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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 27, Iss. 12 — Dec. 1, 2010
  • pp: 2551–2557

Hue manifold

Rumi Tokunaga and Alexander D. Logvinenko  »View Author Affiliations

JOSA A, Vol. 27, Issue 12, pp. 2551-2557 (2010)

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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

OCIS Codes
(330.0330) Vision, color, and visual optics : Vision, color, and visual optics
(330.1720) Vision, color, and visual optics : Color vision

ToC Category:
Vision, Color, and Visual Optics

Original Manuscript: March 29, 2010
Revised Manuscript: August 25, 2010
Manuscript Accepted: August 25, 2010
Published: November 5, 2010

Rumi Tokunaga and Alexander D. Logvinenko, "Hue manifold," J. Opt. Soc. Am. A 27, 2551-2557 (2010)

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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).
  15. C. E. Helm, “Multidimensional ratio scaling analysis of perceived color relations,” J. Opt. Soc. Am. 54, 256–262 (1964). [CrossRef] [PubMed]
  16. 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]
  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).
  21. 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.
  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.

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