Abstract

The minimally distinct border (MDB) method for comparing two fields of differing chromaticity was first reported by Boynton and Kaiser in 1968, and has been the subject of further experimental and theoretical investigation since that time. The evidence suggests that the MDB criterion is achieved when the two fields being compared produce equal effects upon the achromatic channels of the photopic visual system. The comparisons prove to be transitive and Abney’s law is strictly obeyed; spectral sensitivity evaluated by the MDB is very similar to that obtained by flicker photometry. An advantage of the MDB over flicker photometry is that the strength of the border at the MDB setting can be evaluated. This is done either by border matches with an achromatic comparison field, or with direct subjective estimates. At the MDB setting, the more saturated of two fields appears brighter than the other one. This implies that the chromatic channels of the visual system contribute to brightness as well as to chromaticness. The MDB criterion provides a new method for saturation scaling: Chromatic stimuli are juxtaposed in turn with white, and the strength of the border at the MDB setting is taken in each case as an index of saturation. More generally, any two fields can be compared by this method, as we have done with a matrix of 16 spectral stimuli plus white, employed in all possible combinations. Because the results can be accurately displayed in a two-dimensional euclidean space, the MDB method also shows potential as a new basis for color scaling.

© 1973 Optical Society of America

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References

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  1. P. K. Kaiser, R. M. Boynton, and P. A. Herzberg. Vision Res. 11, 953 (1971).
    [CrossRef] [PubMed]
  2. G. Wagner and R. M. Boynton, J. Opt. Soc. Am. 62, 1508 (1972).
    [CrossRef] [PubMed]
  3. R. M. Boynton and P. K. Kaiser. Science 161, 366 (1968).
    [CrossRef] [PubMed]
  4. The blue field should appear more saturated than the yellow one (which would be true if both were monochromatic). The basis for the greater saturation of the blue field lies in its ability to activate a greater ratio of chromatic to achromatic elements than the yellow one. The peripheral basis for the higher saturation of blue could lie in the higher ratio of chromatic to achromatic responsivity, explicit in various quantitative theories of color vision in which two chromatic channels and one achromatic channel are assumed to be utilized in chromatic information processing. These differences are then reflected in higher stages, such as the lateral geniculate nucleus, where DeValois and his associates [J. Opt. Soc. Am. 56, 966 (1966)] have found convincing electrophysiological evidence supporting the existence of such channels. They find, indeed, that a monochromatic blue produces more activity in the chromatic channels, relative to a monochromatic yellow, when the activity of the achromatic channels has been equated. The units about which we speculate here are imagined to underly directly the experience of color and are probably, but not necessarily, located at a higher level of visual processing than the lateral-geniculate stage.
  5. The assumptions of linear summation and cancellation, as made in this example, are probably too simple. But these details do not affect the general argument that is being advanced.
  6. R. M. Boynton and T. S. Greenspon. Vision Res. 12, 495 (1972).
    [CrossRef] [PubMed]
  7. R. M. Boynton and H. G. Wagner, in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven. Proceedings of the 1971 AIC Symposium on Color Metrics (AIC/Holland, c/o Institute for Perception TNO, 1972), Ch. 2, pp. 26–35.
  8. J. B. Kruskal, Psychometrika 29, 28 (1964).

1972 (2)

1971 (1)

P. K. Kaiser, R. M. Boynton, and P. A. Herzberg. Vision Res. 11, 953 (1971).
[CrossRef] [PubMed]

1968 (1)

R. M. Boynton and P. K. Kaiser. Science 161, 366 (1968).
[CrossRef] [PubMed]

1966 (1)

1964 (1)

J. B. Kruskal, Psychometrika 29, 28 (1964).

Boynton, R. M.

G. Wagner and R. M. Boynton, J. Opt. Soc. Am. 62, 1508 (1972).
[CrossRef] [PubMed]

R. M. Boynton and T. S. Greenspon. Vision Res. 12, 495 (1972).
[CrossRef] [PubMed]

P. K. Kaiser, R. M. Boynton, and P. A. Herzberg. Vision Res. 11, 953 (1971).
[CrossRef] [PubMed]

R. M. Boynton and P. K. Kaiser. Science 161, 366 (1968).
[CrossRef] [PubMed]

R. M. Boynton and H. G. Wagner, in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven. Proceedings of the 1971 AIC Symposium on Color Metrics (AIC/Holland, c/o Institute for Perception TNO, 1972), Ch. 2, pp. 26–35.

Greenspon, T. S.

R. M. Boynton and T. S. Greenspon. Vision Res. 12, 495 (1972).
[CrossRef] [PubMed]

Herzberg, P. A.

P. K. Kaiser, R. M. Boynton, and P. A. Herzberg. Vision Res. 11, 953 (1971).
[CrossRef] [PubMed]

Kaiser, P. K.

P. K. Kaiser, R. M. Boynton, and P. A. Herzberg. Vision Res. 11, 953 (1971).
[CrossRef] [PubMed]

R. M. Boynton and P. K. Kaiser. Science 161, 366 (1968).
[CrossRef] [PubMed]

Kruskal, J. B.

