Abstract

The evolution of color categorization is investigated using artificial agent population categorization games, by modeling observer types using Farnsworth–Munsell 100 Hue Test performance to capture human processing constraints on color categorization. Homogeneous populations of both normal and dichromat agents are separately examined. Both types of populations produce near-optimal categorization solutions. While normal observers produce categorization solutions that show rotational invariance, dichromats’ solutions show symmetry-breaking features. In particular, it is found that dichromats’ local confusion regions tend to repel color category boundaries and that global confusion pairs attract category boundaries. The trade-off between these two mechanisms gives rise to population categorization solutions where color boundaries are anchored to a subset of locations in the stimulus space. A companion paper extends these studies to more realistic, heterogeneous agent populations [J. Opt. Soc. Am. A 26, 1424–1436 (2009) ].

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
  2. T. Belpaeme and J. Bleys, “Explaining universal color categories through a constrained acquisition process,” Adapt. Behav. 13, 293-310 (2005).
    [CrossRef]
  3. L. Steels and T. Belpaeme, “Coordinating perceptually grounded categories: a case study for colour,” Behav. Brain Sci. 28, 469-529 (2005).
    [CrossRef] [PubMed]
  4. L. D. Griffin, “The basic colour categories are optimal for classification,” J. R. Soc., Interface 3, 71-85 (2006).
    [CrossRef]
  5. M. Dowman, “Explaining color term typology with an evolutionary model,” Cogn. Sci. 31, 99-132 (2007).
    [CrossRef] [PubMed]
  6. N. L. Komarova, K. A. Jameson, and L. Narens, “Evolutionary models of color categorization based on discrimination,” J. Math. Psychol. 51, 359-382 (2007).
    [CrossRef]
  7. A. Puglisi, A. Baronchelli, and V. Loreto, “Cultural route to the emergence of linguistic categories,” Proc. Natl. Acad. Sci. U.S.A. 105, 7936-7940 (2008).
    [CrossRef] [PubMed]
  8. N. L. Komarova and K. A. Jameson, “Population heterogeneity and color stimulus heterogeneity in agent-based color categorization,” J. Theor. Biol. 253, 680-700 (2008).
    [CrossRef] [PubMed]
  9. T. Regier, P. Kay, and N. Khetarpal, “Color naming reflects optimal partitions of color space,” Proc. Natl. Acad. Sci. U.S.A. 104, 1436-1441 (2007).
    [CrossRef] [PubMed]
  10. M. A. Webster, S. M. Webster, S. Bharadwadj, R. Verma, J. Jaikumar, J. Madan, and E. Vaithilingam, “Variations in normal color vision. III. Unique hues in Indian and United States observers,” J. Opt. Soc. Am. A 19, 1951-1962 (2002).
    [CrossRef]
  11. M. A. Webster and P. Kay, “Individual and population differences in focal colors,” in Anthropology of Color: Interdisciplinary Multilevel Modeling, R.E.MacLaury, G.V.Paramei, and D.Dedrick eds. (Benjamins, 2007), pp. 29-53.
  12. Delwin T. Lindsey and Angela M. Brown, “Universality of color names,” Proc. Natl. Acad. Sci. U.S.A. 103, 16608-16613 (2006).
    [CrossRef] [PubMed]
  13. K. A. Jameson and N. L. Komarova, “Evolutionary models of categorization. II. Investigations based on realistic observer models and population heterogeneity,” J. Opt. Soc. Am. A 26, 1424-1436 (2009).
    [CrossRef]
  14. T. N. Cornsweet, Visual Perception (Academic, 1970).
  15. 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]
  16. D. Farnsworth, The Farnsworth-Munsell 100 Hue Test for the Examination of Color Vision (Munsell Color Company, 1949/1957).
