Abstract

Models for the detection and the discrimination of low-contrast signals by human observers typically assume that the observer is limited by the filtering action of the visual system and by the noisy character of its processing. For some models both the filtering and the noise can be represented by a noise in the stimulus domain, the input equivalent noise of the model. We derive some formulas for computing this noise, describe the calculation of a sample, and discuss some implications of this approach.

© 1985 Optical Society of America

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References

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  1. A. B. Watson, “Detection and recognition of simple spatial forms,” in Physical and Biological Processing of Images, O. J. Braddick, A. C. Slade, eds. (Springer-Verlag, Berlin, 1983), pp. 100–114.Also available as NASA Tech. Mem. 84353 (April1983).
    [CrossRef]
  2. A. B. Watson, A. J. Ahumada, “A model of spatial contrast vision,” Invest. Opthalmol. Visual Sci. 24, 47 (A) (1983).
  3. M. A. Georgeson, G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 627–657 (1975).
  4. T. W. Anderson, An Introduction to Multivariate Statistical Analysis (Wiley, New York, 1958).
  5. A. J. Ahumada, A. B. Watson, “Uniform apparent contrast noise,” Invest. Opthalmol. Visual Sci. 24, 46 (A) (1983).
  6. J. D. Cowan, “Some remarks on channel bandwidths for visual contrast detection,” Neurosci. Prog. Res. Bull. 15, 492 (1977).
  7. A. J. Ahumada, A. B. Watson, “Uniform apparent contrast noise: a picture of the noise of the visual contrast detection system,” NASA Tech. Mem. No. 85867 (July1984).
  8. T. Caelli, G. Moraglia, “Detection of Gabor signals and discrimination of Gabor textures,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).
  9. A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
    [CrossRef] [PubMed]
  10. K. J. Myers, H. H. Barrett, M. C. Borgstrom, G. W. Seeley, D. D. Patton, R. D. Fiete, “Effect of noise power spectra on detectability of low-contrast objects,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).
  11. A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” NASA Tech. Mem. 84352 (April1983).
  12. A. B. Watson, A. J. Ahumada, “A model of human visual motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
    [CrossRef] [PubMed]
  13. D. G. Pelli, “The spatiotemporal spectrum of the equivalent noise of human vision,” Invest. Opthamol. Visual Sci. 24, 46 (A) (1983).

1985 (1)

1984 (2)

T. Caelli, G. Moraglia, “Detection of Gabor signals and discrimination of Gabor textures,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).

K. J. Myers, H. H. Barrett, M. C. Borgstrom, G. W. Seeley, D. D. Patton, R. D. Fiete, “Effect of noise power spectra on detectability of low-contrast objects,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).

1983 (3)

D. G. Pelli, “The spatiotemporal spectrum of the equivalent noise of human vision,” Invest. Opthamol. Visual Sci. 24, 46 (A) (1983).

A. B. Watson, A. J. Ahumada, “A model of spatial contrast vision,” Invest. Opthalmol. Visual Sci. 24, 47 (A) (1983).

A. J. Ahumada, A. B. Watson, “Uniform apparent contrast noise,” Invest. Opthalmol. Visual Sci. 24, 46 (A) (1983).

1981 (1)

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

1977 (1)

J. D. Cowan, “Some remarks on channel bandwidths for visual contrast detection,” Neurosci. Prog. Res. Bull. 15, 492 (1977).

1975 (1)

M. A. Georgeson, G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 627–657 (1975).

Ahumada, A. J.

A. B. Watson, A. J. Ahumada, “A model of human visual motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
[CrossRef] [PubMed]

A. B. Watson, A. J. Ahumada, “A model of spatial contrast vision,” Invest. Opthalmol. Visual Sci. 24, 47 (A) (1983).

A. J. Ahumada, A. B. Watson, “Uniform apparent contrast noise,” Invest. Opthalmol. Visual Sci. 24, 46 (A) (1983).

A. J. Ahumada, A. B. Watson, “Uniform apparent contrast noise: a picture of the noise of the visual contrast detection system,” NASA Tech. Mem. No. 85867 (July1984).

