Abstract

Maximum likelihood difference scaling was used to measure suprathreshold contrast response difference scales for low-frequency Gabor patterns, modulated along luminance and L–M color directions in normal, protanomalous, and deuteranomalous observers. Based on a signal-detection model, perceptual scale values, parameterized as $ d^\prime $, were estimated by maximum likelihood. The difference scales were well fit by a Michaelis–Menten model, permitting estimates of response and contrast gain parameters for each subject. Anomalous observers showed no significant differences in response or contrast gain from normal observers for luminance contrast. For chromatic modulation, however, anomalous observers displayed higher contrast and lower response gain compared to normal observers. These effects cannot be explained by simple pigment shift models, and they support a compensation mechanism to optimize the mapping of the input contrast range to the neural response range. A linear relation between response and contrast gain suggests a neural trade-off between them.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (3)

J. Bosten, “The known unknowns of anomalous trichromacy,” Curr. Opin. Behav. Sci. 30, 228–237 (2019).
[Crossref]

J. Peirce, J. R. Gray, S. Simpson, M. MacAskill, R. Höchenberger, H. Sogo, E. Kastman, and J. K. Lindeløv, “Psychopy2: experiments in behavior made easy,” Behav. Res. Methods 51, 195–203 (2019).
[Crossref]

R. Doron, A. Sterkin, M. Fried, O. Yehezkel, M. Lev, M. Belkin, M. Rosner, A. S. Solomon, Y. Mandel, and U. Polat, “Spatial visual function in anomalous trichromats: Is less more?” PloS One 14, e0209662 (2019).
[Crossref]

2017 (1)

C. B. Wiebel, G. Aguilar, and M. Maertens, “Maximum likelihood difference scales represent perceptual magnitudes and predict appearance matches,” J. Vis. 17(4):1 (2017).
[Crossref]

2016 (1)

E. Bellot, V. Coizet, J. Warnking, K. Knoblauch, E. Moro, and M. Dojat, “Effects of aging on low luminance contrast processing in humans,” NeuroImage 139, 415–426 (2016).
[Crossref]

2015 (1)

D. Bates, M. Mächler, B. Bolker, and S. Walker, “Fitting linear mixed-effects models using lme4,” J. Statist. Softw. 67, 1–48 (2015).
[Crossref]

2014 (1)

A. E. Boehm, D. I. MacLeod, and J. M. Bosten, “Compensation for red-green contrast loss in anomalous trichromats,” J. Vis. 14(13):19 (2014).
[Crossref]

2012 (1)

F. Devinck and K. Knoblauch, “A common signal detection model accounts for both perception and discrimination of the watercolor effect,” J. Vis. 12(3):19 (2012).
[Crossref]

2011 (1)

E. W. Dees and R. C. Baraas, “Fargede filtre gir ikke rød-grønne fargesvake normal fargebedømmelse,” Scand. J. Optom. Visual Sci. 4, 6–13 (2011).
[Crossref]

2009 (1)

M. Kwon, G. E. Legge, F. Fang, A. M. Cheong, and S. He, “Adaptive changes in visual cortex following prolonged contrast reduction,” J. Vis. 9(2):20, 1–16 (2009).
[Crossref]

2008 (1)

K. Knoblauch and L. T. Maloney, “MLDS: maximum likelihood difference scaling in R,” J. Statist. Softw. 25, 1–26 (2008).
[Crossref]

2007 (1)

2005 (2)

A. B. Watson and A. J. Ahumada, “A standard model for foveal detection of spatial contrast,” J. Vis. 5(9):6 (2005).
[Crossref]

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, 950–952 (2005).
[Crossref]

2003 (1)

L. T. Maloney and J. N. Yang, “Maximum likelihood difference scaling,” J. Vis. 3(8):5, 573–585 (2003).
[Crossref]

2001 (1)

T. Twer and D. I. MacLeod, “Optimal nonlinear codes for the perception of natural colours,” Netw. Comput. Neural Syst. 12, 395–407 (2001).

1999 (1)

G. V. Paramei and C. R. Cavonius, “Color spaces of color-normal and color-abnormal observers reconstructed from response times and dissimilarity ratings,” Percept. Psychophys. 61, 1662–1674 (1999).
[Crossref]

1997 (1)

S. K. Shevell and J. C. He, “The visual photopigments of simple deuteranomalous trichromats inferred from color matching,” Vision Res. 37, 1115–1127 (1997).
[Crossref]

1995 (1)

1993 (2)

1992 (2)

S. L. Merbs and J. Nathans, “Absorption spectra of the hybrid pigments responsible for anomalous color vision,” Science 258, 464–466 (1992).
[Crossref]

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

1991 (1)

G. Paramei, C. A. Izmailov, and E. Sokolov, “Multidimensional scaling of large chromatic differences by normal and color-deficient subjects,” Psychol. Sci. 2, 244–249 (1991).
[Crossref]

1988 (1)

1986 (1)

J. Nathans, T. P. Piantanida, R. L. Eddy, T. B. Shows, and D. S. Hogness, “Molecular genetics of inherited variation in human color vision,” Science 232, 203–210 (1986).
[Crossref]

1985 (1)

K. T. Mullen, “The contrast sensitivity of human colour vision to red-green and blue-yellow chromatic gratings,” J. Physiol. 359, 381–400 (1985).
[Crossref]

1984 (1)

A. M. Derrington, J. Krauskopf, and P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. 357, 241–265 (1984).
[Crossref]

1982 (1)

D. Jameson, L. Hurvich, and D. Varner, “Discrimination mechanisms in color deficient systems,” Doc. Ophthal. Proc. Ser. 33, 295–301 (1982).

