Abstract

This study was concerned with the manner in which perceived depth and perceived frontoparallel size varied with physical distance and hence with each other. An equation expressing the relation between perceived size and physical depth was developed and applied to size judgments determined with four observers under two viewing conditions. By use of that equation and an expression of the size–distance invariance hypothesis, an additional equation was developed which related perceived and physical depth. The additional equation, when applied to judgments of perceived depth from the same observers under the same viewing conditions, produced results not in agreement with those expected from the size–distance invariance hypothesis. This is interpreted as evidence against the validity of the size–distance invariance hypothesis in its usual form. The data from the apparent depth judgments also were applied to the problem of the discrepancies in results that have been found in experiments on the perceptual bisection of depth intervals.

© 1964 Optical Society of America

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References

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  1. F. P. Kilpatrick and W. H. Ittelson, Psychol. Rev. 60, 223 (1953).
    [Crossref] [PubMed]
  2. For a different statement of the problem of depth constancy see R. Over, Am. J. Psychol. 74, 308 (1961).
    [Crossref] [PubMed]
  3. A relation similar to Eq. (5) has been developed for use in an equation concerned with the perception of three-dimensional shape [W. C. Gogel, J. Psychol. 50, 179 (1960)].
    [Crossref]
  4. R. H. Thouless, Brit. J. Psychol. 21, 339 (1931).
  5. T. Ueno, Japan. Psychol. Res. 4, 99 (1962).
  6. S. S. Stevens, Am. Psychologist 17, 29 (1962).
    [Crossref]
  7. T. Oyama, Psychol. Bull. 56, 74 (1959).
    [Crossref] [PubMed]
  8. (a)See F. P. Kilpatrick and W. H. Ittelson, Psychol. Rev. 60, 223 (1953); (b)W. Epstein, J. Park, and A. Casey, Psychol. Bull. 58, 491 (1961); (c)and W. C. Gogel, Vision Res. 3, 106 (1963).
  9. W. C. Gogel, E. R. Wist, and G. S. Harker, Am. J. Phychol. 76, 537 (1963).
    [Crossref]
  10. Reference 8(b), pp. 495–496.

1963 (1)

W. C. Gogel, E. R. Wist, and G. S. Harker, Am. J. Phychol. 76, 537 (1963).
[Crossref]

1962 (2)

T. Ueno, Japan. Psychol. Res. 4, 99 (1962).

S. S. Stevens, Am. Psychologist 17, 29 (1962).
[Crossref]

1961 (1)

For a different statement of the problem of depth constancy see R. Over, Am. J. Psychol. 74, 308 (1961).
[Crossref] [PubMed]

1960 (1)

A relation similar to Eq. (5) has been developed for use in an equation concerned with the perception of three-dimensional shape [W. C. Gogel, J. Psychol. 50, 179 (1960)].
[Crossref]

1959 (1)

T. Oyama, Psychol. Bull. 56, 74 (1959).
[Crossref] [PubMed]

1953 (2)

(a)See F. P. Kilpatrick and W. H. Ittelson, Psychol. Rev. 60, 223 (1953); (b)W. Epstein, J. Park, and A. Casey, Psychol. Bull. 58, 491 (1961); (c)and W. C. Gogel, Vision Res. 3, 106 (1963).

F. P. Kilpatrick and W. H. Ittelson, Psychol. Rev. 60, 223 (1953).
[Crossref] [PubMed]

1931 (1)

R. H. Thouless, Brit. J. Psychol. 21, 339 (1931).

Gogel, W. C.

W. C. Gogel, E. R. Wist, and G. S. Harker, Am. J. Phychol. 76, 537 (1963).
[Crossref]

A relation similar to Eq. (5) has been developed for use in an equation concerned with the perception of three-dimensional shape [W. C. Gogel, J. Psychol. 50, 179 (1960)].
[Crossref]

Harker, G. S.

W. C. Gogel, E. R. Wist, and G. S. Harker, Am. J. Phychol. 76, 537 (1963).
[Crossref]

Ittelson, W. H.

(a)See F. P. Kilpatrick and W. H. Ittelson, Psychol. Rev. 60, 223 (1953); (b)W. Epstein, J. Park, and A. Casey, Psychol. Bull. 58, 491 (1961); (c)and W. C. Gogel, Vision Res. 3, 106 (1963).

F. P. Kilpatrick and W. H. Ittelson, Psychol. Rev. 60, 223 (1953).
[Crossref] [PubMed]

Kilpatrick, F. P.

