Abstract

The strength of the border between two regions was assessed by measuring the tendency of the border to disappear during a 5-min fixation period. We measured the total time the border was judged visible when subjects viewed two hemifields with different chromaticities (six wavelength pairs), five luminance contrasts, or with differences in both, at five levels of luminance. For a homochromatic field, border visibility increased linearly with the logarithm of the luminance contrast, regardless of the particular wavelength of the field. For fields with only chromatic differences, border visibility increased linearly with the logarithm of the tritanopic-purity difference (the relative activity of only the long- and middle-wavelength-sensitive cones). For all borders, visibility increased with an increase in luminance level. Thus borders formed by the combination of chromatic differences and luminance contrasts are more visible than borders that have the same chromatic difference or the same luminance contrast alone. For any chromatic difference, calculations of a luminance contrast that would yield the same border visibility were made. These equivalent luminance-contrast functions for border visibility provide a metric for chromatic differences across a range of luminances that allows chromatic and luminance-contrast sensitivities to be compared in a nonarbitrary way. Relative to chromatic differences, luminance contrast is less effective in maintaining border visibility at lower luminance levels. When the borders combine both chromatic differences and luminance contrasts, a root-mean-square model can be used to account for the data. This is consistent with the idea that chromatic and luminance systems make independent contributions to the visibility of borders.