  17. K. Mantere, J. Parkkinen, M. Mäntyjärvi, and T. Jaaskelainen, “Eigenvector interpretation of the Farnsworth-Munsell 100-hue test,” J. Opt. Soc. Am. A 12, 2237-2243 (1995).
    [CrossRef]
  18. R. S. Cook, P. Kay, and T. Regier, “The World Color Survey database: history and use,” in Handbook of Categorisation in Cognitive Science, H.Cohen and C.Lefebvre, eds. (Elsevier, 2005), pp. 223-242.
    [CrossRef]
  19. T. Regier, P. Kay, and R. S. Cook, “Focal colors are universal after all,” Proc. Natl. Acad. Sci. U.S.A. 102, 8386-8391 (2005).
    [CrossRef] [PubMed]
  20. J. Birch, Diagnosis of Defective Colour Vision, 2nd ed. (Butterworth-Heinemann, 2001).
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    [CrossRef]
  22. J. Pokorny, V. C. Smith, G. Verriest, and A. J. L. G. Pinckers, Congenital and Acquired Color Vision Defects (Grune & Stratton, 1979).
  23. G. Wyszecki and W. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982).
  24. L. T. Sharpe, A. Stockman, H. Jägle, and J. Nathans, “Opsin genes, cone photopigments, color vision, and color blindness,” in Color Vision: From Genes to Perception, K.R.Gegenfurtner and L. T. Sharpe, eds. (Cambridge U. Press, 1999), pp. 3-51.
  25. B. Sayim, K. A. Jameson, N. Alvarado, and M. K. Szeszel, “Semantic and perceptual representations of color: evidence of a shared color-naming function,” J. Cogn. Culture 5, 427-486 (2005).
    [CrossRef]
  26. Farnsworth-Munsell Scaling Software, Version 2.1 (MacBeth Division of Kolmorgen Corporation, 1997).
  27. D. Farnsworth, “The Farnsworth-Munsell 100-Hue and Dichotomous Tests for color vision,” J. Opt. Soc. Am. 33, 568-578 (1943).
    [CrossRef]
  28. S. J. Dain, “Clinical colour vision tests,” Clin. Exp. Optom. 87, 276-293 (2004).
    [CrossRef] [PubMed]
  29. The number of sequence inversions (of adjacent caps) needed to recreate a perfect order from the sorting data.
  30. Assuming that dichromats perform similarly to normals away from confusion axes, despite the suggestion of error-free performance outside dichromat local confusion regions in Fig. .
  31. These confusion regions closely resemble some based on the standard Farnsworth method of scoring .
  32. P=0 models an ideal normal-observer's sorting of the FM100 85 caps with zero error (see ), whereas a realistic normal-observer model sorts the 85 caps with probabilistic (p>0) error.
  33. W. R. Garner, The Processing of Information and Structure (Erlbaum, 1974).
  34. K. Jameson and R. G. D'Andrade, “It's not really red, green, yellow, blue: An inquiry into cognitive color space,” in Color Categories in Thought and Language, C.L.Hardin and L.Maffi, eds. (Cambridge U. Press, 1997), pp. 295-319.
    [CrossRef]
  35. K. A. Jameson, “Culture and cognition: What is universal about the representation of color experience?” J. Cogn. Culture 5, 293-347 (2005).
    [CrossRef]
  36. K. A. Jameson, “Sharing perceptually grounded categories in uniform and nonuniform populations,” Behav. Brain Sci. 28, 501-502 (2005).
    [CrossRef]

2009 (1)

2008 (2)

A. Puglisi, A. Baronchelli, and V. Loreto, “Cultural route to the emergence of linguistic categories,” Proc. Natl. Acad. Sci. U.S.A. 105, 7936-7940 (2008).
[CrossRef] [PubMed]

N. L. Komarova and K. A. Jameson, “Population heterogeneity and color stimulus heterogeneity in agent-based color categorization,” J. Theor. Biol. 253, 680-700 (2008).
[CrossRef] [PubMed]

2007 (3)

T. Regier, P. Kay, and N. Khetarpal, “Color naming reflects optimal partitions of color space,” Proc. Natl. Acad. Sci. U.S.A. 104, 1436-1441 (2007).
[CrossRef] [PubMed]

