Abstract

Color constancy is often modeled on the assumption that color appearance in natural scenes is a function of the visual system’s estimates of surface reflectance. Some stimuli, however, do not look like illuminated surfaces. Instead, they appear to be self-luminous. We hypothesized that the appearance of luminosity occurs when the visual system estimates a reflectance spectrum that is outside the gamut of physically realizable surfaces. To test this idea, we measured luminosity thresholds as a function of stimulus chromaticity and illuminant spectral power distribution. Observers adjusted the luminance of a test patch until it just appeared self-luminous. The test patch was spot illuminated by a computer-controlled projection colorimeter viewed in an experimental room lit diffusely by computer-controlled theater lamps. Luminosity thresholds were determined for a number of test patch chromaticities under five experimental illuminants. The luminosity thresholds define a surface in color space. The shape of this surface depends on the illuminant. We were able to describe much of the luminosity threshold variation with a simple model whose parameters define an equivalent illuminant. In the context of our model, the equivalent illuminant may be interpreted as the illuminant perceived by the observer. As part of our model calculations we generalized the classic notion of optimal stimuli by incorporating linear-model constraints. Given the equivalent illuminant, the model predicts that a patch will appear self-luminous when it is not consistent with any physically realizable surface seen under that illuminant. In addition, we show that much of the variation of the equivalent illuminant with the physical illuminant can be modeled with a simple linearity principle. The fact that our model provides a good account of our data extends the physics-based approach to judgments of self-luminosity. This in turn might be taken as support for the notion that the visual system has internalized the physics of reflectance.

