Abstract

It is generally accepted that hues can be arranged so as to make a circle. The circular representation of hue has been supported by multidimensional scaling, which allows for the representation of a set of colored papers as a configuration in a Euclidean space where the distances between the papers correspond to the perceptual dissimilarities between them. In particular, when papers of various hues are evenly illuminated, they are arranged in a one-dimensional circular configuration. However, under variegated illumination we show that the same papers in fact make a two-dimensional configuration that resembles a torus.

© 2010 Optical Society of America

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  1. B. J. Craven and D. H. Foster, “An operational approach to colour constancy,” Vision Res. 32, 1359–1366 (1992).
    [CrossRef] [PubMed]
  2. D. H. Foster, S. M. Nascimento, K. Amano, L. Arend, K. J. Linnell, J. L. Nieves, S. Plet, and J. S. Foster, “Parallel detection of violations of color constancy,” Proc. Natl. Acad. Sci. U.S.A. 98, 8151–8156 (2001).
    [CrossRef] [PubMed]
  3. F. A. Kingdom, “Perceiving light versus material,” Vision Res. 48, 2090–2105 (2008).
    [CrossRef] [PubMed]
  4. E. Mach, The Analysis of Sensations (Dover, 1959) (translated from the 5th German edition, 1885).
  5. A. D. Logvinenko and G. Y. Menshikova, “Trade-off between achromatic colour and perceived illumination as revealed by the use of pseudoscopic inversion of apparent depth,” Perception 23, 1007–1023 (1994).
    [CrossRef] [PubMed]
  6. A. D. Logvinenko, “Pseudoscopic colour illusions,” in The 11th Congress of the International Colour Association (Colour Society of Australia, 2009).
  7. R. G. Kuehni and A. Schwarz, Color Ordered (Oxford University Press, 2008).
  8. W. S. Torgerson, Theory and Methods of Scaling (Wiley, 1958).
  9. R. N. Shepard, “The analysis of proximities: Multidimensional scaling with an unknown distance function. II,” Psychometrika 27, 219–246 (1962).
    [CrossRef]
  10. T. F. Cox and M. A. A. Cox, Multidimensional Scaling (Chapman & Hall/CRC, 2001).
  11. G. Ekman, “Dimensions of color vision,” J. Psychol. 38, 467–474 (1954).
    [CrossRef]
  12. R. M. Boynton and H. G. Wagner, “Color differences assessed by the minimally distinct border methods,” in Color Metrics (AIC/Holland c/o Institute for Perception TNO, 1972).
  13. T. Indow, “Multidimensional studies of the Munsell color solid,” Psychol. Rev. 95, 456–470 (1988).
    [CrossRef] [PubMed]
  14. T. Indow and K. Matsushima, “Local multidimensional mapping of Munsell color space,” Acta Chromatica 2, 16–24 (1969).
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. J. M. Bosten, J. D. Robinson, G. Jordan, and J. D. Mollon, “Multidimensional scaling reveals a color dimension unique to ‘color-deficient’ observers,” Curr. Biol. 15, R950–R952 (2005).
    [CrossRef] [PubMed]
  18. A. D. Logvinenko and L. T. Maloney, “The proximity structure of achromatic surface colors and the impossibility of asymmetric lightness matching,” Percept. Psychophys. 68, 76–83 (2006).
    [CrossRef] [PubMed]
  19. R. Tokunaga, A. D. Logvinenko, and L. T. Maloney, “Dissimilarity of yellow-blue surfaces under neutral light sources differing in intensity: separate contributions of light intensity and chroma,” Visual Neurosci. 25, 395–398 (2008).
    [CrossRef]
  20. Munsell Book of Color (Macbeth Division of Kollmorgen, 1976).
