Abstract

A statistical interpretation of human response to visual noise generated by toner particles deposited on background areas of electrophotographic copies is given. The constants of the theory are estimated from psychophysical measurements made on a set of noise samples. The study indicates that the background noise perception is connected with retinal areas nearly equal in size to those reported for the receptive fields of the ganglions in the fovea centralis.

© 1974 Optical Society of America

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References

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  1. E. W. H. Selwyn, Photogr. J. 75, 571 (1935), Photogr. J. 82, 208 (1942); H. J. Zweig, J. Opt. Soc. Am. 46, 805 (1956); K. F. Stultz, H. J. Zweig, J. Opt. Soc. Am. 49, 693 (1959); A. Marriage, E. Pitts, J. Opt. Soc. Am. 46, 1019 (1956).
    [CrossRef]
  2. L. A. Jones, G. C. Higgins, K. F. Stultz, J. Opt. Soc. Am. 45, 107 (1955); L. A. Jones, G. C. Higgins, K. F. Stultz, H. F. Hoesterey, J. Opt. Soc. Am. 47, 312 (1957).
    [CrossRef]
  3. J. A. C. Yule, W. J. Neilsen, T. A. G. A. Proc. 3, 65 (1951).
  4. K. N. Leibovic, Nervous System Theory (Academic, New York, 1972).
  5. G. Baumgartner, Pflügers Arch. ges. Physiol. 272, 21 (1960).
  6. O. Bryngdahl, Vision Res. 6, 553 (1966).
    [CrossRef] [PubMed]
  7. T. N. Cornsweet, Visual Perception, (Academic, New York, 1971); M. V. Klein, Optics (J. Wiley & Sons, New York, 1970).

1966 (1)

O. Bryngdahl, Vision Res. 6, 553 (1966).
[CrossRef] [PubMed]

1960 (1)

G. Baumgartner, Pflügers Arch. ges. Physiol. 272, 21 (1960).

1955 (1)

1951 (1)

J. A. C. Yule, W. J. Neilsen, T. A. G. A. Proc. 3, 65 (1951).

1935 (1)

E. W. H. Selwyn, Photogr. J. 75, 571 (1935), Photogr. J. 82, 208 (1942); H. J. Zweig, J. Opt. Soc. Am. 46, 805 (1956); K. F. Stultz, H. J. Zweig, J. Opt. Soc. Am. 49, 693 (1959); A. Marriage, E. Pitts, J. Opt. Soc. Am. 46, 1019 (1956).
[CrossRef]

Baumgartner, G.

G. Baumgartner, Pflügers Arch. ges. Physiol. 272, 21 (1960).

Bryngdahl, O.

O. Bryngdahl, Vision Res. 6, 553 (1966).
[CrossRef] [PubMed]

Cornsweet, T. N.

T. N. Cornsweet, Visual Perception, (Academic, New York, 1971); M. V. Klein, Optics (J. Wiley & Sons, New York, 1970).

Higgins, G. C.

Jones, L. A.

Leibovic, K. N.

K. N. Leibovic, Nervous System Theory (Academic, New York, 1972).

Neilsen, W. J.

J. A. C. Yule, W. J. Neilsen, T. A. G. A. Proc. 3, 65 (1951).

Selwyn, E. W. H.

E. W. H. Selwyn, Photogr. J. 75, 571 (1935), Photogr. J. 82, 208 (1942); H. J. Zweig, J. Opt. Soc. Am. 46, 805 (1956); K. F. Stultz, H. J. Zweig, J. Opt. Soc. Am. 49, 693 (1959); A. Marriage, E. Pitts, J. Opt. Soc. Am. 46, 1019 (1956).
[CrossRef]

Stultz, K. F.

Yule, J. A. C.