M. Dowman, “Explaining color term typology with an evolutionary model,” Cogn. Sci. 31, 99-132 (2007).
[CrossRef] [PubMed]

N. L. Komarova, K. A. Jameson, and L. Narens, “Evolutionary models of color categorization based on discrimination,” J. Math. Psychol. 51, 359-382 (2007).
[CrossRef]

2006 (2)

Delwin T. Lindsey and Angela M. Brown, “Universality of color names,” Proc. Natl. Acad. Sci. U.S.A. 103, 16608-16613 (2006).
[CrossRef] [PubMed]

L. D. Griffin, “The basic colour categories are optimal for classification,” J. R. Soc., Interface 3, 71-85 (2006).
[CrossRef]

2005 (6)

T. Belpaeme and J. Bleys, “Explaining universal color categories through a constrained acquisition process,” Adapt. Behav. 13, 293-310 (2005).
[CrossRef]

L. Steels and T. Belpaeme, “Coordinating perceptually grounded categories: a case study for colour,” Behav. Brain Sci. 28, 469-529 (2005).
[CrossRef] [PubMed]

T. Regier, P. Kay, and R. S. Cook, “Focal colors are universal after all,” Proc. Natl. Acad. Sci. U.S.A. 102, 8386-8391 (2005).
[CrossRef] [PubMed]

B. Sayim, K. A. Jameson, N. Alvarado, and M. K. Szeszel, “Semantic and perceptual representations of color: evidence of a shared color-naming function,” J. Cogn. Culture 5, 427-486 (2005).
[CrossRef]

K. A. Jameson, “Culture and cognition: What is universal about the representation of color experience?” J. Cogn. Culture 5, 293-347 (2005).
[CrossRef]

K. A. Jameson, “Sharing perceptually grounded categories in uniform and nonuniform populations,” Behav. Brain Sci. 28, 501-502 (2005).
[CrossRef]

2004 (1)

S. J. Dain, “Clinical colour vision tests,” Clin. Exp. Optom. 87, 276-293 (2004).
[CrossRef] [PubMed]

2003 (1)

P. Kay and T. Regier, “Resolving the question of color naming universals,” Proc. Natl. Acad. Sci. U.S.A. 100, 9085-9089 (2003).
[CrossRef] [PubMed]

2002 (1)

1995 (1)

1992 (1)

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]

1943 (1)

1938 (1)

J. H. Nelson, “Anomalous trichromatism and its relation to normal trichromatism,” Proc. Phys. Soc. 50, 661-702 (1938).
[CrossRef]

Alvarado, N.

B. Sayim, K. A. Jameson, N. Alvarado, and M. K. Szeszel, “Semantic and perceptual representations of color: evidence of a shared color-naming function,” J. Cogn. Culture 5, 427-486 (2005).
[CrossRef]

Baronchelli, A.

A. Puglisi, A. Baronchelli, and V. Loreto, “Cultural route to the emergence of linguistic categories,” Proc. Natl. Acad. Sci. U.S.A. 105, 7936-7940 (2008).
[CrossRef] [PubMed]

Belpaeme, T.

L. Steels and T. Belpaeme, “Coordinating perceptually grounded categories: a case study for colour,” Behav. Brain Sci. 28, 469-529 (2005).
[CrossRef] [PubMed]

T. Belpaeme and J. Bleys, “Explaining universal color categories through a constrained acquisition process,” Adapt. Behav. 13, 293-310 (2005).
[CrossRef]

Bharadwadj, S.

Birch, J.

J. Birch, Diagnosis of Defective Colour Vision, 2nd ed. (Butterworth-Heinemann, 2001).

Bleys, J.

T. Belpaeme and J. Bleys, “Explaining universal color categories through a constrained acquisition process,” Adapt. Behav. 13, 293-310 (2005).
[CrossRef]

Brown, Angela M.