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  22. T. Indow, “Applications of multidimensional scaling in perception,” in Psychophysical Judgement and Measurement, Vol. 2 of Handbook of Perception, E.C.Carterette and M.P.Friedman, eds. (Academic Press, 1974), pp. 493–525.
  23. R. N. Shepard and L. A. Cooper, “Representation of colors in the blind, color-blind, and normally sighted,” Psychol. Sci. 3, 97–104 (1992).
    [CrossRef]
  24. T. Indow, “Global color metric and color-appearance systems,” Color Res. Appl. 5, 5–12 (1980).
    [CrossRef]
  25. R. Tokunaga and A. D. Logvinenko, “Material and lighting dimensions of object colour,” Vision Res. 50, 1740–1747 (2010).
    [CrossRef] [PubMed]
  26. R. Tokunaga and A. D. Logvinenko, “Material and lighting hues of object colour,” Ophthalmic Physiol. Opt. 30, 611–617 (2010).
    [CrossRef] [PubMed]
  27. When evaluating material (and lighting) hue contour length we used dissimilarity values obtained in the experiment rather than the distances between the points in Fig. .
  28. D. Katz, The World of Colour (Kegan Paul, Trench, Trubner, 1935).
  29. P. K. Kaiser and R. M. Boynton, Human Color Vision (The Optical Society of America, 1996).
  30. A. Hurlbert, “Colour constancy,” Curr. Biol. 17, R906–R907 (2007).
    [CrossRef] [PubMed]
  31. D. H. Foster, “Color appearance,” in The Senses: A Comprehensive Reference, Vol. 2, Vision II, A.I.Basbaum, A.Kaneko, G.M.Shepherd, G.Westheimer, T.D.Albright, R.H.Masland, P.Dallos, D.Oertel, S.Firestein, G.K.Beauchamp, M.C.Bushnell, J.H.Kaas, and E.Gardner, eds. (Academic Press, 2008), pp. 119–132.
    [CrossRef]
  32. D. H. Brainard, W. A. Brunt, and J. M. Speigle, “Color constancy in the nearly natural image. I. Asymmetric matches,” J. Opt. Soc. Am. A 14, 2091–2110 (1997).
    [CrossRef]
  33. D. H. Foster, “Does colour constancy exist?” Trends Cogn. Sci. 7, 439–443 (2003).
    [CrossRef] [PubMed]
  34. D. H. Brainard, “Color constancy,” in The Sage Encyclopedia of Perception, B.Goldstein, ed. (SAGE, 2009), pp. 253–257.
  35. C. van Trigt, “Linear models in color constancy theory,” J. Opt. Soc. Am. A 24, 2684–2691 (2007).
    [CrossRef]
  36. A. D. Logvinenko and R. Tokunaga, “Colour constancy as measured by least dissimilar matching” (submitted to Seeing & Perceiving).
  37. R. Mausfeld, “Colour perception: From Grassmann codes to a dual code for object and illumination colours” in Color Vision: Perspectives from Different Disciplines, W.Backhaus, R.Kliegel, and J.S.Werner, eds. (De Gruyter, 1998), pp. 219–250.
    [CrossRef]
  38. R. Mausfeld, “‘Colour’ as part of the format of different perceptual primitives: the dual coding of colour,” in Colour Perception: Mind and the Physical World, R.Mausfeld and D.Heyer, eds. (Oxford University Press, 2003), pp. 381–430.
  39. D. I. MacLeod, “New dimensions in color perception,” Trends Cogn. Sci. 7, 97–99 (2003).
    [CrossRef] [PubMed]
  40. A. D. Logvinenko, “Object-colour space revisited,” in CGIV—5th European Conference on Colour in Graphics, Imaging, and Vision (The Society for Imaging Science and Technology, 2010), CD-ROM, pp. 207–214.

2010

R. Tokunaga and A. D. Logvinenko, “Material and lighting dimensions of object colour,” Vision Res. 50, 1740–1747 (2010).
[CrossRef] [PubMed]

R. Tokunaga and A. D. Logvinenko, “Material and lighting hues of object colour,” Ophthalmic Physiol. Opt. 30, 611–617 (2010).
[CrossRef] [PubMed]

A. D. Logvinenko, “Object-colour space revisited,” in CGIV—5th European Conference on Colour in Graphics, Imaging, and Vision (The Society for Imaging Science and Technology, 2010), CD-ROM, pp. 207–214.