© 1996 Optical Society of America

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References

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  1. D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Dir. Psychol. Sci. 2, 165–170 (1993).
    [Crossref]
  2. K. Buhler, “Gegenbemerkungen,” Psychol. Forsch. 5, 182–188 (1924), as discussed in Ref. 3.
    [Crossref]
  3. G. Kreezer, “Luminous appearances,” J. Gen. Psychol. 4, 247–281 (1930).
    [Crossref]
  4. R. M. Evans, “Fluorescence and gray content of surface colors,” J. Opt. Soc. Am. 49, 1049–1059 (1959).
    [Crossref]
  5. R. M. Evans, “Variables of perceived color,” J. Opt. Soc. Am. 54, 1467–1474 (1964).
    [Crossref] [PubMed]
  6. R. M. Evans, B. K. Swenholt, “Chromatic strength of colors: dominant wavelength and purity,” J. Opt. Soc. Am. 57, 1319–1324 (1967).
    [Crossref] [PubMed]
  7. R. M. Evans, B. K. Swenholt, “Chromatic strength of colors. Part II. The Munsell system,” J. Opt. Soc. Am. 58, 580–584 (1968).
    [Crossref] [PubMed]
  8. R. M. Evans, B. K. Swenholt, “Chromatic strength of colors. III. Chromatic surrounds and discussion,” J. Opt. Soc. Am. 59, 628–634 (1969).
    [Crossref] [PubMed]
  9. S. Ullman, “On visual detection of light sources,” Biol. Cybern. 21, 205–212 (1976).
    [Crossref] [PubMed]
  10. F. Bonato, A. L. Gilchrist, “The perception of luminosity on different backgrounds and in different illuminations,” Perception 23, 991–1006 (1994).
    [Crossref] [PubMed]
  11. M. Ikeda, K. Motonaga, N. Matsuzawa, T. Ishida, “Threshold determination for unnatural color appearance with local illumination,” Kogaku 22, 289–298 (1993).
  12. M. Ikeda, S. Fukumura, N. Matsuzawa, T. Ishida, “Influence of surrounding visual information on the recognition threshold of local illumination,” Kogaku 23, 42–49 (1994).
  13. Our usage of the term luminosity threshold follows that of Kreezer3 and of Bonato and Gilchrist.10 The term luminosity is used in the literature both to describe physical properties of light14 and to describe perceptual experience.15 Ideal terminology would distinguish these two uses, but at present we feel that less confusion will be generated by our use of luminosity threshold than if we attempt to define new terminology.
  14. D. L. MacAdam, Color Measurement: Theme and Variations (Springer-Verlag, New York, 1981).
  15. D. Judd, G. Wyszecki, Color in Business, Science, and Industry (Wiley, New York, 1975).
  16. R. N. Shepard, “The perceptual organization of colors: an adaptation to regularities of the terrestrial world?” in The Adapted Mind: Evolutionary Psychology and the Generation of Culture, J. H. Barkow, L. Cosmides, J. Tooby, eds. (Oxford U. Press, New York, 1992).
  17. CIE, Colorimetry, 2nd ed. (Bureau Central de la CIE, Paris, 1986).
  18. D. H. Brainard, “Colorimetry,” in Handbook of Optics: Vol. 1. Fundamentals, Techniques, and Design, M. Bass, ed. (McGraw-Hill, New York, 1995).
  19. J. M. Speigle, D. H. Brainard, “Fluorescence thresholds depend on the illumination,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, 1656 (1994).
  20. L. T. Maloney, B. Wandell, “A computational model of color constancy,” Invest. Ophthalmol. Vis. Suppl. 26, 206 (1985).
  21. M. D’Zmura, G. Iverson, “Color constancy. I. Basic theory of two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2148–2165 (1993).
    [Crossref]
  22. E. Hering, “Der Raumsinn und die Bewegungen des Auges,” in Handbuch der Physiologie, B.L. Hermann, ed. (Vogel, Leipzig, 1879), Vol. 3, Part 1, as discussed in Ref. 3 above.
  23. D. L. MacAdam, “The theory of the maximum visual efficiency of colored materials,” J. Opt. Soc. Am. 25, 249–252 (1935).
    [Crossref]
  24. A. L. Gilchrist, S. Delman, A. Jacobsen, “The classification and integration of edges as critical to the perception of reflectance and illumination,” Percept. Psychophys. 33, 425–436 (1983).
    [Crossref] [PubMed]
  25. A. L. Gilchrist, “Lightness contrast and failures of constancy: a common explanation,” Percept. Psychophys. 43, 415–424 (1988).
    [Crossref] [PubMed]
  26. G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
    [Crossref]
  27. D. H. Brainard, W. T. Freeman, “Bayesian method for recovering surface and illuminant properties from photoreceptor responses,” in Human Vision, Visual Processing, and Digital Display V, B. E. Rogowitz, J. P. Allebach, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2179, 364–376 (1994).
    [Crossref]
  28. D. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vision 5, 5–36 (1990).
    [Crossref]
  29. G. D. Finlayson, “Color constancy in diagonal chromaticity space,” in Proceedings of the 5th International Conference on Computer Vision (IEEE, Cambridge, Mass., 1995), pp. 218–223.
  30. M. D’Zmura, G. Iverson, B. Singer, “Probabilistic color constancy,” in Geometric Representations of Perceptual Phenomena: Papers in Honor of Tarow Indow’s 70th Birthday, R. D. Luce, M. D’Zmura, D. Hoffman, G. Iverson, A. K. Romney, eds., (Erlbaum, Hillsdale, N.J., 1995).
  31. J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).
  32. D. B. Judd, D. L. MacAdam, G. W. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
    [Crossref]
  33. L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. A 3, 1673–1683 (1986).
    [Crossref] [PubMed]
  34. The other combinations of linear models we tried were (1) the CIE three-dimensional daylight model together with a three-dimensional linear model for the Munsell papers, (2) the CIE three-dimensional daylight model together with a six-dimensional linear model for the Munsell papers, and (3) a two-dimensional linear model for illuminants obtained from a principal-components analysis of our experimental illuminants together with the four-dimensional linear model for Munsell papers. These choices did not provide a better fit than the combination we used. We evaluated only choice (2) on a subset of our data, because it was computationally expensive to compute the model fits for a six-dimensional-surface linear model.
  35. K. L. Kelly, K. S. Gibson, D. Nickerson, “Tristimulus specification of the Munsell Book of Color from spectrophotometric measurements,” J. Opt. Soc. Am. 33, 355–376 (1943).
    [Crossref]
  36. D. Nickerson, “Spectrophotometric data for a collection of Munsell samples” (U.S. Department of Agriculture, Washington, D.C., 1957; available from Munsell Color Company, Baltimore, Md.).
  37. V. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
    [Crossref] [PubMed]
  38. P. DeMarco, J. Pokorny, V. C. Smith, “Full-spectrum cone sensitivity functions for X-chromosome-linked anomalous trichromats,” J. Opt. Soc. Am. A 9, 1465–1476 (1992).
    [Crossref] [PubMed]
  39. F. G. Ashby, W. W. Lee, “Predicting similarity and categorization from identification,” J. Exp. Psychol. Gen. 120, 150–172 (1991).
    [Crossref] [PubMed]
  40. D. H. Brainard, B. A. Wandell, “Asymmetric color-matching: how color appearance depends on the illuminant,” J. Opt. Soc. Am. A 9, 1433–1448 (1992).
    [Crossref] [PubMed]
  41. E. Schrodinger, “Theorie der pigmente von grosster Leuchtkraft,” Ann. Phys. 62, 603–622 (1920), as discussed in Ref. 50 below.
    [Crossref]
  42. S. Rosch, “Die Kennzeichnung der Farben,” Phys. Z. 29, 83–91 (1928), as discussed in Ref. 50 below.
  43. G. Wyszecki, W. S. Stiles, Color Science—Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).
  44. M. Richter, K. Witt, “The story of the DIN color system,” Color Res. Appl. 11, 138–145 (1986).
    [Crossref]
  45. M. R. Pointer, “The gamut of real surface colours,” Color Res. Appl. 5, 145–155 (1980).
    [Crossref]
  46. W. T. Freeman, D. H. Brainard, “Bayesian decision theory, the local mass estimate, and color constancy,” in Proceedings of the 5th International Conference on Computer Vision (IEEE, Cambridge, Mass., 1995), pp. 210–217.
  47. D. Marr, Vision, (Freeman, San Francisco, 1982).
  48. J. Little, C. Moler, matlab User’s Guide (The Math-Works, Natick, Mass., 1991).
  49. A. Grace, Optimization Toolbox for Use withmatlab User’s Guide (The MathWorks, Natick, Mass., 1990).
  50. G. Wyszecki, “Color Appearance,” in Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986).

