Abstract

Theories of color-difference measurement provide a quantitative means for predicting whether two lights will be discriminable to an average observer. Consider the following color-measurement hypothesis. Suppose that two lights evoke responses from the color channels that we write as vectors, U and U′. The vector difference dU = UU′ is itself a set of channel responses that will result from the presentation of some light. I test the hypothesis that U and U′ will be discriminable only if the light that gives rise to their differential, dU, is detectable. In the absence of a luminance component in the difference stimulus, dU, the vector-difference hypothesis holds well. In the presence of a luminance component, the theory is clearly false. When a luminance component is present, discrimination judgments depend largely on whether the lights U and U′ are in separate, categorical regions of color space.

© 1985 Optical Society of America

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References

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  1. G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).
  2. B. A. Wandell, “Measurements of small color differences,” Psychol. Rev. 89, 281–302 (1982).
    [Crossref] [PubMed]
  3. F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).
  4. D. Sagi, S. Hochstein, “Discriminability of suprathreshold compound spatial frequency gratings,” Vision Res. 23, 1595–1608 (1983).
    [Crossref] [PubMed]
  5. A. B. Watson, “Detection and recognition of simple spatial forms,”.
  6. H. R. Wilson, D. J. Gelb, “Modified line-element theory for spatial-frequency and width discrimination,” J. Opt. Soc. Am. A 1, 124–131 (1984).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  13. D. Gabor, “Theory of Communication,” J. EE (London) 93, 429–457 (1946).
  14. R. F. Quick, “A vector magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
    [Crossref]
  15. L. T. Maloney, B. A. Wandell, “A model of a single visual channel’s response to weak test lights,” Vision Res. 24, 633–640 (1984).
    [Crossref]
  16. A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979).
    [Crossref] [PubMed]
  17. L. T. Maloney, B. A. Wandell, “The slope of the psychometric functions at different wavelengths,” Invest. Ophthalmol. Visual Sci. Suppl. 24, 183A (1983).
  18. J. Nachmias, “On the psychometric function for contrast detection,” Vision Res. 21, 215–223 (1981).
    [Crossref] [PubMed]
  19. W. S. Stiles, “Mechanism concepts in colour theory,” J. Colour Group 11, 106–123 (1967).
  20. B. A. Wandell, P. Ahumada, D. K. Welsh, “Reaction times to weak test lights,” Vision Res. 24, 647–652 (1984).
    [Crossref] [PubMed]
  21. J. Thornton, E. N. Pugh, “Red/green color opponency at detection threshold,” Science 219, 191–193 (1983).
    [Crossref] [PubMed]
  22. D. H. Kelly, D. van Norren, “Two-band model of heterochromatic flicker,”J. Opt. Soc. Am. 67, 1081–1091 (1977).
    [Crossref] [PubMed]
  23. S. L. Guth, N. J. Donley, R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
    [Crossref] [PubMed]
  24. B. A. Wandell, E. N. Pugh, “Detection of long-duration, long-wavelength incremental flashes by a chromatically coded pathway,” Vision Res. 20, 625–636 (1980).
    [Crossref] [PubMed]
  25. A clear example expressing the view that flickering lights cause a luminance response may be found in Ref. 23, p. 568:We have long theorized that judgments made in a flicker photometric situation are mediated by the non-opponent system. This is almost self-evident, since flicker photometry demands that judgments of minimum flicker be made after chromatic fusion has occurred. That is, the procedure is presumably dependent upon the fact that the non-opponent system is temporally more sensitive than the chromatic system.