2009

A. D. Logvinenko, “Pseudoscopic colour illusions,” in The 11th Congress of the International Colour Association (Colour Society of Australia, 2009).

D. H. Brainard, “Color constancy,” in The Sage Encyclopedia of Perception, B.Goldstein, ed. (SAGE, 2009), pp. 253–257.

2008

R. G. Kuehni and A. Schwarz, Color Ordered (Oxford University Press, 2008).

F. A. Kingdom, “Perceiving light versus material,” Vision Res. 48, 2090–2105 (2008).
[CrossRef] [PubMed]

D. H. Foster, “Color appearance,” in The Senses: A Comprehensive Reference, Vol. 2, Vision II, A.I.Basbaum, A.Kaneko, G.M.Shepherd, G.Westheimer, T.D.Albright, R.H.Masland, P.Dallos, D.Oertel, S.Firestein, G.K.Beauchamp, M.C.Bushnell, J.H.Kaas, and E.Gardner, eds. (Academic Press, 2008), pp. 119–132.
[CrossRef]

R. Tokunaga, A. D. Logvinenko, and L. T. Maloney, “Dissimilarity of yellow-blue surfaces under neutral light sources differing in intensity: separate contributions of light intensity and chroma,” Visual Neurosci. 25, 395–398 (2008).
[CrossRef]

R. Tokunaga, A. D. Logvinenko, and L. T. Maloney, “Multidimensional scaling of Munsell papers using quadruple comparisons,” in Interim Meeting of the International Colour Association (The Swedish Colour Centre Foundation/Scandinavian Colour Institute AB, 2008), Paper No. 072.

2007

2006

A. D. Logvinenko and L. T. Maloney, “The proximity structure of achromatic surface colors and the impossibility of asymmetric lightness matching,” Percept. Psychophys. 68, 76–83 (2006).
[CrossRef] [PubMed]

2005

J. M. Bosten, J. D. Robinson, G. Jordan, and J. D. Mollon, “Multidimensional scaling reveals a color dimension unique to ‘color-deficient’ observers,” Curr. Biol. 15, R950–R952 (2005).
[CrossRef] [PubMed]

2003

D. H. Foster, “Does colour constancy exist?” Trends Cogn. Sci. 7, 439–443 (2003).
[CrossRef] [PubMed]

R. Mausfeld, “‘Colour’ as part of the format of different perceptual primitives: the dual coding of colour,” in Colour Perception: Mind and the Physical World, R.Mausfeld and D.Heyer, eds. (Oxford University Press, 2003), pp. 381–430.

D. I. MacLeod, “New dimensions in color perception,” Trends Cogn. Sci. 7, 97–99 (2003).
[CrossRef] [PubMed]

2001

T. F. Cox and M. A. A. Cox, Multidimensional Scaling (Chapman & Hall/CRC, 2001).

D. H. Foster, S. M. Nascimento, K. Amano, L. Arend, K. J. Linnell, J. L. Nieves, S. Plet, and J. S. Foster, “Parallel detection of violations of color constancy,” Proc. Natl. Acad. Sci. U.S.A. 98, 8151–8156 (2001).
[CrossRef] [PubMed]

1998

R. Mausfeld, “Colour perception: From Grassmann codes to a dual code for object and illumination colours” in Color Vision: Perspectives from Different Disciplines, W.Backhaus, R.Kliegel, and J.S.Werner, eds. (De Gruyter, 1998), pp. 219–250.
[CrossRef]

1997

1996

P. K. Kaiser and R. M. Boynton, Human Color Vision (The Optical Society of America, 1996).

1994

A. D. Logvinenko and G. Y. Menshikova, “Trade-off between achromatic colour and perceived illumination as revealed by the use of pseudoscopic inversion of apparent depth,” Perception 23, 1007–1023 (1994).
[CrossRef] [PubMed]