Delwin T. Lindsey and Angela M. Brown, “Universality of color names,” Proc. Natl. Acad. Sci. U.S.A. 103, 16608-16613 (2006).
[CrossRef] [PubMed]

Cook, R. S.

T. Regier, P. Kay, and R. S. Cook, “Focal colors are universal after all,” Proc. Natl. Acad. Sci. U.S.A. 102, 8386-8391 (2005).
[CrossRef] [PubMed]

R. S. Cook, P. Kay, and T. Regier, “The World Color Survey database: history and use,” in Handbook of Categorisation in Cognitive Science, H.Cohen and C.Lefebvre, eds. (Elsevier, 2005), pp. 223-242.
[CrossRef]

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]

Cornsweet, T. N.

T. N. Cornsweet, Visual Perception (Academic, 1970).

Dain, S. J.

S. J. Dain, “Clinical colour vision tests,” Clin. Exp. Optom. 87, 276-293 (2004).
[CrossRef] [PubMed]

D'Andrade, R. G.

K. Jameson and R. G. D'Andrade, “It's not really red, green, yellow, blue: An inquiry into cognitive color space,” in Color Categories in Thought and Language, C.L.Hardin and L.Maffi, eds. (Cambridge U. Press, 1997), pp. 295-319.
[CrossRef]

Dowman, M.

M. Dowman, “Explaining color term typology with an evolutionary model,” Cogn. Sci. 31, 99-132 (2007).
[CrossRef] [PubMed]

Farnsworth, D.

D. Farnsworth, “The Farnsworth-Munsell 100-Hue and Dichotomous Tests for color vision,” J. Opt. Soc. Am. 33, 568-578 (1943).
[CrossRef]

D. Farnsworth, The Farnsworth-Munsell 100 Hue Test for the Examination of Color Vision (Munsell Color Company, 1949/1957).

Garner, W. R.

W. R. Garner, The Processing of Information and Structure (Erlbaum, 1974).

Griffin, L. D.

L. D. Griffin, “The basic colour categories are optimal for classification,” J. R. Soc., Interface 3, 71-85 (2006).
[CrossRef]

Jaaskelainen, T.

Jägle, H.

L. T. Sharpe, A. Stockman, H. Jägle, and J. Nathans, “Opsin genes, cone photopigments, color vision, and color blindness,” in Color Vision: From Genes to Perception, K.R.Gegenfurtner and L. T. Sharpe, eds. (Cambridge U. Press, 1999), pp. 3-51.

Jaikumar, J.

Jameson, K.

K. Jameson and R. G. D'Andrade, “It's not really red, green, yellow, blue: An inquiry into cognitive color space,” in Color Categories in Thought and Language, C.L.Hardin and L.Maffi, eds. (Cambridge U. Press, 1997), pp. 295-319.
[CrossRef]

Jameson, K. A.

K. A. Jameson and N. L. Komarova, “Evolutionary models of categorization. II. Investigations based on realistic observer models and population heterogeneity,” J. Opt. Soc. Am. A 26, 1424-1436 (2009).
[CrossRef]

N. L. Komarova and K. A. Jameson, “Population heterogeneity and color stimulus heterogeneity in agent-based color categorization,” J. Theor. Biol. 253, 680-700 (2008).
[CrossRef] [PubMed]

N. L. Komarova, K. A. Jameson, and L. Narens, “Evolutionary models of color categorization based on discrimination,” J. Math. Psychol. 51, 359-382 (2007).
[CrossRef]

B. Sayim, K. A. Jameson, N. Alvarado, and M. K. Szeszel, “Semantic and perceptual representations of color: evidence of a shared color-naming function,” J. Cogn. Culture 5, 427-486 (2005).
[CrossRef]

K. A. Jameson, “Culture and cognition: What is universal about the representation of color experience?” J. Cogn. Culture 5, 293-347 (2005).
[CrossRef]

K. A. Jameson, “Sharing perceptually grounded categories in uniform and nonuniform populations,” Behav. Brain Sci. 28, 501-502 (2005).
[CrossRef]

Kay, P.