1994 (3)

F. Bonato, A. L. Gilchrist, “The perception of luminosity on different backgrounds and in different illuminations,” Perception 23, 991–1006 (1994).
[Crossref] [PubMed]

M. Ikeda, S. Fukumura, N. Matsuzawa, T. Ishida, “Influence of surrounding visual information on the recognition threshold of local illumination,” Kogaku 23, 42–49 (1994).

J. M. Speigle, D. H. Brainard, “Fluorescence thresholds depend on the illumination,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, 1656 (1994).

1993 (3)

M. Ikeda, K. Motonaga, N. Matsuzawa, T. Ishida, “Threshold determination for unnatural color appearance with local illumination,” Kogaku 22, 289–298 (1993).

M. D’Zmura, G. Iverson, “Color constancy. I. Basic theory of two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2148–2165 (1993).
[Crossref]

D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Dir. Psychol. Sci. 2, 165–170 (1993).
[Crossref]

1992 (2)

1991 (1)

F. G. Ashby, W. W. Lee, “Predicting similarity and categorization from identification,” J. Exp. Psychol. Gen. 120, 150–172 (1991).
[Crossref] [PubMed]

1990 (1)

D. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vision 5, 5–36 (1990).
[Crossref]

1988 (1)

A. L. Gilchrist, “Lightness contrast and failures of constancy: a common explanation,” Percept. Psychophys. 43, 415–424 (1988).
[Crossref] [PubMed]

1986 (2)

1985 (1)

L. T. Maloney, B. Wandell, “A computational model of color constancy,” Invest. Ophthalmol. Vis. Suppl. 26, 206 (1985).

1983 (1)

A. L. Gilchrist, S. Delman, A. Jacobsen, “The classification and integration of edges as critical to the perception of reflectance and illumination,” Percept. Psychophys. 33, 425–436 (1983).
[Crossref] [PubMed]

1980 (2)

M. R. Pointer, “The gamut of real surface colours,” Color Res. Appl. 5, 145–155 (1980).
[Crossref]

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[Crossref]

1976 (1)

S. Ullman, “On visual detection of light sources,” Biol. Cybern. 21, 205–212 (1976).
[Crossref] [PubMed]

1975 (1)

V. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[Crossref] [PubMed]

1969 (1)

1968 (1)

1967 (1)

1964 (3)

1959 (1)

1943 (1)

1935 (1)

1930 (1)

G. Kreezer, “Luminous appearances,” J. Gen. Psychol. 4, 247–281 (1930).
[Crossref]

1928 (1)

S. Rosch, “Die Kennzeichnung der Farben,” Phys. Z. 29, 83–91 (1928), as discussed in Ref. 50 below.

1924 (1)

K. Buhler, “Gegenbemerkungen,” Psychol. Forsch. 5, 182–188 (1924), as discussed in Ref. 3.
[Crossref]

1920 (1)

E. Schrodinger, “Theorie der pigmente von grosster Leuchtkraft,” Ann. Phys. 62, 603–622 (1920), as discussed in Ref. 50 below.
[Crossref]

Ashby, F. G.