1992

B. J. Craven and D. H. Foster, “An operational approach to colour constancy,” Vision Res. 32, 1359–1366 (1992).
[CrossRef] [PubMed]

R. N. Shepard and L. A. Cooper, “Representation of colors in the blind, color-blind, and normally sighted,” Psychol. Sci. 3, 97–104 (1992).
[CrossRef]

1991

G. V. Paramei, Ch. A. Izmailov, and E. N. Sokolov, “Multidimensional scaling of large chromatic differences by normal and color-deficient subjects,” Psychol. Sci. 2, 244–248 (1991).
[CrossRef]

1988

T. Indow, “Multidimensional studies of the Munsell color solid,” Psychol. Rev. 95, 456–470 (1988).
[CrossRef] [PubMed]

1980

T. Indow, “Global color metric and color-appearance systems,” Color Res. Appl. 5, 5–12 (1980).
[CrossRef]

1976

Munsell Book of Color (Macbeth Division of Kollmorgen, 1976).

1974

T. Indow, “Applications of multidimensional scaling in perception,” in Psychophysical Judgement and Measurement, Vol. 2 of Handbook of Perception, E.C.Carterette and M.P.Friedman, eds. (Academic Press, 1974), pp. 493–525.

1972

R. M. Boynton and H. G. Wagner, “Color differences assessed by the minimally distinct border methods,” in Color Metrics (AIC/Holland c/o Institute for Perception TNO, 1972).

1969

T. Indow and K. Matsushima, “Local multidimensional mapping of Munsell color space,” Acta Chromatica 2, 16–24 (1969).

1964

1962

R. N. Shepard, “The analysis of proximities: Multidimensional scaling with an unknown distance function. II,” Psychometrika 27, 219–246 (1962).
[CrossRef]

1959

E. Mach, The Analysis of Sensations (Dover, 1959) (translated from the 5th German edition, 1885).

1958

W. S. Torgerson, Theory and Methods of Scaling (Wiley, 1958).

1954

G. Ekman, “Dimensions of color vision,” J. Psychol. 38, 467–474 (1954).
[CrossRef]

1935

D. Katz, The World of Colour (Kegan Paul, Trench, Trubner, 1935).

Amano, K.

D. H. Foster, S. M. Nascimento, K. Amano, L. Arend, K. J. Linnell, J. L. Nieves, S. Plet, and J. S. Foster, “Parallel detection of violations of color constancy,” Proc. Natl. Acad. Sci. U.S.A. 98, 8151–8156 (2001).
[CrossRef] [PubMed]

Arend, L.

D. H. Foster, S. M. Nascimento, K. Amano, L. Arend, K. J. Linnell, J. L. Nieves, S. Plet, and J. S. Foster, “Parallel detection of violations of color constancy,” Proc. Natl. Acad. Sci. U.S.A. 98, 8151–8156 (2001).
[CrossRef] [PubMed]

Bosten, J. M.

J. M. Bosten, J. D. Robinson, G. Jordan, and J. D. Mollon, “Multidimensional scaling reveals a color dimension unique to ‘color-deficient’ observers,” Curr. Biol. 15, R950–R952 (2005).
[CrossRef] [PubMed]

Boynton, R. M.

P. K. Kaiser and R. M. Boynton, Human Color Vision (The Optical Society of America, 1996).

R. M. Boynton and H. G. Wagner, “Color differences assessed by the minimally distinct border methods,” in Color Metrics (AIC/Holland c/o Institute for Perception TNO, 1972).

Brainard, D. H.

D. H. Brainard, “Color constancy,” in The Sage Encyclopedia of Perception, B.Goldstein, ed. (SAGE, 2009), pp. 253–257.

D. H. Brainard, W. A. Brunt, and J. M. Speigle, “Color constancy in the nearly natural image. I. Asymmetric matches,” J. Opt. Soc. Am. A 14, 2091–2110 (1997).
[CrossRef]

Brunt, W. A.

