Abstract

In a space where Cartesian coordinates represent the excitations of the three cone types involved in color vision, a plane of constant luminance provides a chromaticity diagram in which excitation of each cone type (at constant luminance) is represented by a linear scale (horizontal or vertical), and in which the center-of-gravity rule applies with weights proportional to luminance.

© 1979 Optical Society of America

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  1. T. N. Cornsweet, Visual Perception (Academic, New York, 1970),p. 189.
  2. In this paper the long-wavelength cones (loosely, red-sensitive cones) are referred to as R cones, the midspectral (green-sensitive) cones as G cones and the short wavelength (blue-sensitive) cones as B cones. The quantities R, G, and B are here used to stand for the excitations of the respective cone types by any given stimulus. The corresponding spectral sensitivities are the values of R, G, and B for an equal energy spectrum. The estimated spectral sensitivities for the three cone types used in constructing Figs. 1 and 2, expressed as linear combinations of Judd’s 1951 color matching functions, x¯j, y¯j, z¯j, areRλ=0.15514x¯jλ+0.54312y¯jλ−0.03286z¯jλ,Gλ=−0.15514x¯jλ+0.45684y¯jλ−0.03286z¯jλ,Bλ=0.01608z¯jλ.These are the spectral sensitivities of V. C. Smith and J. Pokorny [Vision Res. 15, 161–172 (1975)].The coefficient applied to z¯jλ is chosen for convenience, as explained in the text in connection with Fig. 2. Diagrams like the one proposed here could be constructed for any set of spectral sensitivities having the property that the sensitivities of the R and G cones summate to give the photopic luminosity function.
    [Crossref] [PubMed]
  3. The first true chromaticity diagram, suggested by J. Clerk Maxwell, Trans. R. Soc Edin. 21, 275–298 (1855), was of this form but the equilateral triangle has not been popular in recent times.A. Konig and C. Dieterici, Z. Psych.Physiol. Sinnesorg. 4, 241–347 (1893)W. A. H. Rushton, Invest. Ophthalmol. 10, 311–322 (1971) have proposed equilateral triangle diagrams based on cone excitations.
    [Crossref] [PubMed]
  4. For evidence that the B cones make no contribution to luminance, as measured by flicker photometry or by the approximately equivalent minimally distant border method, see Smith and Pokorny (Ref. 2),B. W. Tansley and R. M. Boynton, Vision Res. 18, 683–697 (1978),B. W. Tansley and R. J. Glushko, Vision Res. 18, 699–706 (1978).
    [Crossref]
  5. This drawback is characteristic of the CIE chromaticity diagram and all other chromaticity diagrams that have previously been proposed.
  6. A nonlinear transformation of a similar diagram, sharing this advantage, was introduced by R. W. Rockeck [The Vertebrate Retina (W. H. Freeman, San Francisco, 1973), p. 737] for the analysis of color discrimination.
  7. There is in fact reason to expect otherwise [see, for example, Fig. 6.57 on p. 558 of G. Wyszecki and W. S. Stiles, Color Science, (Wiley, New York, 1967)].
  8. Working copies of the chromaticity diagram, and tables of the chromaticity coordinates (rλ, bλ) for spectral lights, are available from the authors.

1978 (1)

For evidence that the B cones make no contribution to luminance, as measured by flicker photometry or by the approximately equivalent minimally distant border method, see Smith and Pokorny (Ref. 2),B. W. Tansley and R. M. Boynton, Vision Res. 18, 683–697 (1978),B. W. Tansley and R. J. Glushko, Vision Res. 18, 699–706 (1978).
[Crossref]

1975 (1)

In this paper the long-wavelength cones (loosely, red-sensitive cones) are referred to as R cones, the midspectral (green-sensitive) cones as G cones and the short wavelength (blue-sensitive) cones as B cones. The quantities R, G, and B are here used to stand for the excitations of the respective cone types by any given stimulus. The corresponding spectral sensitivities are the values of R, G, and B for an equal energy spectrum. The estimated spectral sensitivities for the three cone types used in constructing Figs. 1 and 2, expressed as linear combinations of Judd’s 1951 color matching functions, x¯j, y¯j, z¯j, areRλ=0.15514x¯jλ+0.54312y¯jλ−0.03286z¯jλ,Gλ=−0.15514x¯jλ+0.45684y¯jλ−0.03286z¯jλ,Bλ=0.01608z¯jλ.These are the spectral sensitivities of V. C. Smith and J. Pokorny [Vision Res. 15, 161–172 (1975)].The coefficient applied to z¯jλ is chosen for convenience, as explained in the text in connection with Fig. 2. Diagrams like the one proposed here could be constructed for any set of spectral sensitivities having the property that the sensitivities of the R and G cones summate to give the photopic luminosity function.
[Crossref] [PubMed]

1855 (1)

The first true chromaticity diagram, suggested by J. Clerk Maxwell, Trans. R. Soc Edin. 21, 275–298 (1855), was of this form but the equilateral triangle has not been popular in recent times.A. Konig and C. Dieterici, Z. Psych.Physiol. Sinnesorg. 4, 241–347 (1893)W. A. H. Rushton, Invest. Ophthalmol. 10, 311–322 (1971) have proposed equilateral triangle diagrams based on cone excitations.
[Crossref] [PubMed]

Boynton, R. M.