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” NASA Tech. Mem. 84352 (April1983).

Anderson, T. W.

T. W. Anderson, An Introduction to Multivariate Statistical Analysis (Wiley, New York, 1958).

Barlow, H. B.

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Barrett, H. H.

K. J. Myers, H. H. Barrett, M. C. Borgstrom, G. W. Seeley, D. D. Patton, R. D. Fiete, “Effect of noise power spectra on detectability of low-contrast objects,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).

Borgstrom, M. C.

K. J. Myers, H. H. Barrett, M. C. Borgstrom, G. W. Seeley, D. D. Patton, R. D. Fiete, “Effect of noise power spectra on detectability of low-contrast objects,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).

Burgess, A. E.

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Caelli, T.

T. Caelli, G. Moraglia, “Detection of Gabor signals and discrimination of Gabor textures,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).

Cowan, J. D.

J. D. Cowan, “Some remarks on channel bandwidths for visual contrast detection,” Neurosci. Prog. Res. Bull. 15, 492 (1977).

Fiete, R. D.

K. J. Myers, H. H. Barrett, M. C. Borgstrom, G. W. Seeley, D. D. Patton, R. D. Fiete, “Effect of noise power spectra on detectability of low-contrast objects,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).

Georgeson, M. A.

M. A. Georgeson, G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 627–657 (1975).

Jennings, R. J.

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Moraglia, G.

T. Caelli, G. Moraglia, “Detection of Gabor signals and discrimination of Gabor textures,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).

Myers, K. J.

K. J. Myers, H. H. Barrett, M. C. Borgstrom, G. W. Seeley, D. D. Patton, R. D. Fiete, “Effect of noise power spectra on detectability of low-contrast objects,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).

Patton, D. D.

K. J. Myers, H. H. Barrett, M. C. Borgstrom, G. W. Seeley, D. D. Patton, R. D. Fiete, “Effect of noise power spectra on detectability of low-contrast objects,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).

Pelli, D. G.

D. G. Pelli, “The spatiotemporal spectrum of the equivalent noise of human vision,” Invest. Opthamol. Visual Sci. 24, 46 (A) (1983).

Seeley, G. W.

K. J. Myers, H. H. Barrett, M. C. Borgstrom, G. W. Seeley, D. D. Patton, R. D. Fiete, “Effect of noise power spectra on detectability of low-contrast objects,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).

Sullivan, G. D.

M. A. Georgeson, G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 627–657 (1975).

Wagner, R. F.

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Watson, A. B.

A. B. Watson, A. J. Ahumada, “A model of human visual motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
[CrossRef] [PubMed]

A. B. Watson, A. J. Ahumada, “A model of spatial contrast vision,” Invest. Opthalmol. Visual Sci. 24, 47 (A) (1983).

A. J. Ahumada, A. B. Watson, “Uniform apparent contrast noise,” Invest. Opthalmol. Visual Sci. 24, 46 (A) (1983).

A. B. Watson, “Detection and recognition of simple spatial forms,” in Physical and Biological Processing of Images, O. J. Braddick, A. C. Slade, eds. (Springer-Verlag, Berlin, 1983), pp. 100–114.Also available as NASA Tech. Mem. 84353 (April1983).
[CrossRef]

A. J. Ahumada, A. B. Watson, “Uniform apparent contrast noise: a picture of the noise of the visual contrast detection system,” NASA Tech. Mem. No. 85867 (July1984).

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” NASA Tech. Mem. 84352 (April1983).

Invest. Opthalmol. Visual Sci. (2)

A. B. Watson, A. J. Ahumada, “A model of spatial contrast vision,” Invest. Opthalmol. Visual Sci. 24, 47 (A) (1983).

A. J. Ahumada, A. B. Watson, “Uniform apparent contrast noise,” Invest. Opthalmol. Visual Sci. 24, 46 (A) (1983).

Invest. Opthamol. Visual Sci. (1)

D. G. Pelli, “The spatiotemporal spectrum of the equivalent noise of human vision,” Invest. Opthamol. Visual Sci. 24, 46 (A) (1983).