Cooper, L. A.

R. N. Shepard and L. A. Cooper, “Representation of colors in the blind, color-blind, and normally sighted,” Psychol. Sci. 3, 97–104 (1992).
[CrossRef]

Cox, M. A. A.

T. F. Cox and M. A. A. Cox, Multidimensional Scaling (Chapman & Hall/CRC, 2001).

Cox, T. F.

T. F. Cox and M. A. A. Cox, Multidimensional Scaling (Chapman & Hall/CRC, 2001).

Craven, B. J.

B. J. Craven and D. H. Foster, “An operational approach to colour constancy,” Vision Res. 32, 1359–1366 (1992).
[CrossRef] [PubMed]

Ekman, G.

G. Ekman, “Dimensions of color vision,” J. Psychol. 38, 467–474 (1954).
[CrossRef]

Foster, D. H.

D. H. Foster, “Color appearance,” in The Senses: A Comprehensive Reference, Vol. 2, Vision II, A.I.Basbaum, A.Kaneko, G.M.Shepherd, G.Westheimer, T.D.Albright, R.H.Masland, P.Dallos, D.Oertel, S.Firestein, G.K.Beauchamp, M.C.Bushnell, J.H.Kaas, and E.Gardner, eds. (Academic Press, 2008), pp. 119–132.
[CrossRef]

D. H. Foster, “Does colour constancy exist?” Trends Cogn. Sci. 7, 439–443 (2003).
[CrossRef] [PubMed]

D. H. Foster, S. M. Nascimento, K. Amano, L. Arend, K. J. Linnell, J. L. Nieves, S. Plet, and J. S. Foster, “Parallel detection of violations of color constancy,” Proc. Natl. Acad. Sci. U.S.A. 98, 8151–8156 (2001).
[CrossRef] [PubMed]

B. J. Craven and D. H. Foster, “An operational approach to colour constancy,” Vision Res. 32, 1359–1366 (1992).
[CrossRef] [PubMed]

Foster, J. S.

D. H. Foster, S. M. Nascimento, K. Amano, L. Arend, K. J. Linnell, J. L. Nieves, S. Plet, and J. S. Foster, “Parallel detection of violations of color constancy,” Proc. Natl. Acad. Sci. U.S.A. 98, 8151–8156 (2001).
[CrossRef] [PubMed]

Helm, C. E.

Hurlbert, A.

A. Hurlbert, “Colour constancy,” Curr. Biol. 17, R906–R907 (2007).
[CrossRef] [PubMed]

Indow, T.

T. Indow, “Multidimensional studies of the Munsell color solid,” Psychol. Rev. 95, 456–470 (1988).
[CrossRef] [PubMed]

T. Indow, “Global color metric and color-appearance systems,” Color Res. Appl. 5, 5–12 (1980).
[CrossRef]

T. Indow, “Applications of multidimensional scaling in perception,” in Psychophysical Judgement and Measurement, Vol. 2 of Handbook of Perception, E.C.Carterette and M.P.Friedman, eds. (Academic Press, 1974), pp. 493–525.

T. Indow and K. Matsushima, “Local multidimensional mapping of Munsell color space,” Acta Chromatica 2, 16–24 (1969).

Izmailov, Ch. A.

G. V. Paramei, Ch. A. Izmailov, and E. N. Sokolov, “Multidimensional scaling of large chromatic differences by normal and color-deficient subjects,” Psychol. Sci. 2, 244–248 (1991).
[CrossRef]

Jordan, G.

J. M. Bosten, J. D. Robinson, G. Jordan, and J. D. Mollon, “Multidimensional scaling reveals a color dimension unique to ‘color-deficient’ observers,” Curr. Biol. 15, R950–R952 (2005).
[CrossRef] [PubMed]

Kaiser, P. K.