1980 (1)

G. E. Legge and J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. A 70, 1458–1471 (1980).
[Crossref]

1978 (1)

M. Romeskie, “Chromatic opponent-response functions of anomalous trichromats,” Vision Res. 18, 1521–1532 (1978).
[Crossref]

1977 (2)

M. Alpern and J. Moeller, “The red and green cone visual pigments of deuteranomalous trichromacy,” J. Physiol. 266, 647–675 (1977).
[Crossref]

J. Pokorny and V. C. Smith, “Evaluation of single-pigment shift model of anomalous trichromacy,” J. Opt. Soc. Am. A 67, 1196–1209 (1977).
[Crossref]

1973 (2)

1954 (1)

M. Aguilar and W. Stiles, “Saturation of the rod mechanism of the retina at high levels of stimulation,” Opt. Acta 1, 59–65 (1954).
[Crossref]

1940 (1)

W. M. McKeon and W. Wright, “The characteristics of protanomalous vision,” Proc. Phys. Soc. 52, 464–479 (1940).
[Crossref]

1881 (1)

J. Strutt, “Experiments on colour,” Nature 25, 64–66 (1881).
[Crossref]

Adams, A. J.

Aguilar, G.

C. B. Wiebel, G. Aguilar, and M. Maertens, “Maximum likelihood difference scales represent perceptual magnitudes and predict appearance matches,” J. Vis. 17(4):1 (2017).
[Crossref]

Aguilar, M.

M. Aguilar and W. Stiles, “Saturation of the rod mechanism of the retina at high levels of stimulation,” Opt. Acta 1, 59–65 (1954).
[Crossref]

Ahumada, A. J.

A. B. Watson and A. J. Ahumada, “A standard model for foveal detection of spatial contrast,” J. Vis. 5(9):6 (2005).
[Crossref]

Alpern, M.

M. Alpern and J. Moeller, “The red and green cone visual pigments of deuteranomalous trichromacy,” J. Physiol. 266, 647–675 (1977).
[Crossref]

Baraas, R. C.

E. W. Dees and R. C. Baraas, “Fargede filtre gir ikke rød-grønne fargesvake normal fargebedømmelse,” Scand. J. Optom. Visual Sci. 4, 6–13 (2011).
[Crossref]

Bates, D.

D. Bates, M. Mächler, B. Bolker, and S. Walker, “Fitting linear mixed-effects models using lme4,” J. Statist. Softw. 67, 1–48 (2015).
[Crossref]

J. Pinheiro, D. Bates, S. DebRoy, and D. Sarkar, and R Core Team, nlme: Linear and Nonlinear Mixed Effects Models (2019), R package version 3.1-141.

Belkin, M.

R. Doron, A. Sterkin, M. Fried, O. Yehezkel, M. Lev, M. Belkin, M. Rosner, A. S. Solomon, Y. Mandel, and U. Polat, “Spatial visual function in anomalous trichromats: Is less more?” PloS One 14, e0209662 (2019).
[Crossref]

Bellot, E.

E. Bellot, V. Coizet, J. Warnking, K. Knoblauch, E. Moro, and M. Dojat, “Effects of aging on low luminance contrast processing in humans,” NeuroImage 139, 415–426 (2016).
[Crossref]

Boehm, A. E.

A. E. Boehm, D. I. MacLeod, and J. M. Bosten, “Compensation for red-green contrast loss in anomalous trichromats,” J. Vis. 14(13):19 (2014).
[Crossref]

Bolker, B.

D. Bates, M. Mächler, B. Bolker, and S. Walker, “Fitting linear mixed-effects models using lme4,” J. Statist. Softw. 67, 1–48 (2015).
[Crossref]

Bosten, J.

J. Bosten, “The known unknowns of anomalous trichromacy,” Curr. Opin. Behav. Sci. 30, 228–237 (2019).
[Crossref]

Bosten, J. M.

A. E. Boehm, D. I. MacLeod, and J. M. Bosten, “Compensation for red-green contrast loss in anomalous trichromats,” J. Vis. 14(13):19 (2014).
[Crossref]

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, 950–952 (2005).
[Crossref]

Cavonius, C.

M. Müller, C. Cavonius, and J. Mollon, “Constructing the color space of the deuteranomalous observer,” in Colour Vision Deficiencies X (Springer, 1991), pp. 377–387.

Cavonius, C. R.

G. V. Paramei and C. R. Cavonius, “Color spaces of color-normal and color-abnormal observers reconstructed from response times and dissimilarity ratings,” Percept. Psychophys. 61, 1662–1674 (1999).
[Crossref]

Chaparro, A.

A. Chaparro, C. Stromeyer, E. Huang, R. Kronauer, and R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
[Crossref]

Charrier, C.

Cheong, A. M.

M. Kwon, G. E. Legge, F. Fang, A. M. Cheong, and S. He, “Adaptive changes in visual cortex following prolonged contrast reduction,” J. Vis. 9(2):20, 1–16 (2009).
[Crossref]

Cherifi, H.

Coizet, V.

E. Bellot, V. Coizet, J. Warnking, K. Knoblauch, E. Moro, and M. Dojat, “Effects of aging on low luminance contrast processing in humans,” NeuroImage 139, 415–426 (2016).
[Crossref]

Crognale, M. A.

DebRoy, S.

J. Pinheiro, D. Bates, S. DebRoy, and D. Sarkar, and R Core Team, nlme: Linear and Nonlinear Mixed Effects Models (2019), R package version 3.1-141.

Dees, E. W.

