Abstract

The hue discrimination curve (HDC) that characterizes performances over the entire hue circle was determined by using sinusoidally modulated spectral power distributions of 1.5c/300nm with fixed amplitude and twelve reference phases. To investigate relationship between hue discrimination and appearance, observers further performed a free color naming and unique hue tasks. The HDC consistently displayed two minima and two maxima; discrimination is optimal at the yellow/orange and blue/magenta boundaries and pessimal in green and in the extra-spectral magenta colors. A linear model based on Müller zone theory correctly predicts a periodical profile but with a phase-opponency (minima/maxima at 180° apart) which is inconsistent with the empirical HDC’s profile.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2010 (1)

M. V. Danilova and J. D. Mollon, “Parafoveal color discrimination: A chromaticity locus of enhanced discrimination,” J.Vis. 10, 1–9 (2010).

2007 (1)

2006 (3)

H. Sun, H. E. Smithson, Q. Zaidi, and B. B. Lee, “Specificity of cone inputs to macaque retinal ganglion cells,” J. Neurophysiol. 95, 837–849 (2006).
[CrossRef]

A. L. Gilbert, T. Regier, P. Kay, and R. B. Ivry, “Whorf hypothesis is supported in the right visual field but not the left,” Proc. Natl. Acad. Sci. U.S.A. 103, 489–494 (2006).
[CrossRef]

Y. Mizokami, J. S. Werner, M. A. Crognale, and M. A. Webster, “Nonlinearities in color coding: Compensating color appearance for the eye’s spectral sensitivity,” J. Vis. 6, 996–1007 (2006).
[CrossRef]

2005 (1)

S. M. Wuerger, P. Atkinson, and S. Cropper, “The cone inputs to the unique-hue mechanisms,” Vis. Res. 45, 3210–3223(2005).
[CrossRef]

2004 (1)

R. G. Kuehni, “Variability in unique hue selection: A surprising phenomenon,” Color Res. Appl. 29, 158–162 (2004).

2003 (1)

V. Bonnardel and F. J. Varela, “Color vision in the comb frequency domain,” Biol. Res. Preg. Perinatology 36, 119–134 (2003).

2002 (1)

2001 (2)

V. Bonnardel and E. M. Valero, “Study of colour discrimination with comb-filtered spectra,” Vis. Res. 41, 541–548 (2001).
[CrossRef]

K. A. Jameson, S. M. Highnote, and L. M. Wasserman, “Richer color experience in observers with multiple photopigment opsin genes,” Psychon. Bull. Rev. 8, 244–261 (2001).

2000 (3)

1996 (1)

V. Bonnardel, H. Bellemare, and J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vis. Res. 36, 2713–2720 (1996).
[CrossRef]

1995 (1)

1994 (1)

N. Smeulders, F. W. Campbell, and P. R. Andrews, “The role of delineation and spatial frequency in the perception of the colours of the spectrum,” Vis. Res. 34, 927–936 (1994).
[CrossRef]

1982 (1)

H. Barlow, “What causes trichromacy? A theoretical analysis using comb-filtered spectra,” Vis. Res. 22, 635–643 (1982).
[CrossRef]

1969 (1)

T. Holtsmark and A. Valberg, “Colour discrimination and hue,” Nature 224, 366–367 (1969).
[CrossRef]

1934 (1)

W. D. Wright and F. H. G. Pitt, “Hue-discrimination in normal colour-vision,” Proc. Phys. Soc. 46, 459–473 (1934).

Andrews, P. R.

N. Smeulders, F. W. Campbell, and P. R. Andrews, “The role of delineation and spatial frequency in the perception of the colours of the spectrum,” Vis. Res. 34, 927–936 (1994).
[CrossRef]

Atkinson, P.

S. M. Wuerger, P. Atkinson, and S. Cropper, “The cone inputs to the unique-hue mechanisms,” Vis. Res. 45, 3210–3223(2005).
[CrossRef]

Barlow, H.