© 1981 Optical Society of America

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  1. K. Koffka, "The environmental field: visual organization and its laws," in Principles of Gestalt Psychology (Harcourt, Brace, New York, 1935), pp. 126–129.
  2. C. B. Rubinstein and J. O. Limb, "Colour border sharpness," in Colour 73 (Survey Lectures and Abstracts of the Papers Presented at the Second Congress of the International Colour Association) (Adam Hilger, London, 1973), pp. 377–380.
  3. R. M. Boynton and P. K. Kaiser, "Vision: the additivity law made to work for heterochromatic photometry with bipartite fields," Science 161, 366–368 (1968).
  4. P. K. Kaiser, P. Herzberg, and R. M. Boynton, "Chromatic border distinctness and its relation to saturation," Vision Res. 11, 953–968 (1971).
  5. Another means of expressing equivalent achromatic contrast had been reported previously by MacAdam [D. L. MacAdam, "Color discrimination and the influence of color contrast on visual acuity," Rev. Opt. Theor. Instrum. 28, 161 (1949)]. With Landolt rings of different colors on equiluminous gray backgrounds, which produced the same visual acuity as rings that differed from the background only in luminance, he found that, when the target and background differed in both chromaticity and luminance, acuity was the same as that produced by a luminance contrast equivalent to the square root of the sum of the squares of (1) the luminance contrast equivalent to the chromatic contrast alone and (2) the actual luminance contrast.
  6. G. Wagner and R. M. Boynton, "A comparison of four methods of heterochromatic photometry," J. Opt. Soc. Am. 62, 1508–1515 (1972).
  7. S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, and M. M. Patterson, "Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of trichromatic-opponent colors theory," Vision Res. 8, 913–928 (1968).
  8. V. C. Smith and J. Pokorny, "Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm," Vision Res. 15, 161–171 (1975).
  9. B. W. Tansley and R. J. Glushko, "Spectral sensitivity of long-wavelength-sensitive photoreceptors in dichromats determined by elimination of border percepts," Vision Res. 18, 699–706 (1977).
  10. A. Eisner and D. I. A. MacLeod, "Blue-sensitive cones do not contribute to luminance," J. Opt. Soc. Am. 70, 121–122 (1980).
  11. F. Ward and R. M. Boynton, "Scaling of large chromatic differences," Vision Res. 14, 943–949 (1974).
  12. B. W. Tansley and R. M. Boynton, "A line, not a space, represents visual distinctness of borders formed by different colors," Science 191, 954–957 (1976).
  13. B. W. Tansley and R. M. Boynton, "Chromatic border perception: the role of red- and green-sensitive cones," Vision Res. 18, 683–697 (1977).
  14. A. Valberg and B. W. Tansley, "A tritanopic purity difference function to describe the properties of minimally distinct borders," J. Opt. Soc. Am. 67, 1330–1336 (1977).
  15. B. W. Tansley and A. Valberg, "Chromatic border distinctness: not an index of hue or saturation differences," J. Opt. Soc. Am. 69, 113–118 (1979).
  16. E. Hering, "Adaptation of the eye to fixed retinal images," in Outlines of a Theory of the Light Sense (translated by L. M. Hurvich and D. Jameson) (Harvard U. Press, Cambridge, Mass., 1964), pp. 279–284.
  17. K. J. McCree, "Color confusion produced by voluntary fixation," Opt. Acta 7, 281–290 (1960).
  18. J. Krauskopf, "Effect of retinal image stabilization on the appearance of heterochromatic targets," J. Opt. Soc. Am. 53, 741–744 (1963).
  19. A. R. Yarbus, Eye Movements and Vision (Plenum, New York, 1967).
  20. R. W. Ditchburn, "Discrimination of luminance and hue," in Eye Movements and Visual Perception (Clarendon, Oxford, 1973), Chap. 9.
  21. S. L. Buck, F. S. Frome, and R. M. Boynton, "Initial distinctness and subsequent fading of minimally distinct borders," J. Opt. Soc. Am. 67, 1126–1128 (1977).
  22. P. L. Walraven, "A closer look at the tritanopic convergence point," Vision Res. 14, 1339–1343 (1974).
  23. The weightings of inputs from the R "red" and G "green" receptors have been chosen such that the 570-nm monochromatic light (the yellowish tritanopic neutral point judged by those who lack short-wavelength cones to match a white light in hue and brightness) is evaluated by the equation given in the text to have tritanopic purity equal to zero. (A 570-nm wavelength appears to be minimally saturated to a normal observer as well.) Since border visibility is the current measure of interest, the absolute value of the tritanopic-purity difference for a light of 570 nm juxtaposed with white light would be calculated. Thus the factor of 1.66 becomes an arbitrary constant for this and all other pairs of light. These particular two lights at equal luminance fall along a tritanopic-confusion line with other pairs of lights that have the same ratio of R to G cone responses. To normal trichromatic observers, all such pairs will form almost invisible borders, but each pair will have different colors and saturation [seeRef. (15)].
  24. See Ref. 5 and cf. Ref. 25 for a discussion of the benefits of the application of a sums-of-squares relation to proposed systems of component mechanisms. If chromatic and luminance systems make independent contributions to border visibility, the separate contribution of each could be represented by the component distances of orthogonal vectors in a two-dimensional space. Then the visibility of borders between two fields that differ in both chromaticity and luminance depends on the distance between the ends of the vectors that represent the component contributions. The square of distance between these endpoints can be calculated by the Pythagorean rule in two-dimensional Euclidean space as the sum of the squares of the distances along the orthogonal axes of the luminance-contrast conponent and the chromatic- or tritanopic-purity-difference component (as expressed by the luminance contrast necessary to produce the same border visibility in a homochromatic field).
  25. G. Wyszecki and W. S. Stiles, in Color Science (Wiley, New York, 1967), Sec. 6.7.
  26. C. R. Ingling, Jr., and B. A. Drum, "Retinal receptive fields: correlations between psychophysics and electrophysiology," Vision Res. 13, 1151–1163 (1972).
  27. D. Regan and C. W. Tyler, "Some dynamic features of colour vision," Vision Res. 11, 1307–1324 (1970).
  28. H. DeLange, "Research into the dynamic nature of the human fovea-cortex systems with intermittent and modulated light. I. Attenuation characteristics with white and colored light," J. Opt. Soc. Am. 48, 777–784 (1958).
  29. D. H. Kelly, "Theory of flicker and transient responses. I. Uniform fields," J. Opt. Soc. Am. 61, 537–546 (1971).
  30. C. M. Cicerone and D. G. Green, "Relative modulation sensitivities of the red and green color mechanisms," Vision Res. 18, 1593–1598 (1978).
  31. M. A. Nelson and R. L. Halberg, "Visual contrast sensitivity functions obtained with colored and achromatic gratings," Hum. Factors 21, 225–228 (1979).
  32. R. M. Boynton, M. M.Hayhoe, and D. I. A. MacLeod, "The gap effect: chromatic and achromatic visual discrimination as affected by field separation," Opt. Acta 24, 159–177 (1976).
  33. P. Gouras and E. Zrenner, "Enhancement of luminance flicker by color-opponent mechanisms," Science 205, 587–589 (1979).
  34. R. L. DeValois and P. L. Pease, "Contours and contrast: response of monkey lateral geniculate nucleus cells to luminance and color figures," Science 171, 694–696 (1971).
  35. R. L. DeValois and K. K. DeValois, "Neural coding of color," in Handbook of Perception (Academic, New York, 1975), Vol. 5, pp. 117–166.