E. W. Dees and R. C. Baraas, “Fargede filtre gir ikke rød-grønne fargesvake normal fargebedømmelse,” Scand. J. Optom. Visual Sci. 4, 6–13 (2011).
[Crossref]

DeMarco, P.

Derrington, A. M.

A. M. Derrington, J. Krauskopf, and P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. 357, 241–265 (1984).
[Crossref]

Devinck, F.

F. Devinck and K. Knoblauch, “A common signal detection model accounts for both perception and discrimination of the watercolor effect,” J. Vis. 12(3):19 (2012).
[Crossref]

Dojat, M.

E. Bellot, V. Coizet, J. Warnking, K. Knoblauch, E. Moro, and M. Dojat, “Effects of aging on low luminance contrast processing in humans,” NeuroImage 139, 415–426 (2016).
[Crossref]

Doron, R.

R. Doron, A. Sterkin, M. Fried, O. Yehezkel, M. Lev, M. Belkin, M. Rosner, A. S. Solomon, Y. Mandel, and U. Polat, “Spatial visual function in anomalous trichromats: Is less more?” PloS One 14, e0209662 (2019).
[Crossref]

Eddy, R. L.

J. Nathans, T. P. Piantanida, R. L. Eddy, T. B. Shows, and D. S. Hogness, “Molecular genetics of inherited variation in human color vision,” Science 232, 203–210 (1986).
[Crossref]

Eskew, R. T.

A. Chaparro, C. Stromeyer, E. Huang, R. Kronauer, and R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
[Crossref]

Fang, F.

M. Kwon, G. E. Legge, F. Fang, A. M. Cheong, and S. He, “Adaptive changes in visual cortex following prolonged contrast reduction,” J. Vis. 9(2):20, 1–16 (2009).
[Crossref]

Foley, J. M.

G. E. Legge and J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. A 70, 1458–1471 (1980).
[Crossref]

Fried, M.

R. Doron, A. Sterkin, M. Fried, O. Yehezkel, M. Lev, M. Belkin, M. Rosner, A. S. Solomon, Y. Mandel, and U. Polat, “Spatial visual function in anomalous trichromats: Is less more?” PloS One 14, e0209662 (2019).
[Crossref]

Gray, J. R.

J. Peirce, J. R. Gray, S. Simpson, M. MacAskill, R. Höchenberger, H. Sogo, E. Kastman, and J. K. Lindeløv, “Psychopy2: experiments in behavior made easy,” Behav. Res. Methods 51, 195–203 (2019).
[Crossref]

Hægerström-Portnoy, G.

He, J. C.

S. K. Shevell and J. C. He, “The visual photopigments of simple deuteranomalous trichromats inferred from color matching,” Vision Res. 37, 1115–1127 (1997).
[Crossref]

He, S.

M. Kwon, G. E. Legge, F. Fang, A. M. Cheong, and S. He, “Adaptive changes in visual cortex following prolonged contrast reduction,” J. Vis. 9(2):20, 1–16 (2009).
[Crossref]

Höchenberger, R.

J. Peirce, J. R. Gray, S. Simpson, M. MacAskill, R. Höchenberger, H. Sogo, E. Kastman, and J. K. Lindeløv, “Psychopy2: experiments in behavior made easy,” Behav. Res. Methods 51, 195–203 (2019).
[Crossref]

Hogness, D. S.

J. Nathans, T. P. Piantanida, R. L. Eddy, T. B. Shows, and D. S. Hogness, “Molecular genetics of inherited variation in human color vision,” Science 232, 203–210 (1986).
[Crossref]

Huang, E.

A. Chaparro, C. Stromeyer, E. Huang, R. Kronauer, and R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
[Crossref]

Hurvich, L.

D. Jameson, L. Hurvich, and D. Varner, “Discrimination mechanisms in color deficient systems,” Doc. Ophthal. Proc. Ser. 33, 295–301 (1982).

Hurvich, L. M.

L. M. Hurvich, “Color vision deficiencies,” in Visual Psychophysics (Springer, 1972), pp. 582–624.

Izmailov, C. A.

G. Paramei, C. A. Izmailov, and E. Sokolov, “Multidimensional scaling of large chromatic differences by normal and color-deficient subjects,” Psychol. Sci. 2, 244–249 (1991).
[Crossref]

Jameson, D.

D. Jameson, L. Hurvich, and D. Varner, “Discrimination mechanisms in color deficient systems,” Doc. Ophthal. Proc. Ser. 33, 295–301 (1982).

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, 950–952 (2005).
[Crossref]

Kastman, E.

J. Peirce, J. R. Gray, S. Simpson, M. MacAskill, R. Höchenberger, H. Sogo, E. Kastman, and J. K. Lindeløv, “Psychopy2: experiments in behavior made easy,” Behav. Res. Methods 51, 195–203 (2019).
[Crossref]

Katz, I.

Knoblauch, K.

E. Bellot, V. Coizet, J. Warnking, K. Knoblauch, E. Moro, and M. Dojat, “Effects of aging on low luminance contrast processing in humans,” NeuroImage 139, 415–426 (2016).
[Crossref]

F. Devinck and K. Knoblauch, “A common signal detection model accounts for both perception and discrimination of the watercolor effect,” J. Vis. 12(3):19 (2012).
[Crossref]

K. Knoblauch and L. T. Maloney, “MLDS: maximum likelihood difference scaling in R,” J. Statist. Softw. 25, 1–26 (2008).
[Crossref]

C. Charrier, L. T. Maloney, H. Cherifi, and K. Knoblauch, “Maximum likelihood difference scaling of image quality in compression-degraded images,” J. Opt. Soc. Am. A 24, 3418–3426 (2007).
[Crossref]

K. Knoblauch and M. J. McMahon, “Discrimination of binocular color mixtures in dichromacy: evaluation of the Maxwell–Cornsweet conjecture,” J. Opt. Soc. Am. A 12, 2219–2229 (1995).
[Crossref]

K. Knoblauch and L. T. Maloney, Modeling Psychophysical Data in R (Springer, 2012), Vol. 32.

Krauskopf, J.

