Abstract

A model of threshold and suprathreshold vision in relation to variation of object size is proposed. An important factor in suprathreshold vision is the signal-contrast loss in optical and neural components; in threshold vision, an important additional factor is the manner in which the brain acts on retinal noise. The signal-contrast loss has been measured in terms of a suprathreshold signal-transfer function for circular signals. In threshold vision, the noise processes are shown to predominate and the signal-contrast losses to be insignificant. Therefore signal-transfer functions cannot be deduced solely from threshold measurements; indeed, peak performance in suprathreshold vision is reached at object size one-tenth that at threshold. In suprathreshold vision, performance is shown to depend on a balance between optical unsharpness and neural sharpening (lateral inhibition). Contrast loss due to neural unsharpness (summation) appears to be insignificant in foveal vision and only partially significant in peripheral vision. Hence neural properties such as transfer functions, receptive-field sizes, and the spatial extent of neural interactions cannot be deduced from over-all measurements on the eye without correction for optical unsharpness.

© 1972 Optical Society of America

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References

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  1. The term threshold vision here relates to simultaneous contrast or incremental (including decremental) threshold, although the concepts discussed may well apply also to absolute thresholds.
  2. G. A. Hay, Nature 211, 1380 (1966).
    [CrossRef] [PubMed]
  3. Signal contrast at any stage in the visual process is here defined in the form C= |I1 −I0|/I0, where I0 and I1 are the mean luminances, brightnesses, pulse rates, etc., associated with the background and a specified part of the object detail, respectively.
  4. F. Ratliff, Mach Bands (Holden–Day, San Francisco, 1965).
  5. The present analysis refers to the steady-state sensation of natural vision in which the effects of temporal phenomena such as saccades are averaged.
  6. O. Dupuy, Vision Res. 8, 1507 (1968).
    [CrossRef] [PubMed]
  7. R. H. Morgan, Am. J. Roentgenol. 93, 982 (1965).
  8. Hl. de Vries, Physica 10, 553 (1943).
    [CrossRef]
  9. A. Rose, Proc. IRE,  30, 295 (1942).
    [CrossRef]
  10. A. Rose, J. Opt. Soc. Am. 38, 196 (1948).
    [CrossRef] [PubMed]
  11. H. R. Blackwell, J. Opt. Soc. Am. 36, 624 (1946).
    [CrossRef] [PubMed]
  12. J. J. DePalma and E. M. Lowry, J. Opt. Soc. Am. 52, 328 (1962).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  15. L. L. Sloan, Vision Res. 8, 901 (1968).
    [CrossRef] [PubMed]
  16. J. Mandelbaum and L. L. Sloan, Am. J. Ophthalmol. 30, 581 (1947).
    [PubMed]
  17. O. Bryngdahl, J. Opt. Soc. Am. 56, 811 (1966).
    [CrossRef] [PubMed]
  18. N. W. Taylor, J. Opt. Soc. Am. 52, 820 (1962).
    [CrossRef]
  19. R. W. Gubisch, J. Opt. Soc. Am. 57, 407 (1967).
    [CrossRef]
  20. J. E. Dowling and B. B. Boycott, Proc. Roy. Soc. (London) B166, 80 (1966).
  21. F. W. Campbell and R. W. Gubisch, J. Physiol. (London) 186, 558 (1966).