1980 (1)

1979 (3)

B. W. Tansley and A. Valberg, "Chromatic border distinctness: not an index of hue or saturation differences," J. Opt. Soc. Am. 69, 113–118 (1979).

M. A. Nelson and R. L. Halberg, "Visual contrast sensitivity functions obtained with colored and achromatic gratings," Hum. Factors 21, 225–228 (1979).

P. Gouras and E. Zrenner, "Enhancement of luminance flicker by color-opponent mechanisms," Science 205, 587–589 (1979).

1978 (1)

C. M. Cicerone and D. G. Green, "Relative modulation sensitivities of the red and green color mechanisms," Vision Res. 18, 1593–1598 (1978).

1977 (4)

B. W. Tansley and R. J. Glushko, "Spectral sensitivity of long-wavelength-sensitive photoreceptors in dichromats determined by elimination of border percepts," Vision Res. 18, 699–706 (1977).

B. W. Tansley and R. M. Boynton, "Chromatic border perception: the role of red- and green-sensitive cones," Vision Res. 18, 683–697 (1977).

A. Valberg and B. W. Tansley, "A tritanopic purity difference function to describe the properties of minimally distinct borders," J. Opt. Soc. Am. 67, 1330–1336 (1977).

S. L. Buck, F. S. Frome, and R. M. Boynton, "Initial distinctness and subsequent fading of minimally distinct borders," J. Opt. Soc. Am. 67, 1126–1128 (1977).

1976 (2)

B. W. Tansley and R. M. Boynton, "A line, not a space, represents visual distinctness of borders formed by different colors," Science 191, 954–957 (1976).

R. M. Boynton, M. M.Hayhoe, and D. I. A. MacLeod, "The gap effect: chromatic and achromatic visual discrimination as affected by field separation," Opt. Acta 24, 159–177 (1976).

1975 (1)

V. C. Smith and J. Pokorny, "Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm," Vision Res. 15, 161–171 (1975).

1974 (2)

F. Ward and R. M. Boynton, "Scaling of large chromatic differences," Vision Res. 14, 943–949 (1974).

P. L. Walraven, "A closer look at the tritanopic convergence point," Vision Res. 14, 1339–1343 (1974).

1972 (2)

C. R. Ingling, Jr., and B. A. Drum, "Retinal receptive fields: correlations between psychophysics and electrophysiology," Vision Res. 13, 1151–1163 (1972).

G. Wagner and R. M. Boynton, "A comparison of four methods of heterochromatic photometry," J. Opt. Soc. Am. 62, 1508–1515 (1972).

1971 (3)

P. K. Kaiser, P. Herzberg, and R. M. Boynton, "Chromatic border distinctness and its relation to saturation," Vision Res. 11, 953–968 (1971).

R. L. DeValois and P. L. Pease, "Contours and contrast: response of monkey lateral geniculate nucleus cells to luminance and color figures," Science 171, 694–696 (1971).

D. H. Kelly, "Theory of flicker and transient responses. I. Uniform fields," J. Opt. Soc. Am. 61, 537–546 (1971).

1970 (1)

D. Regan and C. W. Tyler, "Some dynamic features of colour vision," Vision Res. 11, 1307–1324 (1970).

1968 (2)

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, and M. M. Patterson, "Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of trichromatic-opponent colors theory," Vision Res. 8, 913–928 (1968).

R. M. Boynton and P. K. Kaiser, "Vision: the additivity law made to work for heterochromatic photometry with bipartite fields," Science 161, 366–368 (1968).