A. M. Derrington, J. Krauskopf, and P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. 357, 241–265 (1984).
[Crossref]

Kronauer, R.

A. Chaparro, C. Stromeyer, E. Huang, R. Kronauer, and R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
[Crossref]

Kwon, M.

M. Kwon, G. E. Legge, F. Fang, A. M. Cheong, and S. He, “Adaptive changes in visual cortex following prolonged contrast reduction,” J. Vis. 9(2):20, 1–16 (2009).
[Crossref]

Legge, G. E.

M. Kwon, G. E. Legge, F. Fang, A. M. Cheong, and S. He, “Adaptive changes in visual cortex following prolonged contrast reduction,” J. Vis. 9(2):20, 1–16 (2009).
[Crossref]

G. E. Legge and J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. A 70, 1458–1471 (1980).
[Crossref]

Lennie, P.

A. M. Derrington, J. Krauskopf, and P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. 357, 241–265 (1984).
[Crossref]

Lev, M.

R. Doron, A. Sterkin, M. Fried, O. Yehezkel, M. Lev, M. Belkin, M. Rosner, A. S. Solomon, Y. Mandel, and U. Polat, “Spatial visual function in anomalous trichromats: Is less more?” PloS One 14, e0209662 (2019).
[Crossref]

Lindeløv, J. K.

J. Peirce, J. R. Gray, S. Simpson, M. MacAskill, R. Höchenberger, H. Sogo, E. Kastman, and J. K. Lindeløv, “Psychopy2: experiments in behavior made easy,” Behav. Res. Methods 51, 195–203 (2019).
[Crossref]

MacAskill, M.

J. Peirce, J. R. Gray, S. Simpson, M. MacAskill, R. Höchenberger, H. Sogo, E. Kastman, and J. K. Lindeløv, “Psychopy2: experiments in behavior made easy,” Behav. Res. Methods 51, 195–203 (2019).
[Crossref]

Mächler, M.

D. Bates, M. Mächler, B. Bolker, and S. Walker, “Fitting linear mixed-effects models using lme4,” J. Statist. Softw. 67, 1–48 (2015).
[Crossref]

MacLeod, D. I.

A. E. Boehm, D. I. MacLeod, and J. M. Bosten, “Compensation for red-green contrast loss in anomalous trichromats,” J. Vis. 14(13):19 (2014).
[Crossref]

T. Twer and D. I. MacLeod, “Optimal nonlinear codes for the perception of natural colours,” Netw. Comput. Neural Syst. 12, 395–407 (2001).

M. A. Webster and D. I. MacLeod, “Factors underlying individual differences in the color matches of normal observers,” J. Opt. Soc. Am. A 5, 1722–1735 (1988).
[Crossref]

D. I. MacLeod, “The Verriest Lecture. Colour discrimination, colour constancy and natural scene statistics,” in Normal and Defective Colour Vision, J. Mollon, J. Pokorny, and K. Knoblauch, eds. (Oxford University, 2003), pp. 189–217.

Maertens, M.

C. B. Wiebel, G. Aguilar, and M. Maertens, “Maximum likelihood difference scales represent perceptual magnitudes and predict appearance matches,” J. Vis. 17(4):1 (2017).
[Crossref]

Maloney, L. T.

K. Knoblauch and L. T. Maloney, “MLDS: maximum likelihood difference scaling in R,” J. Statist. Softw. 25, 1–26 (2008).
[Crossref]

C. Charrier, L. T. Maloney, H. Cherifi, and K. Knoblauch, “Maximum likelihood difference scaling of image quality in compression-degraded images,” J. Opt. Soc. Am. A 24, 3418–3426 (2007).
[Crossref]

L. T. Maloney and J. N. Yang, “Maximum likelihood difference scaling,” J. Vis. 3(8):5, 573–585 (2003).
[Crossref]

K. Knoblauch and L. T. Maloney, Modeling Psychophysical Data in R (Springer, 2012), Vol. 32.

Mandel, Y.

R. Doron, A. Sterkin, M. Fried, O. Yehezkel, M. Lev, M. Belkin, M. Rosner, A. S. Solomon, Y. Mandel, and U. Polat, “Spatial visual function in anomalous trichromats: Is less more?” PloS One 14, e0209662 (2019).
[Crossref]

McKeon, W. M.

W. M. McKeon and W. Wright, “The characteristics of protanomalous vision,” Proc. Phys. Soc. 52, 464–479 (1940).
[Crossref]

McMahon, M. J.

Merbs, S. L.

S. L. Merbs and J. Nathans, “Absorption spectra of the hybrid pigments responsible for anomalous color vision,” Science 258, 464–466 (1992).
[Crossref]

Moeller, J.

M. Alpern and J. Moeller, “The red and green cone visual pigments of deuteranomalous trichromacy,” J. Physiol. 266, 647–675 (1977).
[Crossref]

Mollon, J.

M. Müller, C. Cavonius, and J. Mollon, “Constructing the color space of the deuteranomalous observer,” in Colour Vision Deficiencies X (Springer, 1991), pp. 377–387.

B. Regan and J. Mollon, “The relative salience of the cardinal axes of colour space in normal and anomalous trichromats,” in Colour Vision Deficiencies XIII (Springer, 1997), pp. 261–270.

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, 950–952 (2005).
[Crossref]

Moro, E.