H. Barlow, “What causes trichromacy? A theoretical analysis using comb-filtered spectra,” Vis. Res. 22, 635–643 (1982).
[CrossRef]

Bellemare, H.

V. Bonnardel, H. Bellemare, and J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vis. Res. 36, 2713–2720 (1996).
[CrossRef]

Bharadwaj, S.

Bonnardel, V.

V. Bonnardel and F. J. Varela, “Color vision in the comb frequency domain,” Biol. Res. Preg. Perinatology 36, 119–134 (2003).

V. Bonnardel and E. M. Valero, “Study of colour discrimination with comb-filtered spectra,” Vis. Res. 41, 541–548 (2001).
[CrossRef]

V. Bonnardel and L. T. Maloney, “Daylight, biochrome surfaces, and human chromatic response in the fourier domain,” J. Opt. Soc. Am. A 17, 677–686 (2000).
[CrossRef]

V. Bonnardel, H. Bellemare, and J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vis. Res. 36, 2713–2720 (1996).
[CrossRef]

Brainard, D. H.

A. Stockman and D. H. Brainard, “Color vision mechanisms,” in “Handbook of Optics, Volume III: Vision and Vision Optics,” 3rd ed., M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. van Stryland, eds. (McGraw-Hill Professional, 2010), Chap. 11, pp. 11.1–11.104.

Campbell, F. W.

N. Smeulders, F. W. Campbell, and P. R. Andrews, “The role of delineation and spatial frequency in the perception of the colours of the spectrum,” Vis. Res. 34, 927–936 (1994).
[CrossRef]

Crognale, M. A.

Y. Mizokami, J. S. Werner, M. A. Crognale, and M. A. Webster, “Nonlinearities in color coding: Compensating color appearance for the eye’s spectral sensitivity,” J. Vis. 6, 996–1007 (2006).
[CrossRef]

Cropper, S.

S. M. Wuerger, P. Atkinson, and S. Cropper, “The cone inputs to the unique-hue mechanisms,” Vis. Res. 45, 3210–3223(2005).
[CrossRef]

Danilova, M. V.

M. V. Danilova and J. D. Mollon, “Parafoveal color discrimination: A chromaticity locus of enhanced discrimination,” J.Vis. 10, 1–9 (2010).

Gilbert, A. L.

A. L. Gilbert, T. Regier, P. Kay, and R. B. Ivry, “Whorf hypothesis is supported in the right visual field but not the left,” Proc. Natl. Acad. Sci. U.S.A. 103, 489–494 (2006).
[CrossRef]

Harnad, S.

S. Harnad, “Psychophysical and cognitive aspects of categorical perception: A critical overview,” in Categorical Perception: The Groundwork of Cognition,S. Harnad, ed. (Cambridge University , 1987), Chap. 1, pp. 1–52.

Highnote, S. M.

K. A. Jameson, S. M. Highnote, and L. M. Wasserman, “Richer color experience in observers with multiple photopigment opsin genes,” Psychon. Bull. Rev. 8, 244–261 (2001).

Holtsmark, T.

T. Holtsmark and A. Valberg, “Colour discrimination and hue,” Nature 224, 366–367 (1969).
[CrossRef]

Ivry, R. B.

A. L. Gilbert, T. Regier, P. Kay, and R. B. Ivry, “Whorf hypothesis is supported in the right visual field but not the left,” Proc. Natl. Acad. Sci. U.S.A. 103, 489–494 (2006).
[CrossRef]

Jaikumar, J.

Jameson, K. A.

K. A. Jameson, S. M. Highnote, and L. M. Wasserman, “Richer color experience in observers with multiple photopigment opsin genes,” Psychon. Bull. Rev. 8, 244–261 (2001).

Kay, P.