1984 (3)

H. R. Wilson, D. J. Gelb, “Modified line-element theory for spatial-frequency and width discrimination,” J. Opt. Soc. Am. A 1, 124–131 (1984).
[Crossref] [PubMed]

L. T. Maloney, B. A. Wandell, “A model of a single visual channel’s response to weak test lights,” Vision Res. 24, 633–640 (1984).
[Crossref]

B. A. Wandell, P. Ahumada, D. K. Welsh, “Reaction times to weak test lights,” Vision Res. 24, 647–652 (1984).
[Crossref] [PubMed]

1983 (3)

J. Thornton, E. N. Pugh, “Red/green color opponency at detection threshold,” Science 219, 191–193 (1983).
[Crossref] [PubMed]

L. T. Maloney, B. A. Wandell, “The slope of the psychometric functions at different wavelengths,” Invest. Ophthalmol. Visual Sci. Suppl. 24, 183A (1983).

D. Sagi, S. Hochstein, “Discriminability of suprathreshold compound spatial frequency gratings,” Vision Res. 23, 1595–1608 (1983).
[Crossref] [PubMed]

1982 (1)

B. A. Wandell, “Measurements of small color differences,” Psychol. Rev. 89, 281–302 (1982).
[Crossref] [PubMed]

1981 (1)

J. Nachmias, “On the psychometric function for contrast detection,” Vision Res. 21, 215–223 (1981).
[Crossref] [PubMed]

1980 (1)

B. A. Wandell, E. N. Pugh, “Detection of long-duration, long-wavelength incremental flashes by a chromatically coded pathway,” Vision Res. 20, 625–636 (1980).
[Crossref] [PubMed]

1979 (1)

A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979).
[Crossref] [PubMed]

1977 (1)

1974 (1)

R. F. Quick, “A vector magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
[Crossref]

1970 (1)

P. Rosen, M. W. Levine, M. Rosetto, I. Abramov, “A system for controlling the light output of a monochromator by any simple function and for temporally modulating intensity,” Behav. Res. Methods Instrum. 2, 297–300 (1970).
[Crossref]

1969 (1)

S. L. Guth, N. J. Donley, R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
[Crossref] [PubMed]

1968 (1)

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).

1967 (1)

W. S. Stiles, “Mechanism concepts in colour theory,” J. Colour Group 11, 106–123 (1967).

1952 (1)

1951 (1)

1946 (1)

D. Gabor, “Theory of Communication,” J. EE (London) 93, 429–457 (1946).

1945 (1)

1943 (1)

1942 (1)

Abramov, I.

P. Rosen, M. W. Levine, M. Rosetto, I. Abramov, “A system for controlling the light output of a monochromator by any simple function and for temporally modulating intensity,” Behav. Res. Methods Instrum. 2, 297–300 (1970).
[Crossref]

Ahumada, P.

B. A. Wandell, P. Ahumada, D. K. Welsh, “Reaction times to weak test lights,” Vision Res. 24, 647–652 (1984).
[Crossref] [PubMed]

Brown, W. R. J.

Campbell, F. W.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).

Donley, N. J.

S. L. Guth, N. J. Donley, R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
[Crossref] [PubMed]

Gabor, D.

D. Gabor, “Theory of Communication,” J. EE (London) 93, 429–457 (1946).

Gelb, D. J.

Guth, S. L.

S. L. Guth, N. J. Donley, R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
[Crossref] [PubMed]

Hochstein, S.

D. Sagi, S. Hochstein, “Discriminability of suprathreshold compound spatial frequency gratings,” Vision Res. 23, 1595–1608 (1983).
[Crossref] [PubMed]

Kelly, D. H.

Levine, M. W.

P. Rosen, M. W. Levine, M. Rosetto, I. Abramov, “A system for controlling the light output of a monochromator by any simple function and for temporally modulating intensity,” Behav. Res. Methods Instrum. 2, 297–300 (1970).
[Crossref]

MacAdam, D. L.

Maloney, L. T.

L. T. Maloney, B. A. Wandell, “A model of a single visual channel’s response to weak test lights,” Vision Res. 24, 633–640 (1984).
[Crossref]

L. T. Maloney, B. A. Wandell, “The slope of the psychometric functions at different wavelengths,” Invest. Ophthalmol. Visual Sci. Suppl. 24, 183A (1983).

Marrocco, R. T.