E. Bellot, V. Coizet, J. Warnking, K. Knoblauch, E. Moro, and M. Dojat, “Effects of aging on low luminance contrast processing in humans,” NeuroImage 139, 415–426 (2016).
[Crossref]

Mullen, K. T.

K. T. Mullen, “The contrast sensitivity of human colour vision to red-green and blue-yellow chromatic gratings,” J. Physiol. 359, 381–400 (1985).
[Crossref]

Müller, M.

M. Müller, C. Cavonius, and J. Mollon, “Constructing the color space of the deuteranomalous observer,” in Colour Vision Deficiencies X (Springer, 1991), pp. 377–387.

Nathans, J.

S. L. Merbs and J. Nathans, “Absorption spectra of the hybrid pigments responsible for anomalous color vision,” Science 258, 464–466 (1992).
[Crossref]

J. Nathans, T. P. Piantanida, R. L. Eddy, T. B. Shows, and D. S. Hogness, “Molecular genetics of inherited variation in human color vision,” Science 232, 203–210 (1986).
[Crossref]

Paramei, G.

G. Paramei, C. A. Izmailov, and E. Sokolov, “Multidimensional scaling of large chromatic differences by normal and color-deficient subjects,” Psychol. Sci. 2, 244–249 (1991).
[Crossref]

Paramei, G. V.

G. V. Paramei and C. R. Cavonius, “Color spaces of color-normal and color-abnormal observers reconstructed from response times and dissimilarity ratings,” Percept. Psychophys. 61, 1662–1674 (1999).
[Crossref]

Peirce, J.

J. Peirce, J. R. Gray, S. Simpson, M. MacAskill, R. Höchenberger, H. Sogo, E. Kastman, and J. K. Lindeløv, “Psychopy2: experiments in behavior made easy,” Behav. Res. Methods 51, 195–203 (2019).
[Crossref]

Piantanida, T. P.

J. Nathans, T. P. Piantanida, R. L. Eddy, T. B. Shows, and D. S. Hogness, “Molecular genetics of inherited variation in human color vision,” Science 232, 203–210 (1986).
[Crossref]

Pinheiro, J.

J. Pinheiro, D. Bates, S. DebRoy, and D. Sarkar, and R Core Team, nlme: Linear and Nonlinear Mixed Effects Models (2019), R package version 3.1-141.

Pokorny, J.

Polat, U.

R. Doron, A. Sterkin, M. Fried, O. Yehezkel, M. Lev, M. Belkin, M. Rosner, A. S. Solomon, Y. Mandel, and U. Polat, “Spatial visual function in anomalous trichromats: Is less more?” PloS One 14, e0209662 (2019).
[Crossref]

Powell, D. S.

W. Rushton, D. S. Powell, and K. White, “Pigments in anomalous trichromats,” Vision Res. 13, 2017–2031 (1973).
[Crossref]

Rabin, J.

Regan, B.

B. Regan and J. Mollon, “The relative salience of the cardinal axes of colour space in normal and anomalous trichromats,” in Colour Vision Deficiencies XIII (Springer, 1997), pp. 261–270.

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, 950–952 (2005).
[Crossref]

Romeskie, M.

M. Romeskie, “Chromatic opponent-response functions of anomalous trichromats,” Vision Res. 18, 1521–1532 (1978).
[Crossref]

Rosner, M.

R. Doron, A. Sterkin, M. Fried, O. Yehezkel, M. Lev, M. Belkin, M. Rosner, A. S. Solomon, Y. Mandel, and U. Polat, “Spatial visual function in anomalous trichromats: Is less more?” PloS One 14, e0209662 (2019).
[Crossref]

Rushton, W.

W. Rushton, D. S. Powell, and K. White, “Pigments in anomalous trichromats,” Vision Res. 13, 2017–2031 (1973).
[Crossref]

Sarkar, D.

J. Pinheiro, D. Bates, S. DebRoy, and D. Sarkar, and R Core Team, nlme: Linear and Nonlinear Mixed Effects Models (2019), R package version 3.1-141.

Schneck, M. E.

Shevell, S. K.

S. K. Shevell and J. C. He, “The visual photopigments of simple deuteranomalous trichromats inferred from color matching,” Vision Res. 37, 1115–1127 (1997).
[Crossref]

Shows, T. B.

J. Nathans, T. P. Piantanida, R. L. Eddy, T. B. Shows, and D. S. Hogness, “Molecular genetics of inherited variation in human color vision,” Science 232, 203–210 (1986).
[Crossref]

Simpson, S.

J. Peirce, J. R. Gray, S. Simpson, M. MacAskill, R. Höchenberger, H. Sogo, E. Kastman, and J. K. Lindeløv, “Psychopy2: experiments in behavior made easy,” Behav. Res. Methods 51, 195–203 (2019).
[Crossref]

Smith, V. C.

Sogo, H.

J. Peirce, J. R. Gray, S. Simpson, M. MacAskill, R. Höchenberger, H. Sogo, E. Kastman, and J. K. Lindeløv, “Psychopy2: experiments in behavior made easy,” Behav. Res. Methods 51, 195–203 (2019).
[Crossref]

Sokolov, E.

G. Paramei, C. A. Izmailov, and E. Sokolov, “Multidimensional scaling of large chromatic differences by normal and color-deficient subjects,” Psychol. Sci. 2, 244–249 (1991).
[Crossref]

Solomon, A. S.

R. Doron, A. Sterkin, M. Fried, O. Yehezkel, M. Lev, M. Belkin, M. Rosner, A. S. Solomon, Y. Mandel, and U. Polat, “Spatial visual function in anomalous trichromats: Is less more?” PloS One 14, e0209662 (2019).
[Crossref]

Sterkin, A.