A. L. Gilbert, T. Regier, P. Kay, and R. B. Ivry, “Whorf hypothesis is supported in the right visual field but not the left,” Proc. Natl. Acad. Sci. U.S.A. 103, 489–494 (2006).
[CrossRef]

Kuehni, R. G.

R. G. Kuehni, “Variability in unique hue selection: A surprising phenomenon,” Color Res. Appl. 29, 158–162 (2004).

Lee, B. B.

H. Sun, H. E. Smithson, Q. Zaidi, and B. B. Lee, “Specificity of cone inputs to macaque retinal ganglion cells,” J. Neurophysiol. 95, 837–849 (2006).
[CrossRef]

Madan, G.

Malkoc, G.

Maloney, L. T.

Miyahara, E.

Mizokami, Y.

Y. Mizokami, J. S. Werner, M. A. Crognale, and M. A. Webster, “Nonlinearities in color coding: Compensating color appearance for the eye’s spectral sensitivity,” J. Vis. 6, 996–1007 (2006).
[CrossRef]

Mollon, J. D.

M. V. Danilova and J. D. Mollon, “Parafoveal color discrimination: A chromaticity locus of enhanced discrimination,” J.Vis. 10, 1–9 (2010).

V. Bonnardel, H. Bellemare, and J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vis. Res. 36, 2713–2720 (1996).
[CrossRef]

Pitt, F. H. G.

W. D. Wright and F. H. G. Pitt, “Hue-discrimination in normal colour-vision,” Proc. Phys. Soc. 46, 459–473 (1934).

Pokorny, J.

Raker, V. E.

Regier, T.

A. L. Gilbert, T. Regier, P. Kay, and R. B. Ivry, “Whorf hypothesis is supported in the right visual field but not the left,” Proc. Natl. Acad. Sci. U.S.A. 103, 489–494 (2006).
[CrossRef]

Sharpe, T. L.

A. Stockman and T. L. Sharpe, “The spectral sensitivities of the middle- and long-wavelength-sensitive cones derived from measurements in observers of known genotype,” Vis. Res. 40, 1711–1737 (2000).
[CrossRef]

Smeulders, N.

N. Smeulders, F. W. Campbell, and P. R. Andrews, “The role of delineation and spatial frequency in the perception of the colours of the spectrum,” Vis. Res. 34, 927–936 (1994).
[CrossRef]

Smith, V. C.

Smithson, H. E.

H. Sun, H. E. Smithson, Q. Zaidi, and B. B. Lee, “Specificity of cone inputs to macaque retinal ganglion cells,” J. Neurophysiol. 95, 837–849 (2006).
[CrossRef]

Stockman, A.

A. Stockman and T. L. Sharpe, “The spectral sensitivities of the middle- and long-wavelength-sensitive cones derived from measurements in observers of known genotype,” Vis. Res. 40, 1711–1737 (2000).
[CrossRef]

A. Stockman and D. H. Brainard, “Color vision mechanisms,” in “Handbook of Optics, Volume III: Vision and Vision Optics,” 3rd ed., M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. van Stryland, eds. (McGraw-Hill Professional, 2010), Chap. 11, pp. 11.1–11.104.

Sun, H.

H. Sun, H. E. Smithson, Q. Zaidi, and B. B. Lee, “Specificity of cone inputs to macaque retinal ganglion cells,” J. Neurophysiol. 95, 837–849 (2006).
[CrossRef]

Vaithilingham, E.

Valberg, A.

T. Holtsmark and A. Valberg, “Colour discrimination and hue,” Nature 224, 366–367 (1969).
[CrossRef]

Valero, E. M.

V. Bonnardel and E. M. Valero, “Study of colour discrimination with comb-filtered spectra,” Vis. Res. 41, 541–548 (2001).
[CrossRef]

van de Kraats, J.

van Norren, D.

Varela, F. J.

V. Bonnardel and F. J. Varela, “Color vision in the comb frequency domain,” Biol. Res. Preg. Perinatology 36, 119–134 (2003).

Verma, R.