T. Regier, P. Kay, and N. Khetarpal, “Color naming reflects optimal partitions of color space,” Proc. Natl. Acad. Sci. U.S.A. 104, 1436-1441 (2007).
[CrossRef] [PubMed]

T. Regier, P. Kay, and R. S. Cook, “Focal colors are universal after all,” Proc. Natl. Acad. Sci. U.S.A. 102, 8386-8391 (2005).
[CrossRef] [PubMed]

P. Kay and T. Regier, “Resolving the question of color naming universals,” Proc. Natl. Acad. Sci. U.S.A. 100, 9085-9089 (2003).
[CrossRef] [PubMed]

R. S. Cook, P. Kay, and T. Regier, “The World Color Survey database: history and use,” in Handbook of Categorisation in Cognitive Science, H.Cohen and C.Lefebvre, eds. (Elsevier, 2005), pp. 223-242.
[CrossRef]

M. A. Webster and P. Kay, “Individual and population differences in focal colors,” in Anthropology of Color: Interdisciplinary Multilevel Modeling, R.E.MacLaury, G.V.Paramei, and D.Dedrick eds. (Benjamins, 2007), pp. 29-53.

Khetarpal, N.

T. Regier, P. Kay, and N. Khetarpal, “Color naming reflects optimal partitions of color space,” Proc. Natl. Acad. Sci. U.S.A. 104, 1436-1441 (2007).
[CrossRef] [PubMed]

Komarova, N. L.

K. A. Jameson and N. L. Komarova, “Evolutionary models of categorization. II. Investigations based on realistic observer models and population heterogeneity,” J. Opt. Soc. Am. A 26, 1424-1436 (2009).
[CrossRef]

N. L. Komarova and K. A. Jameson, “Population heterogeneity and color stimulus heterogeneity in agent-based color categorization,” J. Theor. Biol. 253, 680-700 (2008).
[CrossRef] [PubMed]

N. L. Komarova, K. A. Jameson, and L. Narens, “Evolutionary models of color categorization based on discrimination,” J. Math. Psychol. 51, 359-382 (2007).
[CrossRef]

Lindsey, Delwin T.

Delwin T. Lindsey and Angela M. Brown, “Universality of color names,” Proc. Natl. Acad. Sci. U.S.A. 103, 16608-16613 (2006).
[CrossRef] [PubMed]

Loreto, V.

A. Puglisi, A. Baronchelli, and V. Loreto, “Cultural route to the emergence of linguistic categories,” Proc. Natl. Acad. Sci. U.S.A. 105, 7936-7940 (2008).
[CrossRef] [PubMed]

Madan, J.

Mantere, K.

Mäntyjärvi, M.

Narens, L.

N. L. Komarova, K. A. Jameson, and L. Narens, “Evolutionary models of color categorization based on discrimination,” J. Math. Psychol. 51, 359-382 (2007).
[CrossRef]

Nathans, J.

L. T. Sharpe, A. Stockman, H. Jägle, and J. Nathans, “Opsin genes, cone photopigments, color vision, and color blindness,” in Color Vision: From Genes to Perception, K.R.Gegenfurtner and L. T. Sharpe, eds. (Cambridge U. Press, 1999), pp. 3-51.

Nelson, J. H.

J. H. Nelson, “Anomalous trichromatism and its relation to normal trichromatism,” Proc. Phys. Soc. 50, 661-702 (1938).
[CrossRef]

Parkkinen, J.

Pinckers, A. J. L. G.

J. Pokorny, V. C. Smith, G. Verriest, and A. J. L. G. Pinckers, Congenital and Acquired Color Vision Defects (Grune & Stratton, 1979).

Pokorny, J.

J. Pokorny, V. C. Smith, G. Verriest, and A. J. L. G. Pinckers, Congenital and Acquired Color Vision Defects (Grune & Stratton, 1979).