R. Doron, A. Sterkin, M. Fried, O. Yehezkel, M. Lev, M. Belkin, M. Rosner, A. S. Solomon, Y. Mandel, and U. Polat, “Spatial visual function in anomalous trichromats: Is less more?” PloS One 14, e0209662 (2019).
[Crossref]

Stiles, W.

M. Aguilar and W. Stiles, “Saturation of the rod mechanism of the retina at high levels of stimulation,” Opt. Acta 1, 59–65 (1954).
[Crossref]

Stromeyer, C.

A. Chaparro, C. Stromeyer, E. Huang, R. Kronauer, and R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
[Crossref]

Strutt, J.

J. Strutt, “Experiments on colour,” Nature 25, 64–66 (1881).
[Crossref]

Switkes, E.

Tregillus, K. E.

K. E. Tregillus, “Color perception in anomalous trichromats: Neuroimaging investigations of neural compensation for losses in spectral sensitivity,” Ph.D. thesis (University of Nevada, 2017).

Twer, T.

T. Twer and D. I. MacLeod, “Optimal nonlinear codes for the perception of natural colours,” Netw. Comput. Neural Syst. 12, 395–407 (2001).

Varner, D.

D. Jameson, L. Hurvich, and D. Varner, “Discrimination mechanisms in color deficient systems,” Doc. Ophthal. Proc. Ser. 33, 295–301 (1982).

Walker, S.

D. Bates, M. Mächler, B. Bolker, and S. Walker, “Fitting linear mixed-effects models using lme4,” J. Statist. Softw. 67, 1–48 (2015).
[Crossref]

Warnking, J.

E. Bellot, V. Coizet, J. Warnking, K. Knoblauch, E. Moro, and M. Dojat, “Effects of aging on low luminance contrast processing in humans,” NeuroImage 139, 415–426 (2016).
[Crossref]

Watson, A. B.

A. B. Watson and A. J. Ahumada, “A standard model for foveal detection of spatial contrast,” J. Vis. 5(9):6 (2005).
[Crossref]

Webster, M. A.

White, K.

W. Rushton, D. S. Powell, and K. White, “Pigments in anomalous trichromats,” Vision Res. 13, 2017–2031 (1973).
[Crossref]

Wiebel, C. B.

C. B. Wiebel, G. Aguilar, and M. Maertens, “Maximum likelihood difference scales represent perceptual magnitudes and predict appearance matches,” J. Vis. 17(4):1 (2017).
[Crossref]

Wood, S. N.

S. N. Wood, Core Statistics (Cambridge University, 2015), Vol. 6.

Wright, W.

W. M. McKeon and W. Wright, “The characteristics of protanomalous vision,” Proc. Phys. Soc. 52, 464–479 (1940).
[Crossref]

Yang, J. N.

L. T. Maloney and J. N. Yang, “Maximum likelihood difference scaling,” J. Vis. 3(8):5, 573–585 (2003).
[Crossref]

Yehezkel, O.

R. Doron, A. Sterkin, M. Fried, O. Yehezkel, M. Lev, M. Belkin, M. Rosner, A. S. Solomon, Y. Mandel, and U. Polat, “Spatial visual function in anomalous trichromats: Is less more?” PloS One 14, e0209662 (2019).
[Crossref]

Behav. Res. Methods (1)

J. Peirce, J. R. Gray, S. Simpson, M. MacAskill, R. Höchenberger, H. Sogo, E. Kastman, and J. K. Lindeløv, “Psychopy2: experiments in behavior made easy,” Behav. Res. Methods 51, 195–203 (2019).
[Crossref]

Curr. Biol. (1)

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, 950–952 (2005).
[Crossref]

Curr. Opin. Behav. Sci. (1)

J. Bosten, “The known unknowns of anomalous trichromacy,” Curr. Opin. Behav. Sci. 30, 228–237 (2019).
[Crossref]

Doc. Ophthal. Proc. Ser. (1)

D. Jameson, L. Hurvich, and D. Varner, “Discrimination mechanisms in color deficient systems,” Doc. Ophthal. Proc. Ser. 33, 295–301 (1982).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

J. Physiol. (3)

K. T. Mullen, “The contrast sensitivity of human colour vision to red-green and blue-yellow chromatic gratings,” J. Physiol. 359, 381–400 (1985).
[Crossref]

A. M. Derrington, J. Krauskopf, and P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. 357, 241–265 (1984).
[Crossref]

M. Alpern and J. Moeller, “The red and green cone visual pigments of deuteranomalous trichromacy,” J. Physiol. 266, 647–675 (1977).
[Crossref]

J. Statist. Softw. (2)

K. Knoblauch and L. T. Maloney, “MLDS: maximum likelihood difference scaling in R,” J. Statist. Softw. 25, 1–26 (2008).
[Crossref]

D. Bates, M. Mächler, B. Bolker, and S. Walker, “Fitting linear mixed-effects models using lme4,” J. Statist. Softw. 67, 1–48 (2015).
[Crossref]

J. Vis. (6)

M. Kwon, G. E. Legge, F. Fang, A. M. Cheong, and S. He, “Adaptive changes in visual cortex following prolonged contrast reduction,” J. Vis. 9(2):20, 1–16 (2009).
[Crossref]

L. T. Maloney and J. N. Yang, “Maximum likelihood difference scaling,” J. Vis. 3(8):5, 573–585 (2003).
[Crossref]

A. E. Boehm, D. I. MacLeod, and J. M. Bosten, “Compensation for red-green contrast loss in anomalous trichromats,” J. Vis. 14(13):19 (2014).
[Crossref]