1963 (1)

1960 (1)

K. J. McCree, "Color confusion produced by voluntary fixation," Opt. Acta 7, 281–290 (1960).

1958 (1)

1949 (1)

Another means of expressing equivalent achromatic contrast had been reported previously by MacAdam [D. L. MacAdam, "Color discrimination and the influence of color contrast on visual acuity," Rev. Opt. Theor. Instrum. 28, 161 (1949)]. With Landolt rings of different colors on equiluminous gray backgrounds, which produced the same visual acuity as rings that differed from the background only in luminance, he found that, when the target and background differed in both chromaticity and luminance, acuity was the same as that produced by a luminance contrast equivalent to the square root of the sum of the squares of (1) the luminance contrast equivalent to the chromatic contrast alone and (2) the actual luminance contrast.

Alexander, J. V.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, and M. M. Patterson, "Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of trichromatic-opponent colors theory," Vision Res. 8, 913–928 (1968).

Boynton, R. M.

B. W. Tansley and R. M. Boynton, "Chromatic border perception: the role of red- and green-sensitive cones," Vision Res. 18, 683–697 (1977).

S. L. Buck, F. S. Frome, and R. M. Boynton, "Initial distinctness and subsequent fading of minimally distinct borders," J. Opt. Soc. Am. 67, 1126–1128 (1977).

R. M. Boynton, M. M.Hayhoe, and D. I. A. MacLeod, "The gap effect: chromatic and achromatic visual discrimination as affected by field separation," Opt. Acta 24, 159–177 (1976).

B. W. Tansley and R. M. Boynton, "A line, not a space, represents visual distinctness of borders formed by different colors," Science 191, 954–957 (1976).

F. Ward and R. M. Boynton, "Scaling of large chromatic differences," Vision Res. 14, 943–949 (1974).

G. Wagner and R. M. Boynton, "A comparison of four methods of heterochromatic photometry," J. Opt. Soc. Am. 62, 1508–1515 (1972).

P. K. Kaiser, P. Herzberg, and R. M. Boynton, "Chromatic border distinctness and its relation to saturation," Vision Res. 11, 953–968 (1971).

R. M. Boynton and P. K. Kaiser, "Vision: the additivity law made to work for heterochromatic photometry with bipartite fields," Science 161, 366–368 (1968).

Buck, S. L.

Chumbly, J. I.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, and M. M. Patterson, "Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of trichromatic-opponent colors theory," Vision Res. 8, 913–928 (1968).

Cicerone, C. M.

C. M. Cicerone and D. G. Green, "Relative modulation sensitivities of the red and green color mechanisms," Vision Res. 18, 1593–1598 (1978).

DeLange, H.

DeValois, K. K.

R. L. DeValois and K. K. DeValois, "Neural coding of color," in Handbook of Perception (Academic, New York, 1975), Vol. 5, pp. 117–166.

DeValois, R. L.

R. L. DeValois and P. L. Pease, "Contours and contrast: response of monkey lateral geniculate nucleus cells to luminance and color figures," Science 171, 694–696 (1971).

R. L. DeValois and K. K. DeValois, "Neural coding of color," in Handbook of Perception (Academic, New York, 1975), Vol. 5, pp. 117–166.

Ditchburn, R. W.

R. W. Ditchburn, "Discrimination of luminance and hue," in Eye Movements and Visual Perception (Clarendon, Oxford, 1973), Chap. 9.

Drum, B. A.

C. R. Ingling, Jr., and B. A. Drum, "Retinal receptive fields: correlations between psychophysics and electrophysiology," Vision Res. 13, 1151–1163 (1972).

Eisner, A.

Frome, F. S.

Gilman, C. B.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, and M. M. Patterson, "Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of trichromatic-opponent colors theory," Vision Res. 8, 913–928 (1968).

Glushko, R. J.

B. W. Tansley and R. J. Glushko, "Spectral sensitivity of long-wavelength-sensitive photoreceptors in dichromats determined by elimination of border percepts," Vision Res. 18, 699–706 (1977).

Gouras, P.

P. Gouras and E. Zrenner, "Enhancement of luminance flicker by color-opponent mechanisms," Science 205, 587–589 (1979).

Green, D. G.

C. M. Cicerone and D. G. Green, "Relative modulation sensitivities of the red and green color mechanisms," Vision Res. 18, 1593–1598 (1978).