Wasserman, L. M.

K. A. Jameson, S. M. Highnote, and L. M. Wasserman, “Richer color experience in observers with multiple photopigment opsin genes,” Psychon. Bull. Rev. 8, 244–261 (2001).

Webster, M. A.

Webster, S. M.

Werner, J. S.

Y. Mizokami, J. S. Werner, M. A. Crognale, and M. A. Webster, “Nonlinearities in color coding: Compensating color appearance for the eye’s spectral sensitivity,” J. Vis. 6, 996–1007 (2006).
[CrossRef]

Wright, W. D.

W. D. Wright and F. H. G. Pitt, “Hue-discrimination in normal colour-vision,” Proc. Phys. Soc. 46, 459–473 (1934).

Wuerger, S. M.

S. M. Wuerger, P. Atkinson, and S. Cropper, “The cone inputs to the unique-hue mechanisms,” Vis. Res. 45, 3210–3223(2005).
[CrossRef]

Zaidi, Q.

H. Sun, H. E. Smithson, Q. Zaidi, and B. B. Lee, “Specificity of cone inputs to macaque retinal ganglion cells,” J. Neurophysiol. 95, 837–849 (2006).
[CrossRef]

Biol. Res. Preg. Perinatology (1)

V. Bonnardel and F. J. Varela, “Color vision in the comb frequency domain,” Biol. Res. Preg. Perinatology 36, 119–134 (2003).

Color Res. Appl. (1)

R. G. Kuehni, “Variability in unique hue selection: A surprising phenomenon,” Color Res. Appl. 29, 158–162 (2004).

J. Neurophysiol. (1)

H. Sun, H. E. Smithson, Q. Zaidi, and B. B. Lee, “Specificity of cone inputs to macaque retinal ganglion cells,” J. Neurophysiol. 95, 837–849 (2006).
[CrossRef]

J. Opt. Soc. Am. A (5)

J. Vis. (1)

Y. Mizokami, J. S. Werner, M. A. Crognale, and M. A. Webster, “Nonlinearities in color coding: Compensating color appearance for the eye’s spectral sensitivity,” J. Vis. 6, 996–1007 (2006).
[CrossRef]

J.Vis. (1)

M. V. Danilova and J. D. Mollon, “Parafoveal color discrimination: A chromaticity locus of enhanced discrimination,” J.Vis. 10, 1–9 (2010).

Nature (1)

T. Holtsmark and A. Valberg, “Colour discrimination and hue,” Nature 224, 366–367 (1969).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

A. L. Gilbert, T. Regier, P. Kay, and R. B. Ivry, “Whorf hypothesis is supported in the right visual field but not the left,” Proc. Natl. Acad. Sci. U.S.A. 103, 489–494 (2006).
[CrossRef]

Proc. Phys. Soc. (1)

W. D. Wright and F. H. G. Pitt, “Hue-discrimination in normal colour-vision,” Proc. Phys. Soc. 46, 459–473 (1934).

Psychon. Bull. Rev. (1)

K. A. Jameson, S. M. Highnote, and L. M. Wasserman, “Richer color experience in observers with multiple photopigment opsin genes,” Psychon. Bull. Rev. 8, 244–261 (2001).

Vis. Res. (6)

N. Smeulders, F. W. Campbell, and P. R. Andrews, “The role of delineation and spatial frequency in the perception of the colours of the spectrum,” Vis. Res. 34, 927–936 (1994).
[CrossRef]

H. Barlow, “What causes trichromacy? A theoretical analysis using comb-filtered spectra,” Vis. Res. 22, 635–643 (1982).
[CrossRef]

V. Bonnardel, H. Bellemare, and J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vis. Res. 36, 2713–2720 (1996).
[CrossRef]

V. Bonnardel and E. M. Valero, “Study of colour discrimination with comb-filtered spectra,” Vis. Res. 41, 541–548 (2001).
[CrossRef]