F. G. Ashby, W. W. Lee, “Predicting similarity and categorization from identification,” J. Exp. Psychol. Gen. 120, 150–172 (1991).
[Crossref] [PubMed]

Bonato, F.

F. Bonato, A. L. Gilchrist, “The perception of luminosity on different backgrounds and in different illuminations,” Perception 23, 991–1006 (1994).
[Crossref] [PubMed]

Brainard, D. H.

J. M. Speigle, D. H. Brainard, “Fluorescence thresholds depend on the illumination,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, 1656 (1994).

D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Dir. Psychol. Sci. 2, 165–170 (1993).
[Crossref]

D. H. Brainard, B. A. Wandell, “Asymmetric color-matching: how color appearance depends on the illuminant,” J. Opt. Soc. Am. A 9, 1433–1448 (1992).
[Crossref] [PubMed]

D. H. Brainard, W. T. Freeman, “Bayesian method for recovering surface and illuminant properties from photoreceptor responses,” in Human Vision, Visual Processing, and Digital Display V, B. E. Rogowitz, J. P. Allebach, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2179, 364–376 (1994).
[Crossref]

D. H. Brainard, “Colorimetry,” in Handbook of Optics: Vol. 1. Fundamentals, Techniques, and Design, M. Bass, ed. (McGraw-Hill, New York, 1995).

W. T. Freeman, D. H. Brainard, “Bayesian decision theory, the local mass estimate, and color constancy,” in Proceedings of the 5th International Conference on Computer Vision (IEEE, Cambridge, Mass., 1995), pp. 210–217.

Buchsbaum, G.

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[Crossref]

Buhler, K.

K. Buhler, “Gegenbemerkungen,” Psychol. Forsch. 5, 182–188 (1924), as discussed in Ref. 3.
[Crossref]

Chichilnisky, E.-J.

D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Dir. Psychol. Sci. 2, 165–170 (1993).
[Crossref]

Cohen, J.

J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).

D’Zmura, M.

M. D’Zmura, G. Iverson, “Color constancy. I. Basic theory of two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2148–2165 (1993).
[Crossref]

M. D’Zmura, G. Iverson, B. Singer, “Probabilistic color constancy,” in Geometric Representations of Perceptual Phenomena: Papers in Honor of Tarow Indow’s 70th Birthday, R. D. Luce, M. D’Zmura, D. Hoffman, G. Iverson, A. K. Romney, eds., (Erlbaum, Hillsdale, N.J., 1995).

Delman, S.

A. L. Gilchrist, S. Delman, A. Jacobsen, “The classification and integration of edges as critical to the perception of reflectance and illumination,” Percept. Psychophys. 33, 425–436 (1983).
[Crossref] [PubMed]

DeMarco, P.

Evans, R. M.

Finlayson, G. D.

G. D. Finlayson, “Color constancy in diagonal chromaticity space,” in Proceedings of the 5th International Conference on Computer Vision (IEEE, Cambridge, Mass., 1995), pp. 218–223.

Forsyth, D.

D. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vision 5, 5–36 (1990).
[Crossref]

Freeman, W. T.

D. H. Brainard, W. T. Freeman, “Bayesian method for recovering surface and illuminant properties from photoreceptor responses,” in Human Vision, Visual Processing, and Digital Display V, B. E. Rogowitz, J. P. Allebach, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2179, 364–376 (1994).
[Crossref]

W. T. Freeman, D. H. Brainard, “Bayesian decision theory, the local mass estimate, and color constancy,” in Proceedings of the 5th International Conference on Computer Vision (IEEE, Cambridge, Mass., 1995), pp. 210–217.

Fukumura, S.

M. Ikeda, S. Fukumura, N. Matsuzawa, T. Ishida, “Influence of surrounding visual information on the recognition threshold of local illumination,” Kogaku 23, 42–49 (1994).