S. L. Guth, N. J. Donley, R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
[Crossref] [PubMed]

Nachmias, J.

J. Nachmias, “On the psychometric function for contrast detection,” Vision Res. 21, 215–223 (1981).
[Crossref] [PubMed]

Pugh, E. N.

J. Thornton, E. N. Pugh, “Red/green color opponency at detection threshold,” Science 219, 191–193 (1983).
[Crossref] [PubMed]

B. A. Wandell, E. N. Pugh, “Detection of long-duration, long-wavelength incremental flashes by a chromatically coded pathway,” Vision Res. 20, 625–636 (1980).
[Crossref] [PubMed]

Quick, R. F.

R. F. Quick, “A vector magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
[Crossref]

Robson, J. G.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).

Rosen, P.

P. Rosen, M. W. Levine, M. Rosetto, I. Abramov, “A system for controlling the light output of a monochromator by any simple function and for temporally modulating intensity,” Behav. Res. Methods Instrum. 2, 297–300 (1970).
[Crossref]

Rosetto, M.

P. Rosen, M. W. Levine, M. Rosetto, I. Abramov, “A system for controlling the light output of a monochromator by any simple function and for temporally modulating intensity,” Behav. Res. Methods Instrum. 2, 297–300 (1970).
[Crossref]

Sagi, D.

D. Sagi, S. Hochstein, “Discriminability of suprathreshold compound spatial frequency gratings,” Vision Res. 23, 1595–1608 (1983).
[Crossref] [PubMed]

Silberstein, L.

Stiles, W. S.

W. S. Stiles, “Mechanism concepts in colour theory,” J. Colour Group 11, 106–123 (1967).

G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).

Thornton, J.

J. Thornton, E. N. Pugh, “Red/green color opponency at detection threshold,” Science 219, 191–193 (1983).
[Crossref] [PubMed]

van Norren, D.

Wandell, B. A.

B. A. Wandell, P. Ahumada, D. K. Welsh, “Reaction times to weak test lights,” Vision Res. 24, 647–652 (1984).
[Crossref] [PubMed]

L. T. Maloney, B. A. Wandell, “A model of a single visual channel’s response to weak test lights,” Vision Res. 24, 633–640 (1984).
[Crossref]

L. T. Maloney, B. A. Wandell, “The slope of the psychometric functions at different wavelengths,” Invest. Ophthalmol. Visual Sci. Suppl. 24, 183A (1983).

B. A. Wandell, “Measurements of small color differences,” Psychol. Rev. 89, 281–302 (1982).
[Crossref] [PubMed]

B. A. Wandell, E. N. Pugh, “Detection of long-duration, long-wavelength incremental flashes by a chromatically coded pathway,” Vision Res. 20, 625–636 (1980).
[Crossref] [PubMed]

Watson, A. B.

A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979).
[Crossref] [PubMed]

A. B. Watson, “Detection and recognition of simple spatial forms,”.

Welsh, D. K.

B. A. Wandell, P. Ahumada, D. K. Welsh, “Reaction times to weak test lights,” Vision Res. 24, 647–652 (1984).
[Crossref] [PubMed]

Wilson, H. R.

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).

Behav. Res. Methods Instrum. (1)

P. Rosen, M. W. Levine, M. Rosetto, I. Abramov, “A system for controlling the light output of a monochromator by any simple function and for temporally modulating intensity,” Behav. Res. Methods Instrum. 2, 297–300 (1970).
[Crossref]

Invest. Ophthalmol. Visual Sci. Suppl. (1)

L. T. Maloney, B. A. Wandell, “The slope of the psychometric functions at different wavelengths,” Invest. Ophthalmol. Visual Sci. Suppl. 24, 183A (1983).

J. Colour Group (1)

W. S. Stiles, “Mechanism concepts in colour theory,” J. Colour Group 11, 106–123 (1967).

J. EE (London) (1)

D. Gabor, “Theory of Communication,” J. EE (London) 93, 429–457 (1946).

J. Opt. Soc. Am. (6)

J. Opt. Soc. Am. A (1)

J. Physiol. (London) (1)

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).