1968 (3)

O. Dupuy, Vision Res. 8, 1507 (1968).
[CrossRef] [PubMed]

A. S. Patel and R. W. Jones, J. Opt. Soc. Am. 58, 696 (1968).
[CrossRef] [PubMed]

L. L. Sloan, Vision Res. 8, 901 (1968).
[CrossRef] [PubMed]

1967 (1)

1966 (4)

J. E. Dowling and B. B. Boycott, Proc. Roy. Soc. (London) B166, 80 (1966).

F. W. Campbell and R. W. Gubisch, J. Physiol. (London) 186, 558 (1966).

G. A. Hay, Nature 211, 1380 (1966).
[CrossRef] [PubMed]

O. Bryngdahl, J. Opt. Soc. Am. 56, 811 (1966).
[CrossRef] [PubMed]

1965 (1)

R. H. Morgan, Am. J. Roentgenol. 93, 982 (1965).

1962 (2)

1961 (1)

1948 (1)

1947 (1)

J. Mandelbaum and L. L. Sloan, Am. J. Ophthalmol. 30, 581 (1947).
[PubMed]

1946 (1)

1943 (1)

Hl. de Vries, Physica 10, 553 (1943).
[CrossRef]

1942 (1)

A. Rose, Proc. IRE,  30, 295 (1942).
[CrossRef]

Blackwell, H. R.

Boycott, B. B.

J. E. Dowling and B. B. Boycott, Proc. Roy. Soc. (London) B166, 80 (1966).

Bryngdahl, O.

Campbell, F. W.

F. W. Campbell and R. W. Gubisch, J. Physiol. (London) 186, 558 (1966).

de Vries, Hl.

Hl. de Vries, Physica 10, 553 (1943).
[CrossRef]

DePalma, J. J.

Dowling, J. E.

J. E. Dowling and B. B. Boycott, Proc. Roy. Soc. (London) B166, 80 (1966).

Dupuy, O.

O. Dupuy, Vision Res. 8, 1507 (1968).
[CrossRef] [PubMed]

Gubisch, R. W.

R. W. Gubisch, J. Opt. Soc. Am. 57, 407 (1967).
[CrossRef]

F. W. Campbell and R. W. Gubisch, J. Physiol. (London) 186, 558 (1966).

Hay, G. A.

G. A. Hay, Nature 211, 1380 (1966).
[CrossRef] [PubMed]

Jones, R. W.

Lowry, E. M.

Mandelbaum, J.

J. Mandelbaum and L. L. Sloan, Am. J. Ophthalmol. 30, 581 (1947).
[PubMed]

Morgan, R. H.

R. H. Morgan, Am. J. Roentgenol. 93, 982 (1965).

Patel, A. S.

Ratliff, F.

F. Ratliff, Mach Bands (Holden–Day, San Francisco, 1965).

Rose, A.

Sloan, L. L.

L. L. Sloan, Vision Res. 8, 901 (1968).
[CrossRef] [PubMed]

J. Mandelbaum and L. L. Sloan, Am. J. Ophthalmol. 30, 581 (1947).
[PubMed]

Taylor, N. W.

Am. J. Ophthalmol. (1)

J. Mandelbaum and L. L. Sloan, Am. J. Ophthalmol. 30, 581 (1947).
[PubMed]

Am. J. Roentgenol. (1)

R. H. Morgan, Am. J. Roentgenol. 93, 982 (1965).

J. Opt. Soc. Am. (8)

J. Physiol. (London) (1)

F. W. Campbell and R. W. Gubisch, J. Physiol. (London) 186, 558 (1966).

Nature (1)

G. A. Hay, Nature 211, 1380 (1966).
[CrossRef] [PubMed]

Physica (1)

Hl. de Vries, Physica 10, 553 (1943).
[CrossRef]

Proc. IRE (1)

A. Rose, Proc. IRE,  30, 295 (1942).
[CrossRef]

Proc. Roy. Soc. (London) (1)

J. E. Dowling and B. B. Boycott, Proc. Roy. Soc. (London) B166, 80 (1966).

Vision Res. (2)

L. L. Sloan, Vision Res. 8, 901 (1968).
[CrossRef] [PubMed]

O. Dupuy, Vision Res. 8, 1507 (1968).
[CrossRef] [PubMed]

Other (4)

The term threshold vision here relates to simultaneous contrast or incremental (including decremental) threshold, although the concepts discussed may well apply also to absolute thresholds.

