni-kiel.de).

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