P. K. Kaiser and R. M. Boynton, Human Color Vision (The Optical Society of America, 1996).

Katz, D.

D. Katz, The World of Colour (Kegan Paul, Trench, Trubner, 1935).

Kingdom, F. A.

F. A. Kingdom, “Perceiving light versus material,” Vision Res. 48, 2090–2105 (2008).
[CrossRef] [PubMed]

Kuehni, R. G.

R. G. Kuehni and A. Schwarz, Color Ordered (Oxford University Press, 2008).

Linnell, K. J.

D. H. Foster, S. M. Nascimento, K. Amano, L. Arend, K. J. Linnell, J. L. Nieves, S. Plet, and J. S. Foster, “Parallel detection of violations of color constancy,” Proc. Natl. Acad. Sci. U.S.A. 98, 8151–8156 (2001).
[CrossRef] [PubMed]

Logvinenko, A. D.

A. D. Logvinenko, “Object-colour space revisited,” in CGIV—5th European Conference on Colour in Graphics, Imaging, and Vision (The Society for Imaging Science and Technology, 2010), CD-ROM, pp. 207–214.

R. Tokunaga and A. D. Logvinenko, “Material and lighting dimensions of object colour,” Vision Res. 50, 1740–1747 (2010).
[CrossRef] [PubMed]

R. Tokunaga and A. D. Logvinenko, “Material and lighting hues of object colour,” Ophthalmic Physiol. Opt. 30, 611–617 (2010).
[CrossRef] [PubMed]

A. D. Logvinenko, “Pseudoscopic colour illusions,” in The 11th Congress of the International Colour Association (Colour Society of Australia, 2009).

R. Tokunaga, A. D. Logvinenko, and L. T. Maloney, “Dissimilarity of yellow-blue surfaces under neutral light sources differing in intensity: separate contributions of light intensity and chroma,” Visual Neurosci. 25, 395–398 (2008).
[CrossRef]

R. Tokunaga, A. D. Logvinenko, and L. T. Maloney, “Multidimensional scaling of Munsell papers using quadruple comparisons,” in Interim Meeting of the International Colour Association (The Swedish Colour Centre Foundation/Scandinavian Colour Institute AB, 2008), Paper No. 072.

A. D. Logvinenko and L. T. Maloney, “The proximity structure of achromatic surface colors and the impossibility of asymmetric lightness matching,” Percept. Psychophys. 68, 76–83 (2006).
[CrossRef] [PubMed]

A. D. Logvinenko and G. Y. Menshikova, “Trade-off between achromatic colour and perceived illumination as revealed by the use of pseudoscopic inversion of apparent depth,” Perception 23, 1007–1023 (1994).
[CrossRef] [PubMed]

A. D. Logvinenko and R. Tokunaga, “Colour constancy as measured by least dissimilar matching” (submitted to Seeing & Perceiving).

Mach, E.

E. Mach, The Analysis of Sensations (Dover, 1959) (translated from the 5th German edition, 1885).

MacLeod, D. I.

D. I. MacLeod, “New dimensions in color perception,” Trends Cogn. Sci. 7, 97–99 (2003).
[CrossRef] [PubMed]

Maloney, L. T.

R. Tokunaga, A. D. Logvinenko, and L. T. Maloney, “Multidimensional scaling of Munsell papers using quadruple comparisons,” in Interim Meeting of the International Colour Association (The Swedish Colour Centre Foundation/Scandinavian Colour Institute AB, 2008), Paper No. 072.

R. Tokunaga, A. D. Logvinenko, and L. T. Maloney, “Dissimilarity of yellow-blue surfaces under neutral light sources differing in intensity: separate contributions of light intensity and chroma,” Visual Neurosci. 25, 395–398 (2008).
[CrossRef]

A. D. Logvinenko and L. T. Maloney, “The proximity structure of achromatic surface colors and the impossibility of asymmetric lightness matching,” Percept. Psychophys. 68, 76–83 (2006).
[CrossRef] [PubMed]

Matsushima, K.