Kybernetik (1)

R. F. Quick, “A vector magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
[Crossref]

Psychol. Rev. (1)

B. A. Wandell, “Measurements of small color differences,” Psychol. Rev. 89, 281–302 (1982).
[Crossref] [PubMed]

Science (1)

J. Thornton, E. N. Pugh, “Red/green color opponency at detection threshold,” Science 219, 191–193 (1983).
[Crossref] [PubMed]

Vision Res. (7)

S. L. Guth, N. J. Donley, R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
[Crossref] [PubMed]

B. A. Wandell, E. N. Pugh, “Detection of long-duration, long-wavelength incremental flashes by a chromatically coded pathway,” Vision Res. 20, 625–636 (1980).
[Crossref] [PubMed]

D. Sagi, S. Hochstein, “Discriminability of suprathreshold compound spatial frequency gratings,” Vision Res. 23, 1595–1608 (1983).
[Crossref] [PubMed]

L. T. Maloney, B. A. Wandell, “A model of a single visual channel’s response to weak test lights,” Vision Res. 24, 633–640 (1984).
[Crossref]

A. B. Watson, “Probability summation over time,” Vision Res. 19, 515–522 (1979).
[Crossref] [PubMed]

B. A. Wandell, P. Ahumada, D. K. Welsh, “Reaction times to weak test lights,” Vision Res. 24, 647–652 (1984).
[Crossref] [PubMed]

J. Nachmias, “On the psychometric function for contrast detection,” Vision Res. 21, 215–223 (1981).
[Crossref] [PubMed]

Other (3)

A. B. Watson, “Detection and recognition of simple spatial forms,”.

G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).

A clear example expressing the view that flickering lights cause a luminance response may be found in Ref. 23, p. 568:We have long theorized that judgments made in a flicker photometric situation are mediated by the non-opponent system. This is almost self-evident, since flicker photometry demands that judgments of minimum flicker be made after chromatic fusion has occurred. That is, the procedure is presumably dependent upon the fact that the non-opponent system is temporally more sensitive than the chromatic system.

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Figures (18)

Fig. 1
Fig. 1

Schematic diagram of one of three channels of the experimental apparatus. See text for explanation.

Fig. 2
Fig. 2

Temporal waveforms of Gaussian and 6-Hz Gabor functions. The horizontal axis is time (seconds), and the vertical axis is linear intensity.

Fig. 3
Fig. 3

Gaussian detection contour for observer bw. The mean adapting level (origin of the graph) is a mixture of 650-nm light at 9.93 log quanta deg−2 sec−1 and 540-nm light at 8.52 log quanta deg−2 sec−1. The chromaticity coordinates of the adapting point are (0.703, 0.296, 0.001) approximately equivalent to 630 nm. The axes measure the percent contrast of each component of the signal. The smooth curve sketches the maximum-likelihood isodetection contour at 81% correct estimated from the model described later in the text.

Fig. 4
Fig. 4

The three panels represent Gaussian data from three more observers. The conditions are the same as for Fig. 3.

Fig. 5
Fig. 5

Sensitivity to a 6-Hz Gabor test stimulus (open circles) compared with the data in Fig. 3 (filled triangles). Adapting conditions are as in Fig. 3.

Fig. 6
Fig. 6

The three panels plot data for several observers using a 6-Hz Gabor function. Adapting conditions are as in Fig. 3.

Fig. 7
Fig. 7

Graphic illustration of the predictions of the vector-difference hypothesis concerning the discriminability of two points, labeled U and U′, that are small perturbations of the adapting field. The two points are predicted to be different if the vector difference between them (solid vector), when displaced to the origin (dashed vector), extends beyond the detection contour.