A. Stockman and T. L. Sharpe, “The spectral sensitivities of the middle- and long-wavelength-sensitive cones derived from measurements in observers of known genotype,” Vis. Res. 40, 1711–1737 (2000).
[CrossRef]

S. M. Wuerger, P. Atkinson, and S. Cropper, “The cone inputs to the unique-hue mechanisms,” Vis. Res. 45, 3210–3223(2005).
[CrossRef]

Other (2)

A. Stockman and D. H. Brainard, “Color vision mechanisms,” in “Handbook of Optics, Volume III: Vision and Vision Optics,” 3rd ed., M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. van Stryland, eds. (McGraw-Hill Professional, 2010), Chap. 11, pp. 11.1–11.104.

S. Harnad, “Psychophysical and cognitive aspects of categorical perception: A critical overview,” in Categorical Perception: The Groundwork of Cognition,S. Harnad, ed. (Cambridge University , 1987), Chap. 1, pp. 1–52.

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Figures (8)

Fig. 1.
Fig. 1.

Chromaticity coordinates of our stimuli plotted in the CIE 1931 diagram lie on an elliptical contour (dashed line) when phase varies from 0 to 360°. Empirical measures of the sinusoidally modulated spectra are shown in Appendix A [Fig. 6(b)]. The locus of background illuminant is indicated by the cross.

Fig. 2.
Fig. 2.

Thresholds Δ(φ) are plotted in function of the reference phase φ for observers VB (black line) and RB (gray line). Minimal thresholds (empty symbols) are located at 330° for the two observers and at 90 and 100° for VB and RB, respectively. Maximal threshold (filled symbols) are located for the two observers at 30° and at 180° and 210° for VB and RB, respectively. Vertical bars indicate the location of unique hues at 79, 122, 220, and 317° for VB and 76, 117, 196, and 320° for RB.

Fig. 3.
Fig. 3.

For each observer, a section of the CIE 1931 diagram showing minimum (empty symbols) and maximum (filled symbols) of discrimination and unique hue (plain circles) loci together with the line that runs from approximately unique yellow (576 nm) to approximately unique blue (476 nm). For the two observers, unique yellow and unique blue are in close proximity with the unique hue line.

Fig. 4.
Fig. 4.

Hue circle obtained from simulated hues corresponding to a 10° phase-step. This simulation, valid for a sRGB color space display, takes into account the background illuminant of our experimental condition. Color names for 12 stimuli in 30° steps are reported for VB (top) and RB (bottom). An additional color name is reported for RB’s optimal discrimination at 100°. Thick black lines indicate the unique hue loci. Minima (1) and maxima (2) of discrimination elicit names corresponding to binary hues.

Fig. 5.
Fig. 5.

Computed hue discrimination curve at stage two (black line) and at stage three (gray line) as proposed by Stockman Brainard (2010) [17] (see Subsection 4.B for explanation).

Fig. 6.
Fig. 6.

(a) Electronic mask profiles, (b) measured SPDs SPDφ(λ) (black lines) and measured unmodulated light E0 (thick gray line), (c) (SPDφ(λ)/E0(λ))1 (black lines) compared to the electronic mask profiles (gray lines), (d) Estimated gain function a(λ) (black line) and its linear approximation A(λ) (thick gray line).

Fig. 7.
Fig. 7.

(a) Stockman and Sharpe (2000) 2° cone spectral sensitivities [18], L(λ), M(λ), and S(λ). (b) Response function calculated with Eq. (4), L(φ), M(φ), and S(φ). (c) Derivative functions corresponding to sensitivity threshold, L(φ), M(φ), and S(φ).

Fig. 8.
Fig. 8.

(a) Spectral sensitivities T(λ)=L(λ)M(λ) and D(λ)=S(λ)0.69×(L(λ)+0.5×M(λ)). (b) Response function calculated with Eq. (5), T(φ) and D(φ). (c) Derivative functions corresponding to sensitivity threshold, T(φ) and D(φ).