T. Indow and K. Matsushima, “Local multidimensional mapping of Munsell color space,” Acta Chromatica 2, 16–24 (1969).

Mausfeld, R.

R. Mausfeld, “‘Colour’ as part of the format of different perceptual primitives: the dual coding of colour,” in Colour Perception: Mind and the Physical World, R.Mausfeld and D.Heyer, eds. (Oxford University Press, 2003), pp. 381–430.

R. Mausfeld, “Colour perception: From Grassmann codes to a dual code for object and illumination colours” in Color Vision: Perspectives from Different Disciplines, W.Backhaus, R.Kliegel, and J.S.Werner, eds. (De Gruyter, 1998), pp. 219–250.
[CrossRef]

Menshikova, G. Y.

A. D. Logvinenko and G. Y. Menshikova, “Trade-off between achromatic colour and perceived illumination as revealed by the use of pseudoscopic inversion of apparent depth,” Perception 23, 1007–1023 (1994).
[CrossRef] [PubMed]

Mollon, J. D.

J. M. Bosten, J. D. Robinson, G. Jordan, and J. D. Mollon, “Multidimensional scaling reveals a color dimension unique to ‘color-deficient’ observers,” Curr. Biol. 15, R950–R952 (2005).
[CrossRef] [PubMed]

Nascimento, S. M.

D. H. Foster, S. M. Nascimento, K. Amano, L. Arend, K. J. Linnell, J. L. Nieves, S. Plet, and J. S. Foster, “Parallel detection of violations of color constancy,” Proc. Natl. Acad. Sci. U.S.A. 98, 8151–8156 (2001).
[CrossRef] [PubMed]

Nieves, J. L.

D. H. Foster, S. M. Nascimento, K. Amano, L. Arend, K. J. Linnell, J. L. Nieves, S. Plet, and J. S. Foster, “Parallel detection of violations of color constancy,” Proc. Natl. Acad. Sci. U.S.A. 98, 8151–8156 (2001).
[CrossRef] [PubMed]

Paramei, G. V.

G. V. Paramei, Ch. A. Izmailov, and E. N. Sokolov, “Multidimensional scaling of large chromatic differences by normal and color-deficient subjects,” Psychol. Sci. 2, 244–248 (1991).
[CrossRef]

Plet, S.

D. H. Foster, S. M. Nascimento, K. Amano, L. Arend, K. J. Linnell, J. L. Nieves, S. Plet, and J. S. Foster, “Parallel detection of violations of color constancy,” Proc. Natl. Acad. Sci. U.S.A. 98, 8151–8156 (2001).
[CrossRef] [PubMed]

Robinson, J. D.

J. M. Bosten, J. D. Robinson, G. Jordan, and J. D. Mollon, “Multidimensional scaling reveals a color dimension unique to ‘color-deficient’ observers,” Curr. Biol. 15, R950–R952 (2005).
[CrossRef] [PubMed]

Schwarz, A.

R. G. Kuehni and A. Schwarz, Color Ordered (Oxford University Press, 2008).

Shepard, R. N.

R. N. Shepard and L. A. Cooper, “Representation of colors in the blind, color-blind, and normally sighted,” Psychol. Sci. 3, 97–104 (1992).
[CrossRef]

R. N. Shepard, “The analysis of proximities: Multidimensional scaling with an unknown distance function. II,” Psychometrika 27, 219–246 (1962).
[CrossRef]

Sokolov, E. N.

G. V. Paramei, Ch. A. Izmailov, and E. N. Sokolov, “Multidimensional scaling of large chromatic differences by normal and color-deficient subjects,” Psychol. Sci. 2, 244–248 (1991).
[CrossRef]

Speigle, J. M.

Tokunaga, R.