F. P. Kilpatrick and W. H. Ittelson, Psychol. Rev. 60, 223 (1953).
[Crossref] [PubMed]

(a)See F. P. Kilpatrick and W. H. Ittelson, Psychol. Rev. 60, 223 (1953); (b)W. Epstein, J. Park, and A. Casey, Psychol. Bull. 58, 491 (1961); (c)and W. C. Gogel, Vision Res. 3, 106 (1963).

Over, R.

For a different statement of the problem of depth constancy see R. Over, Am. J. Psychol. 74, 308 (1961).
[Crossref] [PubMed]

Oyama, T.

T. Oyama, Psychol. Bull. 56, 74 (1959).
[Crossref] [PubMed]

Stevens, S. S.

S. S. Stevens, Am. Psychologist 17, 29 (1962).
[Crossref]

Thouless, R. H.

R. H. Thouless, Brit. J. Psychol. 21, 339 (1931).

Ueno, T.

T. Ueno, Japan. Psychol. Res. 4, 99 (1962).

Wist, E. R.

W. C. Gogel, E. R. Wist, and G. S. Harker, Am. J. Phychol. 76, 537 (1963).
[Crossref]

Am. J. Phychol. (1)

W. C. Gogel, E. R. Wist, and G. S. Harker, Am. J. Phychol. 76, 537 (1963).
[Crossref]

Am. J. Psychol. (1)

For a different statement of the problem of depth constancy see R. Over, Am. J. Psychol. 74, 308 (1961).
[Crossref] [PubMed]

Am. Psychologist (1)

S. S. Stevens, Am. Psychologist 17, 29 (1962).
[Crossref]

Brit. J. Psychol. (1)

R. H. Thouless, Brit. J. Psychol. 21, 339 (1931).

J. Psychol. (1)

A relation similar to Eq. (5) has been developed for use in an equation concerned with the perception of three-dimensional shape [W. C. Gogel, J. Psychol. 50, 179 (1960)].
[Crossref]

Japan. Psychol. Res. (1)

T. Ueno, Japan. Psychol. Res. 4, 99 (1962).

Psychol. Bull. (1)

T. Oyama, Psychol. Bull. 56, 74 (1959).
[Crossref] [PubMed]

Psychol. Rev. (2)

(a)See F. P. Kilpatrick and W. H. Ittelson, Psychol. Rev. 60, 223 (1953); (b)W. Epstein, J. Park, and A. Casey, Psychol. Bull. 58, 491 (1961); (c)and W. C. Gogel, Vision Res. 3, 106 (1963).

F. P. Kilpatrick and W. H. Ittelson, Psychol. Rev. 60, 223 (1953).
[Crossref] [PubMed]

Other (1)

Reference 8(b), pp. 495–496.

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Figures (5)

Fig. 1
Fig. 1

A schematic drawing for considering the perception of size and distance.

Fig. 2
Fig. 2

Top view diagrams illustrating the physical conditions involved in the size and depth judgments.

Fig. 3
Fig. 3

The relation between the logarithm of the perceived size in centimeters of the rectangles and the logarithm of their physical distance in centimeters.

Fig. 4
Fig. 4

The relation between the logarithm of perceived depth (expressed in units of the nearest Object p) and the logarithm of the physical distance in centimeters required to produce that perceived depth.

Fig. 5
Fig. 5

The relation between the physical depth interval required to produce perceptually equal depth intervals and the physical distance of the beginning of the interval from the observer.

Tables (1)

Tables Icon

Table I Values of n, K2, and K3 as determined from the slopes and intersection valuesa of the straight lines of best fit for the data of Figs. 3 and 4.

Equations (23)

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

S v = K 1 θ v D v ,
K 1 = S e / θ e D e = S f / θ f D f , etc .
S v = S e .
S v = S e ( D e / D v ) .
S v = S e ( D v / D e ) n - 1 .
S v = S e ( D v / D e ) ,
S v = S e ,
S v = S e ( D v / D e ) n .
S v = K 2 θ v D v n ,
θ v in radians = S v / D v ,
K 2 = S e / θ e D e n = S f / θ f D f n , etc .
T = Thouless index = log S - log θ log S - log θ ,
S = S v / S e ,             θ = θ v / θ e ,             and             S = S v / S e .
( S / θ ) T = S / θ .
S v = K 2 θ v D v T .
T = n .
D v = K 3 D v n ,
K 3 = D e / D e n = D f / D f n , etc .
log S v = n log D v + log K 2 θ v
log D v = n log D v + log K 3 ,
K 1 = K 2 / K 3 .
D f = d e f + D e
d e f = K 3 ( D f n - D e n ) , etc .