Guth, S. L.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, and M. M. Patterson, "Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of trichromatic-opponent colors theory," Vision Res. 8, 913–928 (1968).

Halberg, R. L.

M. A. Nelson and R. L. Halberg, "Visual contrast sensitivity functions obtained with colored and achromatic gratings," Hum. Factors 21, 225–228 (1979).

Hayhoe, M.M.

R. M. Boynton, M. M.Hayhoe, and D. I. A. MacLeod, "The gap effect: chromatic and achromatic visual discrimination as affected by field separation," Opt. Acta 24, 159–177 (1976).

Hering, E.

E. Hering, "Adaptation of the eye to fixed retinal images," in Outlines of a Theory of the Light Sense (translated by L. M. Hurvich and D. Jameson) (Harvard U. Press, Cambridge, Mass., 1964), pp. 279–284.

Herzberg, P.

P. K. Kaiser, P. Herzberg, and R. M. Boynton, "Chromatic border distinctness and its relation to saturation," Vision Res. 11, 953–968 (1971).

Ingling, Jr., C. R.

C. R. Ingling, Jr., and B. A. Drum, "Retinal receptive fields: correlations between psychophysics and electrophysiology," Vision Res. 13, 1151–1163 (1972).

Kaiser, P. K.

P. K. Kaiser, P. Herzberg, and R. M. Boynton, "Chromatic border distinctness and its relation to saturation," Vision Res. 11, 953–968 (1971).

R. M. Boynton and P. K. Kaiser, "Vision: the additivity law made to work for heterochromatic photometry with bipartite fields," Science 161, 366–368 (1968).

Kelly, D. H.

Koffka, K.

K. Koffka, "The environmental field: visual organization and its laws," in Principles of Gestalt Psychology (Harcourt, Brace, New York, 1935), pp. 126–129.

Krauskopf, J.

Limb, J. O.

C. B. Rubinstein and J. O. Limb, "Colour border sharpness," in Colour 73 (Survey Lectures and Abstracts of the Papers Presented at the Second Congress of the International Colour Association) (Adam Hilger, London, 1973), pp. 377–380.

MacAdam, D. L.

Another means of expressing equivalent achromatic contrast had been reported previously by MacAdam [D. L. MacAdam, "Color discrimination and the influence of color contrast on visual acuity," Rev. Opt. Theor. Instrum. 28, 161 (1949)]. With Landolt rings of different colors on equiluminous gray backgrounds, which produced the same visual acuity as rings that differed from the background only in luminance, he found that, when the target and background differed in both chromaticity and luminance, acuity was the same as that produced by a luminance contrast equivalent to the square root of the sum of the squares of (1) the luminance contrast equivalent to the chromatic contrast alone and (2) the actual luminance contrast.

MacLeod, D. I. A.

A. Eisner and D. I. A. MacLeod, "Blue-sensitive cones do not contribute to luminance," J. Opt. Soc. Am. 70, 121–122 (1980).

R. M. Boynton, M. M.Hayhoe, and D. I. A. MacLeod, "The gap effect: chromatic and achromatic visual discrimination as affected by field separation," Opt. Acta 24, 159–177 (1976).

McCree, K. J.

K. J. McCree, "Color confusion produced by voluntary fixation," Opt. Acta 7, 281–290 (1960).

Nelson, M. A.

M. A. Nelson and R. L. Halberg, "Visual contrast sensitivity functions obtained with colored and achromatic gratings," Hum. Factors 21, 225–228 (1979).

Patterson, M. M.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, and M. M. Patterson, "Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of trichromatic-opponent colors theory," Vision Res. 8, 913–928 (1968).

Pease, P. L.

R. L. DeValois and P. L. Pease, "Contours and contrast: response of monkey lateral geniculate nucleus cells to luminance and color figures," Science 171, 694–696 (1971).

Pokorny, J.

V. C. Smith and J. Pokorny, "Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm," Vision Res. 15, 161–171 (1975).

Regan, D.

D. Regan and C. W. Tyler, "Some dynamic features of colour vision," Vision Res. 11, 1307–1324 (1970).

Rubinstein, C. B.