Signal contrast at any stage in the visual process is here defined in the form C= |I1 −I0|/I0, where I0 and I1 are the mean luminances, brightnesses, pulse rates, etc., associated with the background and a specified part of the object detail, respectively.

F. Ratliff, Mach Bands (Holden–Day, San Francisco, 1965).

The present analysis refers to the steady-state sensation of natural vision in which the effects of temporal phenomena such as saccades are averaged.

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Figures (10)

Fig. 1
Fig. 1

Diagrammatic representation of Signal (a circular area of angular diameter α′) and noise at the comparison site. The function represents a temporal sample of the spatial distribution of the relevant quantity (brightness, pulse rate, etc.) across a diameter of the image. The noise shown is the absolute standard deviation ϕ·Io.

Fig. 2
Fig. 2

Functional representation of the threshold–suprathreshold model of vision.

Fig. 3
Fig. 3

Perception of circular object detail. —— contrast-threshold functions CT(α), – – – – signal-transfer functions for observer MSC A(α), and ···· noise factor F(α). For each graph the logarithm of the background luminance in millilamberts (mL) is shown.

Fig. 4
Fig. 4

The qualitative effect of the combined visual unsharpness and lateral inhibition on the central contrast of circular-object detail of different diameters. A, luminance distribution of object detail across its diameter; B, total point spread function of the eye, including optical and neural unsharpness and neural lateral inhibition (Ref. 4); and C, (subjective) brightness distribution. In optical terms, C represents the convolutions of A with B. It is clear that the central contrast in the subjective image decreases for both small and large object detail.

Fig. 5
Fig. 5

Preliminary measurements of the signal-transfer function for circular detail, for observer GAH. The parameter is the logarithm of the adapting luminance in mL. Shown also for each point is the standard error of the means.

Fig. 6
Fig. 6

Perception of objects with unidimensional sinusoidal luminance distributions (Refs. 13 and 14). —— contrast-threshold function CT(v), – – – – signal-transfer function A(v), and ···· noise factor F(v). For each graph, the logarithm of the mean luminance in mL is shown.

Fig. 7
Fig. 7

Visual acuity for unit contrast as a function of background luminance (Ref. 16), for 0 ° 1 ° + + + + 2 ° } horizontal temporal eccentricity . The acuity is expressed as the threshold diameter in minutes of arc of black circular details on a light background.

Fig. 8
Fig. 8

Signal-transfer functions – – – eye (observer MSC) A(α), —— lens AO(α) (Ref. 19), and ···· DN(α) = A(α)/AO(α), all for circular object detail. For each graph, the logarithm of the object luminance in mL is shown. The values >1 shown for DN(α) result partly from the normalization of A(α); no evidence of the absolute values of DN(α) is presented.

Fig. 9
Fig. 9

DN(α) for the neural system for circular object detail, □ 100, ○ 10, ▽ 1, △ 0.1, ● 0.01, + 0.001, and × 0.0001 mL. —·—· is the signal-transfer function of an ideal receptive field of diameter 25″. The values >1 shown for DN(α) result partly from the normalization of A(α); no evidence of the absolute values of DN(α) is presented.

Fig. 10
Fig. 10

Spatial-frequency transfer functions – – – – eye A(v) (Ref. 13), —— lens AO(v) (Ref. 21), ···· neural system AN(v). —·—· spatial-frequency transfer function of an ideal receptive field of diameter 25″.

Equations (8)

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s T = k · ϕ
s > k · ϕ ,
s ( α ) = C ( α ) · A ( α )
ϕ ( α ) = ϕ p · F ( α ) .
C T ( α ) = k · ϕ p · F ( α ) / A ( α ) .
C ( α ) 1 / A ( α )     ( suprathreshold condition ) .
C T ( α ) F ( α ) / A ( α )     ( threshold condition ) .
0 ° 1 ° + + + + 2 ° } horizontal temporal eccentricity .