Equations (18)

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

SPDφ(λ)=A(λ)E0(λ)(Eφ(λ)1)+E0(λ)withEφ(λ)=1+msin(p(f(1.2λ+480)+φ)).
Eφ(λ)=1+msin(p(f(1.2λ+480)+φ)).
SPDφ(λ)=A(λ)E0(λ)(Eφ(λ)1)+E0(λ).
{L(φ)=λL(λ)SPDφ(λ)dλM(φ)=λM(λ)SPDφ(λ)dλS(φ)=λS(λ)SPDφ(λ)dλ.
Eφ(λ)=1+msin(pf(1.2λ+480)a+pφΦ)=1+msin(a)cos(Φ)+msin(Φ)cos(a)SPDφ(λ)=A(λ)E0(λ)(Eφ(λ)1)+E0(λ)=E0(λ)+msin(a)cos(Φ)A(λ)E0(λ)+msin(Φ)cos(a)A(λ)E0(λ).
L(φ)=λE0(λ)L(λ)dλAL+cos(Φ)mλA(λ)E0(λ)sin(a)L(λ)dλCL+sin(Φ)mλA(λ)E0(λ)cos(a)L(λ)dλDL=AL+CLcos(Φ)+DLsin(Φ),
L(φ)=AL+BLsin(Φ+KL)with:BL=CL2+DL2andKL=arctan(CLDL).
Acosx+Bsinx=Csin(x+p)withC=A2+B2andp=arctan(AB).
Acosx+Bsinx=Csin(x+p)Acosx+Bsinx=Csinxcosp+Ccosxsinp.
{A=CsinpB=Csinp{A2+B2=C2(sin2p+cos2p)=1AB=sinpcosp=tanp{C=A2+B2p=arctan(AB).
{L(φ)=AL+BLsin(Φ+KL)M(φ)=AM+BMsin(Φ+KM)S(φ)=AS+BSsin(Φ+KS).
with fori{L,M,S}Ai=λE0(λ)i(λ)dλBi=mCi2+Di2Ki=arctan(CiDi)Ci=mλA(λ)E0(λ)sin(a)i(λ)dλDi=mλA(λ)E0(λ)cos(a)i(λ)dλanda=pf(1.2λ480),Φ=pφ,p=2π360.
[A(φ)T(φ)D(φ)]Y(φ)=[n11n12n13n21n22n23n31n22n33]M[L(φ)M(φ)S(φ)]X(φ).
Y(φ)=MX(φ),Y(φ)=MX(φ).
(Δφ)2=1Y(φ)TY(φ)=1X(φ)TMTMX(φ).
X(φ)=[pBLcos(pφ+KL)pBMcos(pφ+KM)pBScos(pφ+KS)]=[pBLcos(pφ)cos(KL)pBLsin(pφ)sin(KL)pBMcos(pφ)cos(KM)pBMsin(pφ)sin(KM)pBScos(pφ)cos(KS)pBSsin(pφ)sin(KS)]=pcos(pφ)[BLcos(KL)BMcos(KM)BScos(KS)]Ipsin(pφ)[BLsin(KL)BMsin(KM)BSsin(KS)]JX(φ)=pcos(pφ)Ipsin(pφ)J.
X(φ)TMTMX(φ)=(pcos(pφ)Ipsin(pφ)J)TMTM(pcos(pφ)Ipsin(pφ)J)=p2(cos(pφ))2ITMTMIp2cos(pφ)sin(pφ)(ITMTMJ+JTMTMI)+p2(sin(pφ))2JTMTMJwhich could be written using proof belowX(φ)TMTMX(φ)=A+Bcos(2pφ+K).
Δφ=1A+Bcos(2pφ+K)withA=p22(C+F),B=p22(CF)2+(D+E)2K=arctan(D+ECF)C=ITMTMID=ITMTMJE=JTMTMIF=JTMTMJ.

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