Gibson, K. S.

Gilchrist, A. L.

F. Bonato, A. L. Gilchrist, “The perception of luminosity on different backgrounds and in different illuminations,” Perception 23, 991–1006 (1994).
[Crossref] [PubMed]

A. L. Gilchrist, “Lightness contrast and failures of constancy: a common explanation,” Percept. Psychophys. 43, 415–424 (1988).
[Crossref] [PubMed]

A. L. Gilchrist, S. Delman, A. Jacobsen, “The classification and integration of edges as critical to the perception of reflectance and illumination,” Percept. Psychophys. 33, 425–436 (1983).
[Crossref] [PubMed]

Grace, A.

A. Grace, Optimization Toolbox for Use withmatlab User’s Guide (The MathWorks, Natick, Mass., 1990).

Hering, E.

E. Hering, “Der Raumsinn und die Bewegungen des Auges,” in Handbuch der Physiologie, B.L. Hermann, ed. (Vogel, Leipzig, 1879), Vol. 3, Part 1, as discussed in Ref. 3 above.

Ikeda, M.

M. Ikeda, S. Fukumura, N. Matsuzawa, T. Ishida, “Influence of surrounding visual information on the recognition threshold of local illumination,” Kogaku 23, 42–49 (1994).

M. Ikeda, K. Motonaga, N. Matsuzawa, T. Ishida, “Threshold determination for unnatural color appearance with local illumination,” Kogaku 22, 289–298 (1993).

Ishida, T.

M. Ikeda, S. Fukumura, N. Matsuzawa, T. Ishida, “Influence of surrounding visual information on the recognition threshold of local illumination,” Kogaku 23, 42–49 (1994).

M. Ikeda, K. Motonaga, N. Matsuzawa, T. Ishida, “Threshold determination for unnatural color appearance with local illumination,” Kogaku 22, 289–298 (1993).

Iverson, G.

M. D’Zmura, G. Iverson, “Color constancy. I. Basic theory of two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2148–2165 (1993).
[Crossref]

M. D’Zmura, G. Iverson, B. Singer, “Probabilistic color constancy,” in Geometric Representations of Perceptual Phenomena: Papers in Honor of Tarow Indow’s 70th Birthday, R. D. Luce, M. D’Zmura, D. Hoffman, G. Iverson, A. K. Romney, eds., (Erlbaum, Hillsdale, N.J., 1995).

Jacobsen, A.

A. L. Gilchrist, S. Delman, A. Jacobsen, “The classification and integration of edges as critical to the perception of reflectance and illumination,” Percept. Psychophys. 33, 425–436 (1983).
[Crossref] [PubMed]

Judd, D.

D. Judd, G. Wyszecki, Color in Business, Science, and Industry (Wiley, New York, 1975).

Judd, D. B.

Kelly, K. L.

Kreezer, G.

G. Kreezer, “Luminous appearances,” J. Gen. Psychol. 4, 247–281 (1930).
[Crossref]

Lee, W. W.

F. G. Ashby, W. W. Lee, “Predicting similarity and categorization from identification,” J. Exp. Psychol. Gen. 120, 150–172 (1991).
[Crossref] [PubMed]

Little, J.

J. Little, C. Moler, matlab User’s Guide (The Math-Works, Natick, Mass., 1991).

MacAdam, D. L.

Maloney, L. T.

L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. A 3, 1673–1683 (1986).
[Crossref] [PubMed]

L. T. Maloney, B. Wandell, “A computational model of color constancy,” Invest. Ophthalmol. Vis. Suppl. 26, 206 (1985).

Marr, D.

D. Marr, Vision, (Freeman, San Francisco, 1982).

Matsuzawa, N.

M. Ikeda, S. Fukumura, N. Matsuzawa, T. Ishida, “Influence of surrounding visual information on the recognition threshold of local illumination,” Kogaku 23, 42–49 (1994).

M. Ikeda, K. Motonaga, N. Matsuzawa, T. Ishida, “Threshold determination for unnatural color appearance with local illumination,” Kogaku 22, 289–298 (1993).

Moler, C.

J. Little, C. Moler, matlab User’s Guide (The Math-Works, Natick, Mass., 1991).

Motonaga, K.