J. B. Kruskal, Psychometrika 29, 28 (1964).

Wagner, G.

Wagner, H. G.

R. M. Boynton and H. G. Wagner, in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven. Proceedings of the 1971 AIC Symposium on Color Metrics (AIC/Holland, c/o Institute for Perception TNO, 1972), Ch. 2, pp. 26–35.

J. Opt. Soc. Am. (2)

Psychometrika (1)

J. B. Kruskal, Psychometrika 29, 28 (1964).

Science (1)

R. M. Boynton and P. K. Kaiser. Science 161, 366 (1968).
[CrossRef] [PubMed]

Vision Res. (2)

P. K. Kaiser, R. M. Boynton, and P. A. Herzberg. Vision Res. 11, 953 (1971).
[CrossRef] [PubMed]

R. M. Boynton and T. S. Greenspon. Vision Res. 12, 495 (1972).
[CrossRef] [PubMed]

Other (2)

R. M. Boynton and H. G. Wagner, in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven. Proceedings of the 1971 AIC Symposium on Color Metrics (AIC/Holland, c/o Institute for Perception TNO, 1972), Ch. 2, pp. 26–35.

The assumptions of linear summation and cancellation, as made in this example, are probably too simple. But these details do not affect the general argument that is being advanced.

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Figures (9)

Fig. 1
Fig. 1

The solid curve depicts schematically how the distinctness of an achromatic border increases with objectively specified contrast. The dotted curve depicts the distanctness of a border separating two fields of differing chromaticity. When C = 0, the border is still visible and has a distinctness as shown, which will be at (or near) the MDB. By drawing a horizontal line to the achromatic curve and reflecting downward, an equivalent achromatic contrast (EAC) can be found that yields the same border distinctness as does the MDB for the chromatically differing fields.

Fig. 2
Fig. 2

Fifteen monochromatic stimuli, plus white, were presented as pairs in all 105 possible combinations. In one experiment, the distinctness of the border at MDB was evaluated by the method of equivalent achromatic contrast, using the field configuration shown in Fig. 7 and the logic depicted in Fig. 1. These values are represented on the abscissa. In another experiment, using the same subjects, the distinctness of the borders at MDB was estimated instead by a subjective technique along a scale ranging from zero (no border) to seven (very distinct border). Mean values of this distinctness rating are shown on the ordinate. The two measures of distinctness at MDB are very highly correlated.

Fig. 3
Fig. 3

If λ1 = λ2, achromatic contrast (C) is specified as (L1L2)/(L1 + L2) and can range from 0 to ±1.0. When λ1 ≠ λ2, there is a chromaticity difference between the two half-fields. The experimenter adjusts the quantities inscribed in circles: This includes the spectral distributions of the two fields, the luminance L2 of the left field, and the spatial position X2 of the left field. The subject adjusts the quantities inscribed in squares (the luminance and spatial position of the right field) and does so by turning two knobs in the apparatus. His task is to set L1 and X1 to produce a MDB between the two half-fields. In the experiments reported here, the diameter of the full field is 1° 40 of visual angle, and L2 covers a range corresponding to retinal illuminances ranging from 7 to 50 td.

Fig. 4
Fig. 4

Comparison of relative-luminous-efficiency functions obtained by the method of direct brightness matching (solid curve) and by flicker photometry or MDB (dotted curve). The curves have been normalized at 570 nm, which is the wavelength of minimum saturation. (Adapted from Wagner and Boynton, Ref. 2, Fig. 9.)

Fig. 5
Fig. 5

Additivity of binary mixtures, using the MDB criterion, for seven pairs of spectral stimuli, (a) λ1 = 480 nm, λ2 = 520 nm; (b) λ1 = 480 nm, λ2 = 620 nm; (c) λ1 = 500 nm, λ2 = 600 nm; (d) λ1 = 510 nm, λ2 = 580 nm; (e) λ1 = 480 nm, λ2 = 570 nm; (f) λ1 = 500 nm, λ2 = 540 nm; (g) λ1 = 490 nm, λ2 = 540 nm.

Fig. 6
Fig. 6

Theoretical scheme to show why additivity failures occur for heterochromatic brightness matching (a), but do not when the MDB criterion is used (b).

Fig. 7
Fig. 7

Four-part field in which the distinctness of the MDB for a heterochromatic pair at the bottom is evaluated by adjusting field 1 W until the achromatic border at the top matches the MDB at the bottom for distinctness.

Fig. 8
Fig. 8

EAC as a function of wavelength, based on an experiment using a stimulus field like that shown in Fig. 7, where monochromatic stimuli were compared in each case with a white standard.

Fig. 9
Fig. 9

Two-dimensional plot, using analysis of proximities, of relations among 16 spectral stimuli and white. The distinctness of MDB’s for 136 possible pairs were evaluated as in Fig. 8 (where the actual values for the 16 combinations involving white are shown). These differences were rank ordered and used as input; the plot above shows the optimal positioning of the 17 stimuli so that the rank ordering of the original difference scores is preserved in the relations among these distances on the diagram.