Puglisi, A.

A. Puglisi, A. Baronchelli, and V. Loreto, “Cultural route to the emergence of linguistic categories,” Proc. Natl. Acad. Sci. U.S.A. 105, 7936-7940 (2008).
[CrossRef] [PubMed]

Regier, T.

T. Regier, P. Kay, and N. Khetarpal, “Color naming reflects optimal partitions of color space,” Proc. Natl. Acad. Sci. U.S.A. 104, 1436-1441 (2007).
[CrossRef] [PubMed]

T. Regier, P. Kay, and R. S. Cook, “Focal colors are universal after all,” Proc. Natl. Acad. Sci. U.S.A. 102, 8386-8391 (2005).
[CrossRef] [PubMed]

P. Kay and T. Regier, “Resolving the question of color naming universals,” Proc. Natl. Acad. Sci. U.S.A. 100, 9085-9089 (2003).
[CrossRef] [PubMed]

R. S. Cook, P. Kay, and T. Regier, “The World Color Survey database: history and use,” in Handbook of Categorisation in Cognitive Science, H.Cohen and C.Lefebvre, eds. (Elsevier, 2005), pp. 223-242.
[CrossRef]

Sayim, B.

B. Sayim, K. A. Jameson, N. Alvarado, and M. K. Szeszel, “Semantic and perceptual representations of color: evidence of a shared color-naming function,” J. Cogn. Culture 5, 427-486 (2005).
[CrossRef]

Sharpe, L. T.

L. T. Sharpe, A. Stockman, H. Jägle, and J. Nathans, “Opsin genes, cone photopigments, color vision, and color blindness,” in Color Vision: From Genes to Perception, K.R.Gegenfurtner and L. T. Sharpe, eds. (Cambridge U. Press, 1999), pp. 3-51.

L. T. Sharpe, A. Stockman, H. Jägle, and J. Nathans, “Opsin genes, cone photopigments, color vision, and color blindness,” in Color Vision: From Genes to Perception, K.R.Gegenfurtner and L. T. Sharpe, eds. (Cambridge U. Press, 1999), pp. 3-51.

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]

Smith, V. C.

J. Pokorny, V. C. Smith, G. Verriest, and A. J. L. G. Pinckers, Congenital and Acquired Color Vision Defects (Grune & Stratton, 1979).

Steels, L.

L. Steels and T. Belpaeme, “Coordinating perceptually grounded categories: a case study for colour,” Behav. Brain Sci. 28, 469-529 (2005).
[CrossRef] [PubMed]

Stiles, W.

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

Stockman, A.

L. T. Sharpe, A. Stockman, H. Jägle, and J. Nathans, “Opsin genes, cone photopigments, color vision, and color blindness,” in Color Vision: From Genes to Perception, K.R.Gegenfurtner and L. T. Sharpe, eds. (Cambridge U. Press, 1999), pp. 3-51.

Szeszel, M. K.

B. Sayim, K. A. Jameson, N. Alvarado, and M. K. Szeszel, “Semantic and perceptual representations of color: evidence of a shared color-naming function,” J. Cogn. Culture 5, 427-486 (2005).
[CrossRef]

Vaithilingam, E.

Verma, R.

Verriest, G.

J. Pokorny, V. C. Smith, G. Verriest, and A. J. L. G. Pinckers, Congenital and Acquired Color Vision Defects (Grune & Stratton, 1979).

Webster, M. A.

M. A. Webster, S. M. Webster, S. Bharadwadj, R. Verma, J. Jaikumar, J. Madan, and E. Vaithilingam, “Variations in normal color vision. III. Unique hues in Indian and United States observers,” J. Opt. Soc. Am. A 19, 1951-1962 (2002).
[CrossRef]

M. A. Webster and P. Kay, “Individual and population differences in focal colors,” in Anthropology of Color: Interdisciplinary Multilevel Modeling, R.E.MacLaury, G.V.Paramei, and D.Dedrick eds. (Benjamins, 2007), pp. 29-53.