J. Opt. Soc. Am. A (3)

A. B. Watson, A. J. Ahumada, “A model of human visual motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
[CrossRef] [PubMed]

T. Caelli, G. Moraglia, “Detection of Gabor signals and discrimination of Gabor textures,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).

K. J. Myers, H. H. Barrett, M. C. Borgstrom, G. W. Seeley, D. D. Patton, R. D. Fiete, “Effect of noise power spectra on detectability of low-contrast objects,” J. Opt. Soc. Am. A 1, 1291 (A) (1984).

J. Physiol. (London) (1)

M. A. Georgeson, G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. (London) 252, 627–657 (1975).

Neurosci. Prog. Res. Bull. (1)

J. D. Cowan, “Some remarks on channel bandwidths for visual contrast detection,” Neurosci. Prog. Res. Bull. 15, 492 (1977).

Science (1)

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Other (4)

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” NASA Tech. Mem. 84352 (April1983).

A. J. Ahumada, A. B. Watson, “Uniform apparent contrast noise: a picture of the noise of the visual contrast detection system,” NASA Tech. Mem. No. 85867 (July1984).

T. W. Anderson, An Introduction to Multivariate Statistical Analysis (Wiley, New York, 1958).

A. B. Watson, “Detection and recognition of simple spatial forms,” in Physical and Biological Processing of Images, O. J. Braddick, A. C. Slade, eds. (Springer-Verlag, Berlin, 1983), pp. 100–114.Also available as NASA Tech. Mem. 84353 (April1983).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

A picture of the noise of the contrast detection system referred to its input.

Fig. 2
Fig. 2

A multilayer model for contrast detection.

Fig. 3
Fig. 3

A single-layer model for contrast detection.

Fig. 4
Fig. 4

A single-layer model for contrast detection whose noise is white, the SIN model.

Fig. 5
Fig. 5

The EN model for contrast detection.

Fig. 6
Fig. 6

The EN model with backprojected white noise.

Fig. 7
Fig. 7

White noise. The contrast value of each pixel is approximately normally distributed and independent of all other values.

Fig. 8
Fig. 8

(a) The model’s contrast sensitivity at zero eccentricity as a function of spatial frequency. (b) The amplitude factor of the filter used to make the homogeneous filtered noise from the white noise.

Fig. 9
Fig. 9

The spatially homogeneous filtered noise.

Equations (25)

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

S = ( s i ) , i = 1 , n .
A k = ( a k i j ) k = 1 , m ; i = 1 , n k 1 ; j = 1 , n k
n 0 = n .
R k = ( r kij ) k = 1 , m ; i , j = 1 , n k
A = A 1 A 2 A m
R = R m + A m T R m 1 A m + + H k T R k H k + + H 1 T R 1 H 1 ,
H k = A k + 1 A k + 2 A m .
d ( S ) = z { Prob ( Y | Signal = S ) } z { Prob ( Y | Signal = 0 ) } ,
d ( S ) = S A R 1 A T S T .
C = A B 1 ,
R = B T B .
R E = ( C C T ) 1 .
D = C T ( C C T ) 1 .
D = C 1 .
d [ S ( u , υ , a , b ) ] = g ( u , υ , a , b ) .
f ( u , υ , a , b ) = g ( u , υ , a , b ) 1 / 2 .
s = 1 + c e ,
s ( f ) = exp [ ( f / 14. ) ] 2 ) 0.9 exp [ ( f / 1.0 ) 2 ] ,
a ( f ) = s ( 32 ) / s ( f ) , f < 32 , = 0 , f 32 .
f = ( f x 2 + f y 2 ) 1 / 2
I 2 ( x 2 , y 2 ) = I 1 ( x 1 , y 1 ) .
x 1 = m x 2 , y 1 = m y 2 ,
m = ln ( 1 + c r 2 ) / c r 2 ,
r 2 = ( x 2 2 + y 2 2 ) 1 / 2 .
M ( e ) = 1 / ( 1 + c e ) ,

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