F. Devinck and K. Knoblauch, “A common signal detection model accounts for both perception and discrimination of the watercolor effect,” J. Vis. 12(3):19 (2012).
[Crossref]

C. B. Wiebel, G. Aguilar, and M. Maertens, “Maximum likelihood difference scales represent perceptual magnitudes and predict appearance matches,” J. Vis. 17(4):1 (2017).
[Crossref]

A. B. Watson and A. J. Ahumada, “A standard model for foveal detection of spatial contrast,” J. Vis. 5(9):6 (2005).
[Crossref]

Nature (2)

J. Strutt, “Experiments on colour,” Nature 25, 64–66 (1881).
[Crossref]

A. Chaparro, C. Stromeyer, E. Huang, R. Kronauer, and R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
[Crossref]

Netw. Comput. Neural Syst. (1)

T. Twer and D. I. MacLeod, “Optimal nonlinear codes for the perception of natural colours,” Netw. Comput. Neural Syst. 12, 395–407 (2001).

NeuroImage (1)

E. Bellot, V. Coizet, J. Warnking, K. Knoblauch, E. Moro, and M. Dojat, “Effects of aging on low luminance contrast processing in humans,” NeuroImage 139, 415–426 (2016).
[Crossref]

Opt. Acta (1)

M. Aguilar and W. Stiles, “Saturation of the rod mechanism of the retina at high levels of stimulation,” Opt. Acta 1, 59–65 (1954).
[Crossref]

Percept. Psychophys. (1)

G. V. Paramei and C. R. Cavonius, “Color spaces of color-normal and color-abnormal observers reconstructed from response times and dissimilarity ratings,” Percept. Psychophys. 61, 1662–1674 (1999).
[Crossref]

PloS One (1)

R. Doron, A. Sterkin, M. Fried, O. Yehezkel, M. Lev, M. Belkin, M. Rosner, A. S. Solomon, Y. Mandel, and U. Polat, “Spatial visual function in anomalous trichromats: Is less more?” PloS One 14, e0209662 (2019).
[Crossref]

Proc. Phys. Soc. (1)

W. M. McKeon and W. Wright, “The characteristics of protanomalous vision,” Proc. Phys. Soc. 52, 464–479 (1940).
[Crossref]

Psychol. Sci. (1)

G. Paramei, C. A. Izmailov, and E. Sokolov, “Multidimensional scaling of large chromatic differences by normal and color-deficient subjects,” Psychol. Sci. 2, 244–249 (1991).
[Crossref]

Scand. J. Optom. Visual Sci. (1)

E. W. Dees and R. C. Baraas, “Fargede filtre gir ikke rød-grønne fargesvake normal fargebedømmelse,” Scand. J. Optom. Visual Sci. 4, 6–13 (2011).
[Crossref]

Science (2)

J. Nathans, T. P. Piantanida, R. L. Eddy, T. B. Shows, and D. S. Hogness, “Molecular genetics of inherited variation in human color vision,” Science 232, 203–210 (1986).
[Crossref]

S. L. Merbs and J. Nathans, “Absorption spectra of the hybrid pigments responsible for anomalous color vision,” Science 258, 464–466 (1992).
[Crossref]

Vision Res. (3)

W. Rushton, D. S. Powell, and K. White, “Pigments in anomalous trichromats,” Vision Res. 13, 2017–2031 (1973).
[Crossref]

S. K. Shevell and J. C. He, “The visual photopigments of simple deuteranomalous trichromats inferred from color matching,” Vision Res. 37, 1115–1127 (1997).
[Crossref]

M. Romeskie, “Chromatic opponent-response functions of anomalous trichromats,” Vision Res. 18, 1521–1532 (1978).
[Crossref]

Other (9)

M. Müller, C. Cavonius, and J. Mollon, “Constructing the color space of the deuteranomalous observer,” in Colour Vision Deficiencies X (Springer, 1991), pp. 377–387.

B. Regan and J. Mollon, “The relative salience of the cardinal axes of colour space in normal and anomalous trichromats,” in Colour Vision Deficiencies XIII (Springer, 1997), pp. 261–270.

L. M. Hurvich, “Color vision deficiencies,” in Visual Psychophysics (Springer, 1972), pp. 582–624.

K. Knoblauch and L. T. Maloney, Modeling Psychophysical Data in R (Springer, 2012), Vol. 32.

K. E. Tregillus, “Color perception in anomalous trichromats: Neuroimaging investigations of neural compensation for losses in spectral sensitivity,” Ph.D. thesis (University of Nevada, 2017).

D. I. MacLeod, “The Verriest Lecture. Colour discrimination, colour constancy and natural scene statistics,” in Normal and Defective Colour Vision, J. Mollon, J. Pokorny, and K. Knoblauch, eds. (Oxford University, 2003), pp. 189–217.

S. N. Wood, Core Statistics (Cambridge University, 2015), Vol. 6.

J. Pinheiro, D. Bates, S. DebRoy, and D. Sarkar, and R Core Team, nlme: Linear and Nonlinear Mixed Effects Models (2019), R package version 3.1-141.

R Core Team, R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, 2019).