J. A. C. Yule, W. J. Neilsen, T. A. G. A. Proc. 3, 65 (1951).

J. Opt. Soc. Am. (1)

Pflügers Arch. ges. Physiol. (1)

G. Baumgartner, Pflügers Arch. ges. Physiol. 272, 21 (1960).

Photogr. J. (1)

E. W. H. Selwyn, Photogr. J. 75, 571 (1935), Photogr. J. 82, 208 (1942); H. J. Zweig, J. Opt. Soc. Am. 46, 805 (1956); K. F. Stultz, H. J. Zweig, J. Opt. Soc. Am. 49, 693 (1959); A. Marriage, E. Pitts, J. Opt. Soc. Am. 46, 1019 (1956).
[CrossRef]

T. A. G. A. Proc. (1)

J. A. C. Yule, W. J. Neilsen, T. A. G. A. Proc. 3, 65 (1951).

Vision Res. (1)

O. Bryngdahl, Vision Res. 6, 553 (1966).
[CrossRef] [PubMed]

Other (2)

T. N. Cornsweet, Visual Perception, (Academic, New York, 1971); M. V. Klein, Optics (J. Wiley & Sons, New York, 1970).

K. N. Leibovic, Nervous System Theory (Academic, New York, 1972).

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Figures (12)

Fig. 1
Fig. 1

Two neighboring visibility cells containing k = 3 and ki = 5 particles, respectively.

Fig. 2
Fig. 2

Model of a visibility cell and its neighborhood.

Fig. 3
Fig. 3

P* as the function of coverage with different particle sizes as parameters, dc = 250 μ, v = 0.05.

Fig. 4
Fig. 4

Phase diagram for the appearance of noise, dc = 250 μ, v = 0.05 Pmin* = 0.03.

Fig. 5
Fig. 5

Histograms of particle area distributions of noise samples produced by various sieve combinations.

Fig. 6
Fig. 6

Probability bar charts of detectability distributions for different particle sizes.

Fig. 7
Fig. 7

Probability bar charts of objectionability distributions for different particle sizes.

Fig. 8
Fig. 8

Detectability distributions for different background particle sizes plotted on Gauss scale.

Fig. 9
Fig. 9

Objectionability distributions for different background particle sizes plotted on Gauss scale.

Fig. 10
Fig. 10

Cumulative detectability (·) and objectionability (x) distributions for different particle sizes.

Fig. 11
Fig. 11

Detectability and objectionability threshold coverages of the observers as the function of particle size: B0.5d = detectability threshold for 50% of the observers; B0.20 = objectionability threshold for 20% of the observers; B0.50 = objectionability threshold for 50% of the observers.

Fig. 12
Fig. 12

A receptive field of the retina (a) and possible distributions of illuminance (b), (c) originating noise effect in the field.

Equations (18)

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R k = c r p - k f r p + k f l r t .
R k / R c = [ c r p + k f ( l r t - r p ) ] / c r p .
| R k i R c - R k R c | | ( k i - k ) f ( e r t - r p ) c r p | v .
| R k i R c - R k R c | k i - k f c v .
P k , N = ( N k ) p k ( 1 - p ) N - k ,
p = c / L
N = L s / f .
P k , N = [ ( c s / f ) k / k ! ] exp [ - ( c s / f ) ] .
P k , N u = 0 N P u , N .
P k , N ( u = 0 k - c v / f P u , N + u = k + c v / f N P u , N ) .
N P u , N = 1
P k , N ( u = 0 k - c v / f P u , N + u = k + c v / f N P u , N ) = P k , N ( 1 - u = k - c v / f k + c v / f P u , N ) .
P k , N [ 1 - ( u = k - c v / f k + c v / f P u , N ) 8 ] .
P * = 1 - k = 0 N ( u = k - c v / f k + c v / f P u , N ) 8 P k , N .
P * = 1 - exp ( - 9 c s / f ) k = 0 N [ u = k - c v / f k + c v / f ( c s / f ) u u ! ] 8 ( c s / f ) k k ! .
f a f b A ( f ) d f = 1.
v ( f ) = v 0 / B ( f ) ,
f eff = [ f a f b f A ( f ) B ( f ) d f ] / [ f a f b A ( f ) B ( f ) d f ]

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