M. Ikeda, K. Motonaga, N. Matsuzawa, T. Ishida, “Threshold determination for unnatural color appearance with local illumination,” Kogaku 22, 289–298 (1993).

Nickerson, D.

K. L. Kelly, K. S. Gibson, D. Nickerson, “Tristimulus specification of the Munsell Book of Color from spectrophotometric measurements,” J. Opt. Soc. Am. 33, 355–376 (1943).
[Crossref]

D. Nickerson, “Spectrophotometric data for a collection of Munsell samples” (U.S. Department of Agriculture, Washington, D.C., 1957; available from Munsell Color Company, Baltimore, Md.).

Pointer, M. R.

M. R. Pointer, “The gamut of real surface colours,” Color Res. Appl. 5, 145–155 (1980).
[Crossref]

Pokorny, J.

P. DeMarco, J. Pokorny, V. C. Smith, “Full-spectrum cone sensitivity functions for X-chromosome-linked anomalous trichromats,” J. Opt. Soc. Am. A 9, 1465–1476 (1992).
[Crossref] [PubMed]

V. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[Crossref] [PubMed]

Richter, M.

M. Richter, K. Witt, “The story of the DIN color system,” Color Res. Appl. 11, 138–145 (1986).
[Crossref]

Rosch, S.

S. Rosch, “Die Kennzeichnung der Farben,” Phys. Z. 29, 83–91 (1928), as discussed in Ref. 50 below.

Schrodinger, E.

E. Schrodinger, “Theorie der pigmente von grosster Leuchtkraft,” Ann. Phys. 62, 603–622 (1920), as discussed in Ref. 50 below.
[Crossref]

Shepard, R. N.

R. N. Shepard, “The perceptual organization of colors: an adaptation to regularities of the terrestrial world?” in The Adapted Mind: Evolutionary Psychology and the Generation of Culture, J. H. Barkow, L. Cosmides, J. Tooby, eds. (Oxford U. Press, New York, 1992).

Singer, B.

M. D’Zmura, G. Iverson, B. Singer, “Probabilistic color constancy,” in Geometric Representations of Perceptual Phenomena: Papers in Honor of Tarow Indow’s 70th Birthday, R. D. Luce, M. D’Zmura, D. Hoffman, G. Iverson, A. K. Romney, eds., (Erlbaum, Hillsdale, N.J., 1995).

Smith, V.

V. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[Crossref] [PubMed]

Smith, V. C.

Speigle, J. M.

J. M. Speigle, D. H. Brainard, “Fluorescence thresholds depend on the illumination,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, 1656 (1994).

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science—Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).

Swenholt, B. K.

Ullman, S.

S. Ullman, “On visual detection of light sources,” Biol. Cybern. 21, 205–212 (1976).
[Crossref] [PubMed]

Wandell, B.

L. T. Maloney, B. Wandell, “A computational model of color constancy,” Invest. Ophthalmol. Vis. Suppl. 26, 206 (1985).

Wandell, B. A.

D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Dir. Psychol. Sci. 2, 165–170 (1993).
[Crossref]

D. H. Brainard, B. A. Wandell, “Asymmetric color-matching: how color appearance depends on the illuminant,” J. Opt. Soc. Am. A 9, 1433–1448 (1992).
[Crossref] [PubMed]

Witt, K.

M. Richter, K. Witt, “The story of the DIN color system,” Color Res. Appl. 11, 138–145 (1986).
[Crossref]

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science—Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).

G. Wyszecki, “Color Appearance,” in Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986).

D. Judd, G. Wyszecki, Color in Business, Science, and Industry (Wiley, New York, 1975).

Wyszecki, G. W.

Ann. Phys. (1)

E. Schrodinger, “Theorie der pigmente von grosster Leuchtkraft,” Ann. Phys. 62, 603–622 (1920), as discussed in Ref. 50 below.
[Crossref]

Biol. Cybern. (1)

S. Ullman, “On visual detection of light sources,” Biol. Cybern. 21, 205–212 (1976).
[Crossref] [PubMed]

Color Res. Appl. (2)

M. Richter, K. Witt, “The story of the DIN color system,” Color Res. Appl. 11, 138–145 (1986).
[Crossref]

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M. Ikeda, S. Fukumura, N. Matsuzawa, T. Ishida, “Influence of surrounding visual information on the recognition threshold of local illumination,” Kogaku 23, 42–49 (1994).