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Figures (11)

Fig. 1.
Fig. 1. (a) DeMarco, Pokorny, and Smith fundamentals [8] for normal M and L cones (black solid and dashed, respectively) and average anomalous observers’ M’ and L’ cone spectral sensitivities (grey solid and dashed, respectively). (b) Difference spectra of two long-wavelength sensitive cone spectral sensitivity functions for average normal (black solid, L–M), protanomalous (grey solid, M’–M), and deuteranomalous (black dashed, L–L’) observers. The weights were chosen so that their magnitudes sum to unity and that the net response to an equal-energy light is zero.
Fig. 2.
Fig. 2. (a) Simulated chromatic contrast response curves for normal, protanomalous, and deuteranomalous observers, based on the assumption that the effective chromatic contrast is reduced in anomalous observers. (b) The same three curves plotted on a logarithmically spaced contrast axis.
Fig. 3.
Fig. 3. Three luminance Gabor stimuli from an example difference-scaling trial. The observer judges which of the two bottom stimuli appears most similar in contrast to the top stimulus.
Fig. 4.
Fig. 4. (a) Michaelis–Menten function plotted as a function of contrast with the initial value at $ {c_0} $ . The value of $ \varsigma $ is estimated with respect to $ {c_0} $ . The maximum asymptotic value is shown by the grey dashed line. (b) The same Michaelis–Menten function as in (a), plotted as a function of the log contrast. The log of the contrast gain, $ - \log (g) $ , is defined as the difference between the log contrast at the minimum contrast and that at the semi-saturation constant.
Fig. 5.
Fig. 5. CRDSs estimated by MLDS measured along the luminance (filled symbols) and L–M (unfilled symbols) axes in color space. The top row (a)–(c) shows data from individual normal (N1), protanomalous (P4), and deuteranomalous (D1) observers, plotted in nominal contrast units. The bottom row (d)–(f) shows the same data from the respective observers replotted as a function of cone contrast. The abscissa values are logarithmically spaced on all graphs. The solid curves are Michaelis–Menten functions best-fit by nonlinear least squares. The error bars are 95% confidence intervals.
Fig. 6.
Fig. 6. (a) Individual estimates of the minimally perceived contrast, $ {c_0} $ in nominal contrast units for normal (N), protanomalous (P), and deuteranomalous (D) observers along luminance and L–M axes. The open triangles on the L–M plot for protan and deutan observers correspond to the increase of the mean normal $ {c_0} $ value expected from the reduced separation of the cone spectral sensitivities. (b) Individual estimates of $ {c_0} $ adjusted in units of cone contrast for the three classes of observer and both axes of color space.
Fig. 7.
Fig. 7. (a) Population estimates from nonlinear mixed-effects model for luminance CRDS of normal (solid black), protanomalous (solid grey), and deuteranomalous (dashed black) observers. (b) Population estimates from nonlinear mixed-effects model for L–M CRDS in nominal contrast units for the three classes of observers using the same color coding as in (a).
Fig. 8.
Fig. 8. (a) Population mean and 95% confidence intervals of the response gain parameter, $ {R_m} $ for normal and anomalous trichromatic observers for CRDSs measured along the luminance and L–M axes. (b) Population mean and 95% confidence intervals of the log contrast gain, $ g^\prime $ , for normal and anomalous trichromatic observers for CRDSs measured along the luminance and L–M axes.
Fig. 9.
Fig. 9. Comparison of contrast, $ c $ , ranges over which the psychometric function for luminance contrast detection and MLDS scaling operate. The psychometric function (dashed curve and left ordinate values) is a Weibull function, $ 1 - \exp ( { - {{( {\frac{c}{\alpha }} )}^\beta }} ) $ , with threshold $ \alpha $ based on an estimation of the threshold of a 1 c/deg luminance Gabor function from the ModelFest dataset [38] with $ \beta = 3 $ . The MLDS function (solid curve and right ordinate values) represents the normal population luminance CRDS replotted from Fig. 7(a).
Fig. 10.
Fig. 10. Log contrast gain, $ g^\prime $ , as a function of response gain, $ {R_m} $ , along luminance (circles) and L–M (triangles) axes, for normal (white), protan (grey), and deutan (black) observers. The grey line is the predicted linear regression for all of the data. The black line segments are the best linear fits to the luminance (solid) and L–M (dashed) values for each of the three types of observers.
Fig. 11.
Fig. 11. CRDSs parameterized in terms of $ d^\prime $ for all individual observers on a nominal contrast scale, where the maximum contrast value corresponds to the maximum attainable contrast on the display. The black symbols are for measurements along the luminance axis and the white along the L–M axis. The curves are the best-fit Michaelis–Menten functions by a least-squares method. (a) Normal, (b) protanomalous, and (c) deuteranomalous.

Equations (7)

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R ( c ) = R m α c c 0 ( α c c 0 ) + ς = R m c c 0 / α ( c c 0 / α ) + ς / α ,
f ( x , y ) = L 0 ( 1 ± c θ exp ( x 2 + y 2 2 ) sin 2 π y ) ,
δ ( a , b , c ) = ( ψ ( b ) ψ ( a ) ) ( ψ ( c ) ψ ( b ) ) + ϵ = 2 ψ ( b ) ψ ( a ) ψ ( c ) + ϵ = Δ ( a , b , c ) + ϵ ,
( Ψ ; R ) = i = 1 n R i log ( Φ ( Δ i 2 σ ) ) + ( 1 R i ) log ( 1 Φ ( Δ i 2 σ ) ) ,
d ( c ) = R m c c 0 ( c c 0 ) + ς ,
d ( c ) = R m c c 0 ( c c 0 ) + c 0 ( 1 g ) g = R m g ( c c 0 ) g ( c 2 c 0 ) + c 0 ,
d o ( c ) = ( R m + R t + r o ) exp ( g + g t + g o ) ( c c 0 ) exp ( g + g t + g o ) ( c 2 c 0 ) + c 0 + ϵ i , ϵ i N ( 0 , σ 2 ) , r o N ( 0 , σ r o 2 ) , g o N ( 0 , σ g o 2 ) ,

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