For evidence that the B cones make no contribution to luminance, as measured by flicker photometry or by the approximately equivalent minimally distant border method, see Smith and Pokorny (Ref. 2),B. W. Tansley and R. M. Boynton, Vision Res. 18, 683–697 (1978),B. W. Tansley and R. J. Glushko, Vision Res. 18, 699–706 (1978).
[Crossref]

Cornsweet, T. N.

T. N. Cornsweet, Visual Perception (Academic, New York, 1970),p. 189.

Maxwell, J. Clerk

The first true chromaticity diagram, suggested by J. Clerk Maxwell, Trans. R. Soc Edin. 21, 275–298 (1855), was of this form but the equilateral triangle has not been popular in recent times.A. Konig and C. Dieterici, Z. Psych.Physiol. Sinnesorg. 4, 241–347 (1893)W. A. H. Rushton, Invest. Ophthalmol. 10, 311–322 (1971) have proposed equilateral triangle diagrams based on cone excitations.
[Crossref] [PubMed]

Pokorny, J.

In this paper the long-wavelength cones (loosely, red-sensitive cones) are referred to as R cones, the midspectral (green-sensitive) cones as G cones and the short wavelength (blue-sensitive) cones as B cones. The quantities R, G, and B are here used to stand for the excitations of the respective cone types by any given stimulus. The corresponding spectral sensitivities are the values of R, G, and B for an equal energy spectrum. The estimated spectral sensitivities for the three cone types used in constructing Figs. 1 and 2, expressed as linear combinations of Judd’s 1951 color matching functions, x¯j, y¯j, z¯j, areRλ=0.15514x¯jλ+0.54312y¯jλ−0.03286z¯jλ,Gλ=−0.15514x¯jλ+0.45684y¯jλ−0.03286z¯jλ,Bλ=0.01608z¯jλ.These are the spectral sensitivities of V. C. Smith and J. Pokorny [Vision Res. 15, 161–172 (1975)].The coefficient applied to z¯jλ is chosen for convenience, as explained in the text in connection with Fig. 2. Diagrams like the one proposed here could be constructed for any set of spectral sensitivities having the property that the sensitivities of the R and G cones summate to give the photopic luminosity function.
[Crossref] [PubMed]

Rockeck, R. W.

A nonlinear transformation of a similar diagram, sharing this advantage, was introduced by R. W. Rockeck [The Vertebrate Retina (W. H. Freeman, San Francisco, 1973), p. 737] for the analysis of color discrimination.

Smith, V. C.

In this paper the long-wavelength cones (loosely, red-sensitive cones) are referred to as R cones, the midspectral (green-sensitive) cones as G cones and the short wavelength (blue-sensitive) cones as B cones. The quantities R, G, and B are here used to stand for the excitations of the respective cone types by any given stimulus. The corresponding spectral sensitivities are the values of R, G, and B for an equal energy spectrum. The estimated spectral sensitivities for the three cone types used in constructing Figs. 1 and 2, expressed as linear combinations of Judd’s 1951 color matching functions, x¯j, y¯j, z¯j, areRλ=0.15514x¯jλ+0.54312y¯jλ−0.03286z¯jλ,Gλ=−0.15514x¯jλ+0.45684y¯jλ−0.03286z¯jλ,Bλ=0.01608z¯jλ.These are the spectral sensitivities of V. C. Smith and J. Pokorny [Vision Res. 15, 161–172 (1975)].The coefficient applied to z¯jλ is chosen for convenience, as explained in the text in connection with Fig. 2. Diagrams like the one proposed here could be constructed for any set of spectral sensitivities having the property that the sensitivities of the R and G cones summate to give the photopic luminosity function.
[Crossref] [PubMed]

Stiles, W. S.

There is in fact reason to expect otherwise [see, for example, Fig. 6.57 on p. 558 of G. Wyszecki and W. S. Stiles, Color Science, (Wiley, New York, 1967)].

Tansley, B. W.

For evidence that the B cones make no contribution to luminance, as measured by flicker photometry or by the approximately equivalent minimally distant border method, see Smith and Pokorny (Ref. 2),B. W. Tansley and R. M. Boynton, Vision Res. 18, 683–697 (1978),B. W. Tansley and R. J. Glushko, Vision Res. 18, 699–706 (1978).
[Crossref]

Wyszecki, G.