R. Tokunaga and A. D. Logvinenko, “Material and lighting dimensions of object colour,” Vision Res. 50, 1740–1747 (2010).
[CrossRef] [PubMed]

R. Tokunaga and A. D. Logvinenko, “Material and lighting hues of object colour,” Ophthalmic Physiol. Opt. 30, 611–617 (2010).
[CrossRef] [PubMed]

R. Tokunaga, A. D. Logvinenko, and L. T. Maloney, “Dissimilarity of yellow-blue surfaces under neutral light sources differing in intensity: separate contributions of light intensity and chroma,” Visual Neurosci. 25, 395–398 (2008).
[CrossRef]

R. Tokunaga, A. D. Logvinenko, and L. T. Maloney, “Multidimensional scaling of Munsell papers using quadruple comparisons,” in Interim Meeting of the International Colour Association (The Swedish Colour Centre Foundation/Scandinavian Colour Institute AB, 2008), Paper No. 072.

A. D. Logvinenko and R. Tokunaga, “Colour constancy as measured by least dissimilar matching” (submitted to Seeing & Perceiving).

Torgerson, W. S.

W. S. Torgerson, Theory and Methods of Scaling (Wiley, 1958).

van Trigt, C.

Wagner, H. G.

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Figures (6)

Fig. 1
Fig. 1

Experimental setup and stimulus display. A digital projector (DP) provided the independent illumination of the six fields of the stimulus display (SD), these being covered by white paper with a random-dot design. Seven Munsell papers were presented in the fields 1 and 2. Fields 3 and 4 were used to display the pair of Munsell papers that represented standard dissimilarity. Fields 5 and 6 were illuminated so as to counter-balance the overall illumination. A computer (PC) randomly turned on a pair of light-emitting diodes (one in field 1, and one in field 2), which indicated the pair of Munsell papers to be evaluated. An observer entered the dissimilarity estimate by pressing a button on the response box (RB).

Fig. 2
Fig. 2

Chromaticity of the lights reflected from the Munsell papers under various illuminations presented in the CIE 1976 uniform chromaticity diagram. The shape and face color of the markers specify the color of the paper. [Circle—5R4/14, triangle (up)—5YR7/12, triangle (pointing right)—5Y8/12, square—5G6/10, pentagram—10BG5/8, triangle (pointing down)—5PB5/12, diamond—10P5/12.] The edge color of the markers specifies the color of the illumination. (a) The Munsell papers lit by the same light are connected with a line whose color denotes the color of the illumination. (b) The points representing the same Munsell paper under five different illuminants are connected by a line whose color resembles the color of the paper under daylight.

Fig. 3
Fig. 3

MDS output configurations (material-hue contours) obtained in the preliminary experiment. The quadruple-comparison-based configuration is represented by the jointed-up colored symbols. The transformed rating-based configuration is marked by crosses. Notation of colored symbols is the same as in Fig. 2.

Fig. 4
Fig. 4

(a), (b) Two views of the output configuration produced by the non-metric MDS algorithm obtained in the main experiment. Each point represents a Munsell paper illuminated by a particular light. Notation is the same as in Fig. 2.

Fig. 5
Fig. 5

Dissimilarities versus chromaticity differences. In each plate the vertical axis is the dissimilarity between a pair of Munsell papers illuminated separately by one of the five lights: yellow (Y), blue (B), red (R), green (G), and purple (P); the horizontal axis is the chromaticity difference between the reflected lights evaluated in terms of the CIE 1976 uniform chromaticity diagram. Dissimilarities (respectively, chromaticity differences) of pairs were normalized by the dissimilarity (respectively, the chromaticity difference) of the pair (5Y8/12, 5PB5/12) being used as the standard (see Fig. 1), generated under the lighting conditions in question (i.e., Y-B, P-R, etc.) for each observer individually.

Fig. 6
Fig. 6

Dissimilarities versus chromaticity differences for the pairs of identical papers. Colors of symbols and shapes are the same as in Fig. 2. Figures show how the dissimilarities, produced only by the difference in illumination, correlate with the corresponding chromaticity differences.

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