Fig. 8
Fig. 8

Pairs of points at discrimination threshold. One point in each pair, the pedestal, is plotted as an open symbol. This point is fixed by the experimenter. The position of the second light, the pedestal plus the increment, is plotted as a filled symbol. This point may fall anywhere along a line at 135 deg (counterclockwise) to the horizontal axis, starting at the pedestal. The pedestal points were chosen to fall along a line oriented at 22.5 deg counterclockwise to the horizontal axis. The pedestal contrasts extend over a range up to roughly 2.5 times threshold. Adapting conditions are as in Fig. 3.

Fig. 9
Fig. 9

Additional discrimination thresholds, following the conventions in Fig. 8. The new pedestal directions are at 0 deg (along the horizontal axis) and 45 deg below the horizontal axis. Adapting conditions are as in Fig. 3.

Fig. 10
Fig. 10

Detection contour (open symbols) and several discrimination contours (filled symbols) for Gaussian test stimulus. In the top panel, the discrimination thresholds for various directions around the pedestal are plotted around the position of their respective pedestals (indicated by an ×). In the bottom panel, to permit comparison of the shapes of the discrimination contours, the data have been slid so that the pedestals fall at the origin. Adapting conditions are as in Fig. 3.

Fig. 11
Fig. 11

As in Fig. 10 but for a second observer.

Fig. 12
Fig. 12

Pairs of points at discrimination threshold, using a 6-Hz Gabor function. The plotting conventions are as in Fig. 8. Each panel represents a pedestal at a different direction. Panels: top, 22.5 deg; center, 45 deg; bottom, 67.5 deg. Adapting conditions as in Fig. 3.

Fig. 13
Fig. 13

The filled symbols replot all the pedestal-plus-increment data points from Fig. 12. The lines indicate the range of values of the pedestals in that figure. The pedestal-plus increments fall roughly along a common line despite the wide range of angles swept out by the pedestals. Adapting conditions as in Fig. 3.

Fig. 14
Fig. 14

Discrimination thresholds for pedestals falling along the 135-deg direction and the incremental vector in the 45-deg direction. The adapting conditions for these data were similar to those for the previous data (see Fig. 3), except that a steady blue field at 8.381 log quanta deg−2 sec−1 was added to the steady background. The chromaticity coordinates of the adapting field are off the spectral locus at (0.683, 0.285, 0.032). The observer is ac.

Fig. 15
Fig. 15

A replot of the pedestal plus test data points from Fig. 14. The points fall along a common line.

Fig. 16
Fig. 16

Discrimination thresholds for different directions around a pedestal in the 22.5-deg direction. Adapting field as in Fig. 14. Notice that the shapes of the contours are quite different and that discriminations in the direction away from the pedestal vector strongly violate the vector-difference hypothesis. Observer is bw.

Fig. 17
Fig. 17

Detection contour (open symbols) and discrimination contours (filled symbols) of 6-Hz Gabor functions modulated in the isoluminance plane. The adapting field is described in Fig. 14. Stimulus coordinates for two of the channels are plotted, and the modulation of the third beam (440 nm) can be determined from the other two since the combination of modulations must remain within the isoluminance plane. Although three discrimination contours were measured, only two are shown in this figure in order to avoid cluttering the graph. The third is presented in Fig. 18. Observer is bw.

Fig. 18
Fig. 18

Isoluminance detection contour (open symbols) and three discrimination contours (filled symbols). The discrimination contours have been slid so that their pedestals fall on the origin to permit a comparison of the shapes of the discrimination contours and the detection contour. Adapting conditions are as in Fig. 14. Observer is bw.

Equations (5)

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

i , j = 1 , 3 g i j ( U ) d U i d U j .
L ( t ) = L 0 + C exp [ - ( t - μ 2 σ ) 2 ] ,             t = 0 , 0.01 , 0.02 , , 1.0 ,
L ( t ) = L 0 + C sin ( 2 π f t ) exp [ - ( t - μ 2 σ ) 2 ] ,             t = 0.01 , , 1.0.
P ( cor ) = 1 2 + 1 2 exp [ - ( C α ) β ] ,
( I p - I 0 ) / I 0 .

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