Webster, S. M.

Wyszecki, G.

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

Adapt. Behav. (1)

T. Belpaeme and J. Bleys, “Explaining universal color categories through a constrained acquisition process,” Adapt. Behav. 13, 293-310 (2005).
[CrossRef]

Behav. Brain Sci. (2)

L. Steels and T. Belpaeme, “Coordinating perceptually grounded categories: a case study for colour,” Behav. Brain Sci. 28, 469-529 (2005).
[CrossRef] [PubMed]

K. A. Jameson, “Sharing perceptually grounded categories in uniform and nonuniform populations,” Behav. Brain Sci. 28, 501-502 (2005).
[CrossRef]

Clin. Exp. Optom. (1)

S. J. Dain, “Clinical colour vision tests,” Clin. Exp. Optom. 87, 276-293 (2004).
[CrossRef] [PubMed]

Cogn. Sci. (1)

M. Dowman, “Explaining color term typology with an evolutionary model,” Cogn. Sci. 31, 99-132 (2007).
[CrossRef] [PubMed]

J. Cogn. Culture (2)

B. Sayim, K. A. Jameson, N. Alvarado, and M. K. Szeszel, “Semantic and perceptual representations of color: evidence of a shared color-naming function,” J. Cogn. Culture 5, 427-486 (2005).
[CrossRef]

K. A. Jameson, “Culture and cognition: What is universal about the representation of color experience?” J. Cogn. Culture 5, 293-347 (2005).
[CrossRef]

J. Math. Psychol. (1)

N. L. Komarova, K. A. Jameson, and L. Narens, “Evolutionary models of color categorization based on discrimination,” J. Math. Psychol. 51, 359-382 (2007).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. R. Soc., Interface (1)

L. D. Griffin, “The basic colour categories are optimal for classification,” J. R. Soc., Interface 3, 71-85 (2006).
[CrossRef]

J. Theor. Biol. (1)

N. L. Komarova and K. A. Jameson, “Population heterogeneity and color stimulus heterogeneity in agent-based color categorization,” J. Theor. Biol. 253, 680-700 (2008).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (5)

T. Regier, P. Kay, and N. Khetarpal, “Color naming reflects optimal partitions of color space,” Proc. Natl. Acad. Sci. U.S.A. 104, 1436-1441 (2007).
[CrossRef] [PubMed]

T. Regier, P. Kay, and R. S. Cook, “Focal colors are universal after all,” Proc. Natl. Acad. Sci. U.S.A. 102, 8386-8391 (2005).
[CrossRef] [PubMed]

A. Puglisi, A. Baronchelli, and V. Loreto, “Cultural route to the emergence of linguistic categories,” Proc. Natl. Acad. Sci. U.S.A. 105, 7936-7940 (2008).
[CrossRef] [PubMed]

Delwin T. Lindsey and Angela M. Brown, “Universality of color names,” Proc. Natl. Acad. Sci. U.S.A. 103, 16608-16613 (2006).
[CrossRef] [PubMed]

P. Kay and T. Regier, “Resolving the question of color naming universals,” Proc. Natl. Acad. Sci. U.S.A. 100, 9085-9089 (2003).
[CrossRef] [PubMed]

Proc. Phys. Soc. (1)

J. H. Nelson, “Anomalous trichromatism and its relation to normal trichromatism,” Proc. Phys. Soc. 50, 661-702 (1938).
[CrossRef]

Psychol. Sci. (1)

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]

Other (15)

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Farnsworth-Munsell Scaling Software, Version 2.1 (MacBeth Division of Kolmorgen Corporation, 1997).

J. Pokorny, V. C. Smith, G. Verriest, and A. J. L. G. Pinckers, Congenital and Acquired Color Vision Defects (Grune & Stratton, 1979).

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

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The number of sequence inversions (of adjacent caps) needed to recreate a perfect order from the sorting data.

