Abstract

A simple steady-state model is proposed to explain a well-known phenomenon of subjective brightness, namely that high illuminance greatly increases the apparent contrast of a scene. This effect is obtained in the model by making both the reference level and gain of the system depend on the average illumination. The numerical values of the system parameters evaluated from published data of Hurvich and Jameson are in good agreement with those derived from independent experiments of S. S. Stevens. The basic model can be improved by modifications which make it show qualitatively the stabilized retinal image effect, and edge effects such as Mach bands. The physiological plausibility of the model is discussed briefly and no implausible requirements are found.

© 1962 Optical Society of America

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References

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  1. S. S. Stevens, Science 133, 80 (1961).
    [Crossref] [PubMed]
  2. D. Jameson and L. M. Hurvich, Science 133, 174 (1961).
    [Crossref] [PubMed]
  3. H. Helson, in Psychology: Study of a Science, edited by S. Koch (McGraw-Hill Book Company, Inc., New York, 1959), Vol. 1, p. 565.
  4. Y. Le Grand, Light, Colour, and Vision (John Wiley & Sons, Inc., New York, 1957), p. 250.
  5. R. W. Ditchburn, “Eye movements in relation to perception of color,” in Visual Problems of Color, Symposium, (Chemical Publishing Company, New York, 1961). Vol. 2, p. 51.
  6. Communications Biophysics Group of Research Laboratory of Electronics William M. Siebert, “Processing neuroelectric data,” MIT Tech. Rept. 351 (July7, 1959).
  7. W. R. Lowenstein, Sci. American 203, 98 (1960).
    [Crossref]
  8. D. H. Kelly, J. Opt. Soc. Am. 51, 422 (1961).
    [Crossref] [PubMed]
  9. D. H. Kelly, J. Opt. Soc. Am. 51, 747 (1961).
    [Crossref]
  10. G. v. Békésy, J. Opt. Soc. Am. 50, 1060–1070 (1960).
    [Crossref] [PubMed]

1961 (4)

1960 (2)

Békésy, G. v.

Ditchburn, R. W.

R. W. Ditchburn, “Eye movements in relation to perception of color,” in Visual Problems of Color, Symposium, (Chemical Publishing Company, New York, 1961). Vol. 2, p. 51.

Helson, H.

H. Helson, in Psychology: Study of a Science, edited by S. Koch (McGraw-Hill Book Company, Inc., New York, 1959), Vol. 1, p. 565.

Hurvich, L. M.

D. Jameson and L. M. Hurvich, Science 133, 174 (1961).
[Crossref] [PubMed]

Jameson, D.

D. Jameson and L. M. Hurvich, Science 133, 174 (1961).
[Crossref] [PubMed]

Kelly, D. H.

Le Grand, Y.

Y. Le Grand, Light, Colour, and Vision (John Wiley & Sons, Inc., New York, 1957), p. 250.

Lowenstein, W. R.

W. R. Lowenstein, Sci. American 203, 98 (1960).
[Crossref]

Siebert, William M.

Communications Biophysics Group of Research Laboratory of Electronics William M. Siebert, “Processing neuroelectric data,” MIT Tech. Rept. 351 (July7, 1959).

Stevens, S. S.

S. S. Stevens, Science 133, 80 (1961).
[Crossref] [PubMed]

J. Opt. Soc. Am. (3)

Sci. American (1)

W. R. Lowenstein, Sci. American 203, 98 (1960).
[Crossref]

Science (2)

S. S. Stevens, Science 133, 80 (1961).
[Crossref] [PubMed]

D. Jameson and L. M. Hurvich, Science 133, 174 (1961).
[Crossref] [PubMed]

Other (4)

H. Helson, in Psychology: Study of a Science, edited by S. Koch (McGraw-Hill Book Company, Inc., New York, 1959), Vol. 1, p. 565.

Y. Le Grand, Light, Colour, and Vision (John Wiley & Sons, Inc., New York, 1957), p. 250.

R. W. Ditchburn, “Eye movements in relation to perception of color,” in Visual Problems of Color, Symposium, (Chemical Publishing Company, New York, 1961). Vol. 2, p. 51.

Communications Biophysics Group of Research Laboratory of Electronics William M. Siebert, “Processing neuroelectric data,” MIT Tech. Rept. 351 (July7, 1959).

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Figures (4)

Fig. 1
Fig. 1

Effect of illuminance on apparent brightness. Each solid slanting line corresponds to a given over-all illuminance. Each dashed line corresponds to a given target. The experimental points are those of Hurvich and Jameson. The two families of lines are plotted from the equation logB − logB0 = (α + β logI0) (logI − logI0). The horizontal line represents B = B0.

Fig. 2
Fig. 2

Comparison of the slope of the apparent brightness curves as given by Stevens’ equation, and the author’s approximation to the Hurvich-Jameson experimental results. The ordinate gives the value of the exponent if the equation is expressed in the power form.

Fig. 3
Fig. 3

Schematic diagram of brightness-perception model. Two channels are shown. The model should have a large number of channels, all similarly connected to the averager.

Fig. 4
Fig. 4

Edge effects. The target is half black and half white, The small circles are local averaging areas. The perceived brightness curves show how local averaging leads to Mach bands, increased edge contrast, and loss of brightness discrimination with separation of the areas to be discriminated.

Tables (1)

Tables Icon

Table I Explaining exact operation of model.

Equations (14)

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log B log B 0 = k ( I 0 ) [ log I log I 0 ] .
k ( I 0 ) = α + β log I 0 .
log B log B 0 = ( α + β log I 0 ) ( log I log I 0 ) .
α = 1.74 , β = 0.555 , log B 0 = 0.67 .
log B log B 0 = c [ α + β ( log I c ) ] .
B / B 0 = [ I / I 0 ] k ( I 0 ) ,
2 log I 0 = log I ( α / β )
log I log I 0 = log ( I / I 0 ) , k ( I 0 ) log ( I / I 0 ) = log [ I / I 0 ] k ( I 0 ) .
E = h e s 1 2 + 1 2 s f ( x ) d x h i [ ( r + 1 2 s ) 1 2 s f ( x ) d x + 1 2 s r + 1 2 s f ( x ) d x ] .
h e s = S , 2 h i r = R .
E = ( h e + h i ) 1 2 s 1 2 s f ( x ) d x h i ( r + 1 2 s ) + ( r + 1 2 s ) f ( x ) d x .
E = s ( h e + h i ) f e ( 2 r + s ) h i f 0 .
E = S f e R f 0 + ( R s / 2 r ) ( f e f 0 ) .
E = [ S + ( R s / 2 r ) ] ( f e f 0 ) .