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Perception (1)

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[Crossref] [PubMed]

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Other (18)

D. Nickerson, “Spectrophotometric data for a collection of Munsell samples” (U.S. Department of Agriculture, Washington, D.C., 1957; available from Munsell Color Company, Baltimore, Md.).

The other combinations of linear models we tried were (1) the CIE three-dimensional daylight model together with a three-dimensional linear model for the Munsell papers, (2) the CIE three-dimensional daylight model together with a six-dimensional linear model for the Munsell papers, and (3) a two-dimensional linear model for illuminants obtained from a principal-components analysis of our experimental illuminants together with the four-dimensional linear model for Munsell papers. These choices did not provide a better fit than the combination we used. We evaluated only choice (2) on a subset of our data, because it was computationally expensive to compute the model fits for a six-dimensional-surface linear model.

G. D. Finlayson, “Color constancy in diagonal chromaticity space,” in Proceedings of the 5th International Conference on Computer Vision (IEEE, Cambridge, Mass., 1995), pp. 218–223.

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D. H. Brainard, W. T. Freeman, “Bayesian method for recovering surface and illuminant properties from photoreceptor responses,” in Human Vision, Visual Processing, and Digital Display V, B. E. Rogowitz, J. P. Allebach, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2179, 364–376 (1994).
[Crossref]

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Our usage of the term luminosity threshold follows that of Kreezer3 and of Bonato and Gilchrist.10 The term luminosity is used in the literature both to describe physical properties of light14 and to describe perceptual experience.15 Ideal terminology would distinguish these two uses, but at present we feel that less confusion will be generated by our use of luminosity threshold than if we attempt to define new terminology.

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Figures (13)

Fig. 1
Fig. 1

(a) Top view of the experimental room. The ambient illumination was provided by eight theater stage lamps arranged in four pairs, B and Y. The observer viewed a test patch located on the far wall of the room, which was spot illuminated by a projection colorimeter. This apparatus provided experimental control of the luminance and chromaticity of the light reaching the observer from the test patch. (b) Schematic representation of the observer’s view of the far wall of the experimental room. The far wall contained an array of 8.5-in.×11-in. matte Munsell papers; each panel here is labeled with its Munsell designation. The test patch, Munsell designation N 3/, was located in the middle row and right-hand column of the array and was placed on a dark-gray piece of matte cardboard. Other objects in the room were visible to the observer, including a brown metal bookcase and an off-white table.

Fig. 2
Fig. 2

Stimulus chromaticities for illuminant condition B2, observer DHB. Open symbols, desired chromaticities; filled symbols, chromaticities measured during the postcalibration procedure. Spectrum locus, 380–700 nm, sampled at 10-nm intervals. The density for other observers and conditions was comparable.

Fig. 3
Fig. 3

Contour plots of the luminosity threshold surfaces for observers JMS and DHB as a function of x and y chromaticity, each for a single observer/illuminant condition. Each contour is labeled with its luminance in candelas per square meter. The pairs of plots for each observer illustrate that the shape of the luminosity threshold surface depends on the illumination.

Fig. 4
Fig. 4

Slices through the luminosity threshold surfaces for observer DHB: (a) illuminant Y2 and y chromaticity 0.42; (b) illuminant B2 and y chromaticity 0.42. The solid curves show a model fit, which is discussed below.The thresholds are given in units of cd/m2. The error bars indicate the standard error of the mean computed across sessions.

Fig. 5
Fig. 5

Slices through the luminosity threshold surfaces for observer JMS: illuminants Y1 (open circles) and B1 (open triangles) at a y chromaticity of 0.42. The solid curves show a model fit, which is discussed below. The thresholds are given in candelas per square meter. The error bars indicate the standard error of the mean computed across sessions.

Fig. 6
Fig. 6

Each panel shows a histogram of the luminance error in candelas per square meter between the luminosity thresholds for individual sessions and the corresponding mean threshold. The errors for each observer are accumulated across both sessions and conditions. The RMSE’s for observers JMS, DHB, and KI were 0.26, 2.20, and 1.42 cd/m2, respectively.