Assuming that dichromats perform similarly to normals away from confusion axes, despite the suggestion of error-free performance outside dichromat local confusion regions in Fig. .

These confusion regions closely resemble some based on the standard Farnsworth method of scoring .

P=0 models an ideal normal-observer's sorting of the FM100 85 caps with zero error (see ), whereas a realistic normal-observer model sorts the 85 caps with probabilistic (p>0) error.

W. R. Garner, The Processing of Information and Structure (Erlbaum, 1974).

K. Jameson and R. G. D'Andrade, “It's not really red, green, yellow, blue: An inquiry into cognitive color space,” in Color Categories in Thought and Language, C.L.Hardin and L.Maffi, eds. (Cambridge U. Press, 1997), pp. 295-319.
[CrossRef]

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[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

FM100 stimulus with data used to model protanope (left) and deuteranope (right) agents. Colored lines show deficiency confusion axes: red = protan , green = deutan . ( Blue = tritan ; not modeled here). Deviations from the inner circle illustrate observer sorting errors.

Fig. 2
Fig. 2

Dain’s depiction of FM100 stimuli in CIE (1976) space [28] (reproduced with permission). Inset lines show three global confusion pairs used for protan (solid lines) and deutan (dotted lines) agents modeled.

Fig. 3
Fig. 3

Color categorization and degree of population disagreement in homogeneous normal populations for different values of the sorting error, p. Panels show (a) no sorting errors ( p = 0 ) and (b) sorting errors with probability p = 0.08 . The horizontal axis is the 85 caps of the FM100. The dotted lines (and the left vertical axis) show population-average categorization solutions for a typical run (after 5 × 10 7 iterations). The solid lines (and the right vertical axis) show the amount of population disagreement; it is magnified by a factor of 10 in (a). Other parameters are as in Table 1.

Fig. 4
Fig. 4

Boundary location histograms from 1,000 simulation solutions by homogeneous protanope populations. Horizontal axes show the FM100 85 caps. Vertical axis shows frequency with which a color boundary was established at a given FM100 cap. Results are shown separately for all observed solutions (histograms at left), four-category solutions (middle), and five-category solutions (right). Top row, results under local confusion regions; middle row, results under global confusion pairs; bottom row, results for both confusion features. Other parameters are in Table 1 and as described in Section 2.

Fig. 5
Fig. 5

Boundary location histograms from 1,000 simulation solutions by homogeneous deuteranope populations. Figure layout and parameters are as in Fig. 4.

Fig. 6
Fig. 6

Confusion parameter settings shown with results from homogeneous protanope solutions (from Fig. 4). Top row, local confusions; middle row, global confusions; bottom row, both confusions. The circle depicts the FM100 caps. Caps 1, 21, 42, and 63 provide arbitrary points of reference. Thick black arcs with end caps show local confusion regions. Two-point thick black arrows with confusion pair caps show global confusions. Typical four-category (left), and five-category solutions (right) are shown. In the case of local confusions (top row), dashed double-arrowhead lines mark regions where boundaries occur.

Fig. 7
Fig. 7

Confusion parameter settings shown with results from homogeneous deuteranope solutions (from Fig. 5). Figure layout and features are as in Fig. 6. Unlike the protanope model (Fig. 6), the deuteranope model has a local confusion region that coincides with a global confusion pair (bottom row) and has local confusion regions larger than those in the protanope data. Both differences affect category boundary robustness.

Tables (1)

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Table 1 Simulation Notation

Equations (3)

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C i j sorting = { 1 p , i = j p 2 , j = i ± 1 0 , otherwise } .
C i j local = { exp { ( j i ) 2 w } W i 1 , i , j I 1 or i , j I 2 1 , i = j I 1 , 2 0 , otherwise } ,
C i j global = { 0.5 , i X gl and j = i 0.5 , i X gl and j = g ( i ) 1 , i = j X gl 0 , otherwise } .

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