C. B. Rubinstein and J. O. Limb, "Colour border sharpness," in Colour 73 (Survey Lectures and Abstracts of the Papers Presented at the Second Congress of the International Colour Association) (Adam Hilger, London, 1973), pp. 377–380.

Smith, V. C.

V. C. Smith and J. Pokorny, "Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm," Vision Res. 15, 161–171 (1975).

Stiles, W. S.

G. Wyszecki and W. S. Stiles, in Color Science (Wiley, New York, 1967), Sec. 6.7.

Tansley, B. W.

B. W. Tansley and A. Valberg, "Chromatic border distinctness: not an index of hue or saturation differences," J. Opt. Soc. Am. 69, 113–118 (1979).

B. W. Tansley and R. M. Boynton, "Chromatic border perception: the role of red- and green-sensitive cones," Vision Res. 18, 683–697 (1977).

B. W. Tansley and R. J. Glushko, "Spectral sensitivity of long-wavelength-sensitive photoreceptors in dichromats determined by elimination of border percepts," Vision Res. 18, 699–706 (1977).

A. Valberg and B. W. Tansley, "A tritanopic purity difference function to describe the properties of minimally distinct borders," J. Opt. Soc. Am. 67, 1330–1336 (1977).

B. W. Tansley and R. M. Boynton, "A line, not a space, represents visual distinctness of borders formed by different colors," Science 191, 954–957 (1976).

Tyler, C. W.

D. Regan and C. W. Tyler, "Some dynamic features of colour vision," Vision Res. 11, 1307–1324 (1970).

Valberg, A.

Wagner, G.

Walraven, P. L.

P. L. Walraven, "A closer look at the tritanopic convergence point," Vision Res. 14, 1339–1343 (1974).

Ward, F.

F. Ward and R. M. Boynton, "Scaling of large chromatic differences," Vision Res. 14, 943–949 (1974).

Wyszecki, G.

G. Wyszecki and W. S. Stiles, in Color Science (Wiley, New York, 1967), Sec. 6.7.

Yarbus, A. R.

A. R. Yarbus, Eye Movements and Vision (Plenum, New York, 1967).

Zrenner, E.

P. Gouras and E. Zrenner, "Enhancement of luminance flicker by color-opponent mechanisms," Science 205, 587–589 (1979).

Hum. Factors (1)

M. A. Nelson and R. L. Halberg, "Visual contrast sensitivity functions obtained with colored and achromatic gratings," Hum. Factors 21, 225–228 (1979).

J. Opt. Soc. Am. (8)

Opt. Acta (2)

K. J. McCree, "Color confusion produced by voluntary fixation," Opt. Acta 7, 281–290 (1960).

R. M. Boynton, M. M.Hayhoe, and D. I. A. MacLeod, "The gap effect: chromatic and achromatic visual discrimination as affected by field separation," Opt. Acta 24, 159–177 (1976).

Rev. Opt. Theor. Instrum. (1)

Another means of expressing equivalent achromatic contrast had been reported previously by MacAdam [D. L. MacAdam, "Color discrimination and the influence of color contrast on visual acuity," Rev. Opt. Theor. Instrum. 28, 161 (1949)]. With Landolt rings of different colors on equiluminous gray backgrounds, which produced the same visual acuity as rings that differed from the background only in luminance, he found that, when the target and background differed in both chromaticity and luminance, acuity was the same as that produced by a luminance contrast equivalent to the square root of the sum of the squares of (1) the luminance contrast equivalent to the chromatic contrast alone and (2) the actual luminance contrast.

Science (4)

B. W. Tansley and R. M. Boynton, "A line, not a space, represents visual distinctness of borders formed by different colors," Science 191, 954–957 (1976).

R. M. Boynton and P. K. Kaiser, "Vision: the additivity law made to work for heterochromatic photometry with bipartite fields," Science 161, 366–368 (1968).

P. Gouras and E. Zrenner, "Enhancement of luminance flicker by color-opponent mechanisms," Science 205, 587–589 (1979).

R. L. DeValois and P. L. Pease, "Contours and contrast: response of monkey lateral geniculate nucleus cells to luminance and color figures," Science 171, 694–696 (1971).