There is in fact reason to expect otherwise [see, for example, Fig. 6.57 on p. 558 of G. Wyszecki and W. S. Stiles, Color Science, (Wiley, New York, 1967)].

Trans. R. Soc Edin. (1)

The first true chromaticity diagram, suggested by J. Clerk Maxwell, Trans. R. Soc Edin. 21, 275–298 (1855), was of this form but the equilateral triangle has not been popular in recent times.A. Konig and C. Dieterici, Z. Psych.Physiol. Sinnesorg. 4, 241–347 (1893)W. A. H. Rushton, Invest. Ophthalmol. 10, 311–322 (1971) have proposed equilateral triangle diagrams based on cone excitations.
[Crossref] [PubMed]

Vision Res. (2)

For evidence that the B cones make no contribution to luminance, as measured by flicker photometry or by the approximately equivalent minimally distant border method, see Smith and Pokorny (Ref. 2),B. W. Tansley and R. M. Boynton, Vision Res. 18, 683–697 (1978),B. W. Tansley and R. J. Glushko, Vision Res. 18, 699–706 (1978).
[Crossref]

In this paper the long-wavelength cones (loosely, red-sensitive cones) are referred to as R cones, the midspectral (green-sensitive) cones as G cones and the short wavelength (blue-sensitive) cones as B cones. The quantities R, G, and B are here used to stand for the excitations of the respective cone types by any given stimulus. The corresponding spectral sensitivities are the values of R, G, and B for an equal energy spectrum. The estimated spectral sensitivities for the three cone types used in constructing Figs. 1 and 2, expressed as linear combinations of Judd’s 1951 color matching functions, x¯j, y¯j, z¯j, areRλ=0.15514x¯jλ+0.54312y¯jλ−0.03286z¯jλ,Gλ=−0.15514x¯jλ+0.45684y¯jλ−0.03286z¯jλ,Bλ=0.01608z¯jλ.These are the spectral sensitivities of V. C. Smith and J. Pokorny [Vision Res. 15, 161–172 (1975)].The coefficient applied to z¯jλ is chosen for convenience, as explained in the text in connection with Fig. 2. Diagrams like the one proposed here could be constructed for any set of spectral sensitivities having the property that the sensitivities of the R and G cones summate to give the photopic luminosity function.
[Crossref] [PubMed]

Other (5)

T. N. Cornsweet, Visual Perception (Academic, New York, 1970),p. 189.

This drawback is characteristic of the CIE chromaticity diagram and all other chromaticity diagrams that have previously been proposed.

A nonlinear transformation of a similar diagram, sharing this advantage, was introduced by R. W. Rockeck [The Vertebrate Retina (W. H. Freeman, San Francisco, 1973), p. 737] for the analysis of color discrimination.

There is in fact reason to expect otherwise [see, for example, Fig. 6.57 on p. 558 of G. Wyszecki and W. S. Stiles, Color Science, (Wiley, New York, 1967)].

Working copies of the chromaticity diagram, and tables of the chromaticity coordinates (rλ, bλ) for spectral lights, are available from the authors.

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Figures (3)

FIG. 1
FIG. 1

Cone excitation space. The R and B axes lie in the plane of the paper, and the apparently oblique G axis should be considered as orthogonal to the other two, receding into the distance behind the plane of the paper. In Fig. 1(a) the obliquely oriented equilateral triangle R + G + B = 1 is indicated by dashed lines. In Fig. 1(b) dashed lines indicate the plane of constant luminance R + G = 1, and the spectrum locus in that plane is shown.

FIG. 2
FIG. 2

Proposed (r, b) chromaticity diagram [equivalent to the dashed plane in Fig. 1(b)] showing spectrum locus and confusion lines of protanopes (P) and deuteranopes (D). The point indicated by W is the equal energy white.

FIG. 3
FIG. 3

Projection onto the (r, b) diagram in cone excitation space, illustrated for colors confused by deuteranopes. The confusion lines aan, bbn, ccn, ddn are parallel to the G axis. Connections from these four lines to the origin lie in four planes radiating from the G axis as shown. Thus, the projections of the four lines in the plane of the chromaticity diagram are the converging lines Da, Db, Dc, and Dd, which are where the four radiating planes meet the plane of the diagram.

Equations (2)

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r = R / ( R + G ) g = G / ( R + G ) b = B / ( R + G ) .
Rλ=0.15514x¯jλ+0.54312y¯jλ0.03286z¯jλ,Gλ=0.15514x¯jλ+0.45684y¯jλ0.03286z¯jλ,Bλ=0.01608z¯jλ.