Fig. 7
Fig. 7

Individual session variability for observer DHB. The two panels show slices through the threshold surfaces for the same conditions but collected in different sessions. We obtained the slice data by applying a two-dimensional linear-interpolation algorithm to the raw data and then slicing the interpolation, allowing us to compute slices for arbitrary values of y chromaticity. The thresholds are in candelas per square meter. (a) Illuminant Y2, y chromaticity 0.41; (b) illuminant condition B1, y chromaticity 0.31. The variability across sessions is primarily one of overall luminance; across sessions the relative shape of the slices is approximately constant.

Fig. 8
Fig. 8

Each panel shows a histogram of the luminance error in candelas per square meter between the luminosity thresholds for individual sessions and the mean thresholds after criterion shifts have been taken into account. To model criterion shifts, we found for each observer/illuminant condition the single scale factor that shifted the mean (across session) data for all test patch chromaticities as close as possible to the individual session data. The errors for each observer are accumulated across both sessions and conditions. The RMSE’s for observers JMS, DHB, and KI were 0.21, 1.03, and 0.78 cd/m2, respectively. For observers DHB and KI the errors after scaling were substantially reduced from the raw errors: 2.20 and 1.42 cd/m2, respectively. Observer JMS showed less criterion shift across sessions.

Fig. 9
Fig. 9

Physics of reflective image formation. The light reaching the observer’s eye at each location, Cj(λ), is the wavelength-by-wavelength product of the illuminant spectral power distribution, E(λ), and the surface reflectance function at that location, Sj(λ). We assume that the visual system attempts to parse the color signal into an estimate of illuminant spectral power distribution and surface-reflectance functions, as shown at the lower right.

Fig. 10
Fig. 10

Equivalent-illuminant chromaticities. Each panel compares the chromaticities of the equivalent illuminants to the physical illuminant for one observer. Open symbols, equivalent-illuminant chromaticities; filled symbols, corresponding physical illuminants. Top panels, chromaticities for conditions Y1, B1, and BY; bottom panels, chromaticities for conditions Y2 and B2.

Fig. 11
Fig. 11

Each panel shows a histogram of the luminance error between the luminosity thresholds for individual sessions and the equivalent-illuminant model predictions after criterion shifts have been taken into account. The errors for each observer are accumulated across both sessions and conditions. The RMSE’s for observers JMS, DHB, and KI were 0.49, 1.70, and 1.17 cd/m2, respectively. For observer KI there were some test patch chromaticities for which he was able to set a luminosity threshold but for which the model predicted that the threshold should be zero. This indicates that the test patch chromaticity was outside the gamut of surfaces realizable within our linear model. We did not include these points in the histogram. Table 6 gives the number of points excluded for each modeling condition. Appendix A contains further discussion of this issue.

Fig. 12
Fig. 12

RMSE’s in candelas per square meter for various models. The data-precision model allowed a parameter for each test patch chromaticity. The corresponding RMSE represents the precision of the data after criterion shifts have been taken into account. All other models were fitted to the mean threshold data for each observer/condition as described in the text. Criterion shifts were taken into account by allowing a single scale factor for each individual session.

Fig. 13
Fig. 13

RMSE’s for observers JMS, DHB, and KI with and without the linearity constraint. Both the general and the constrained linear models were fitted to the mean threshold surfaces of each condition. For the constrained linear model the fitting procedure required the set of equivalent illuminants to satisfy the illuminant-linearity constraint. The RMSE’s were 0.49, 1.70, and 1.17 cd/m2 without the linearity constraint and 0.53, 1.77, and 1.24 cd/m2 with the constraint for observers JMS, DHB, and KI, respectively.

Tables (6)

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Table 1 Illuminant 1931 CIE x, y Chromaticities and Luminances for the Five Experimental Conditions

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Table 2 Luminosity Threshold Data for Subject JMSa

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Table 3 Luminosity Threshold Data for Subject DHB

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Table 4 Luminosity Threshold Data for Subject KI

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Table 5 Scale Factors Providing the Best Fit between Mean Thresholds and Thresholds Measured in Each Sessiona

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Table 6 Summary of Model Fitsa

Equations (8)

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

E ( λ ) = a E 1 ( λ ) + b E 2 ( λ )
E ^ ( λ ) = a E ^ 1 ( λ ) + b E ^ 2 ( λ )
s = B s w s ,
e = B e w e ,
r = T diag ( B e w e ) B s w s ,
Y = T y diag ( B e w e ) B s w s .
null ( r 0 ) T diag ( B e w e ) B s w s = 0 .
B s w s 0 ,             B s w s 1.

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