Vision Res. (10)

C. M. Cicerone and D. G. Green, "Relative modulation sensitivities of the red and green color mechanisms," Vision Res. 18, 1593–1598 (1978).

C. R. Ingling, Jr., and B. A. Drum, "Retinal receptive fields: correlations between psychophysics and electrophysiology," Vision Res. 13, 1151–1163 (1972).

D. Regan and C. W. Tyler, "Some dynamic features of colour vision," Vision Res. 11, 1307–1324 (1970).

P. L. Walraven, "A closer look at the tritanopic convergence point," Vision Res. 14, 1339–1343 (1974).

P. K. Kaiser, P. Herzberg, and R. M. Boynton, "Chromatic border distinctness and its relation to saturation," Vision Res. 11, 953–968 (1971).

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gilman, and M. M. Patterson, "Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of trichromatic-opponent colors theory," Vision Res. 8, 913–928 (1968).

V. C. Smith and J. Pokorny, "Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm," Vision Res. 15, 161–171 (1975).

B. W. Tansley and R. J. Glushko, "Spectral sensitivity of long-wavelength-sensitive photoreceptors in dichromats determined by elimination of border percepts," Vision Res. 18, 699–706 (1977).

B. W. Tansley and R. M. Boynton, "Chromatic border perception: the role of red- and green-sensitive cones," Vision Res. 18, 683–697 (1977).

F. Ward and R. M. Boynton, "Scaling of large chromatic differences," Vision Res. 14, 943–949 (1974).

Other (9)

E. Hering, "Adaptation of the eye to fixed retinal images," in Outlines of a Theory of the Light Sense (translated by L. M. Hurvich and D. Jameson) (Harvard U. Press, Cambridge, Mass., 1964), pp. 279–284.

K. Koffka, "The environmental field: visual organization and its laws," in Principles of Gestalt Psychology (Harcourt, Brace, New York, 1935), pp. 126–129.

C. B. Rubinstein and J. O. Limb, "Colour border sharpness," in Colour 73 (Survey Lectures and Abstracts of the Papers Presented at the Second Congress of the International Colour Association) (Adam Hilger, London, 1973), pp. 377–380.

The weightings of inputs from the R "red" and G "green" receptors have been chosen such that the 570-nm monochromatic light (the yellowish tritanopic neutral point judged by those who lack short-wavelength cones to match a white light in hue and brightness) is evaluated by the equation given in the text to have tritanopic purity equal to zero. (A 570-nm wavelength appears to be minimally saturated to a normal observer as well.) Since border visibility is the current measure of interest, the absolute value of the tritanopic-purity difference for a light of 570 nm juxtaposed with white light would be calculated. Thus the factor of 1.66 becomes an arbitrary constant for this and all other pairs of light. These particular two lights at equal luminance fall along a tritanopic-confusion line with other pairs of lights that have the same ratio of R to G cone responses. To normal trichromatic observers, all such pairs will form almost invisible borders, but each pair will have different colors and saturation [seeRef. (15)].

See Ref. 5 and cf. Ref. 25 for a discussion of the benefits of the application of a sums-of-squares relation to proposed systems of component mechanisms. If chromatic and luminance systems make independent contributions to border visibility, the separate contribution of each could be represented by the component distances of orthogonal vectors in a two-dimensional space. Then the visibility of borders between two fields that differ in both chromaticity and luminance depends on the distance between the ends of the vectors that represent the component contributions. The square of distance between these endpoints can be calculated by the Pythagorean rule in two-dimensional Euclidean space as the sum of the squares of the distances along the orthogonal axes of the luminance-contrast conponent and the chromatic- or tritanopic-purity-difference component (as expressed by the luminance contrast necessary to produce the same border visibility in a homochromatic field).

G. Wyszecki and W. S. Stiles, in Color Science (Wiley, New York, 1967), Sec. 6.7.

A. R. Yarbus, Eye Movements and Vision (Plenum, New York, 1967).

R. W. Ditchburn, "Discrimination of luminance and hue," in Eye Movements and Visual Perception (Clarendon, Oxford, 1973), Chap. 9.

R. L. DeValois and K. K. DeValois, "Neural coding of color," in Handbook of Perception (Academic, New York, 1975), Vol. 5, pp. 117–166.

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