Abstract

We have measured the effect of signal-location uncertainty on the detectability of simple visual signals in uncorrelated image noise. An M-alternative forced-choice signal-location identification technique was used with values of M ranging from 2 to 1800. We find high statistical efficiency (50% for aperiodic signals), and results from one value of M can be used to predict all others. The results are consistent with the view that humans can act as suboptimal maximum a posteriori probability observers.

© 1984 Optical Society of America

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References

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  1. D. J. Lasley, T. Cohn, “Detection of a luminance increment: effect of temporal uncertainty,” J. Opt. Soc. Am. 71, 845–850 (1981).
    [CrossRef] [PubMed]
  2. R. P. Chambers, J. S. Courtney-Pratt, “Experiments on the detection of visual signals in noise using computer-generated signals,” Photogr. Sci. Eng. 13, 286–298 (1969).
  3. S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiology 116, 533–538 (1975).
    [PubMed]
  4. R. G. Swensson, P. F. Judy, “Detection of noisy visual targets: models for the effects of spatial uncertainty and signal-to-noise ratio,” Percept. Psychophys. 29, 521–534 (1981).
    [CrossRef] [PubMed]
  5. D. M. Green, D. L. Weber, “Detection of temporally uncertain signals,” J. Acoust. Soc. Am. 67, 1304–1311 (1980).
    [CrossRef] [PubMed]
  6. P. Elliott, “Forced Choice Tables (Appendix 1),” in Signal Detection and Recognition by Human Observers, J. A. Swets, ed. (Wiley, New York, 1964), pp. 679–684.
  7. W. P. Tanner, T. G. Birdsall, “Definitions of d′ and η as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
    [CrossRef]
  8. A. E. Burgess, R. F. Wagner, R. J. J. Jennings, “Statistical efficiency: a measure of human visual signal detection performance,” J. Appl. Photogr. Eng. 8, 76–78 (1982).
  9. A. VanderLugt, “The effects of small displacements of spatial filters,” Appl. Opt. 6, 1221–1226 (1967).
    [CrossRef]

1982 (1)

A. E. Burgess, R. F. Wagner, R. J. J. Jennings, “Statistical efficiency: a measure of human visual signal detection performance,” J. Appl. Photogr. Eng. 8, 76–78 (1982).

1981 (2)

D. J. Lasley, T. Cohn, “Detection of a luminance increment: effect of temporal uncertainty,” J. Opt. Soc. Am. 71, 845–850 (1981).
[CrossRef] [PubMed]

R. G. Swensson, P. F. Judy, “Detection of noisy visual targets: models for the effects of spatial uncertainty and signal-to-noise ratio,” Percept. Psychophys. 29, 521–534 (1981).
[CrossRef] [PubMed]

1980 (1)

D. M. Green, D. L. Weber, “Detection of temporally uncertain signals,” J. Acoust. Soc. Am. 67, 1304–1311 (1980).
[CrossRef] [PubMed]

1975 (1)

S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiology 116, 533–538 (1975).
[PubMed]

1969 (1)

R. P. Chambers, J. S. Courtney-Pratt, “Experiments on the detection of visual signals in noise using computer-generated signals,” Photogr. Sci. Eng. 13, 286–298 (1969).

1967 (1)

1958 (1)

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and η as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

Birdsall, T. G.

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and η as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

Burgess, A. E.

A. E. Burgess, R. F. Wagner, R. J. J. Jennings, “Statistical efficiency: a measure of human visual signal detection performance,” J. Appl. Photogr. Eng. 8, 76–78 (1982).

Chambers, R. P.

R. P. Chambers, J. S. Courtney-Pratt, “Experiments on the detection of visual signals in noise using computer-generated signals,” Photogr. Sci. Eng. 13, 286–298 (1969).

Cohn, T.

Courtney-Pratt, J. S.

R. P. Chambers, J. S. Courtney-Pratt, “Experiments on the detection of visual signals in noise using computer-generated signals,” Photogr. Sci. Eng. 13, 286–298 (1969).

Elliott, P.

P. Elliott, “Forced Choice Tables (Appendix 1),” in Signal Detection and Recognition by Human Observers, J. A. Swets, ed. (Wiley, New York, 1964), pp. 679–684.

Goodenough, D. J.

S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiology 116, 533–538 (1975).
[PubMed]

Green, D. M.

D. M. Green, D. L. Weber, “Detection of temporally uncertain signals,” J. Acoust. Soc. Am. 67, 1304–1311 (1980).
[CrossRef] [PubMed]

Jennings, R. J. J.

A. E. Burgess, R. F. Wagner, R. J. J. Jennings, “Statistical efficiency: a measure of human visual signal detection performance,” J. Appl. Photogr. Eng. 8, 76–78 (1982).

Judy, P. F.

R. G. Swensson, P. F. Judy, “Detection of noisy visual targets: models for the effects of spatial uncertainty and signal-to-noise ratio,” Percept. Psychophys. 29, 521–534 (1981).
[CrossRef] [PubMed]

Lasley, D. J.

Lusted, L. B.

S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiology 116, 533–538 (1975).
[PubMed]

Metz, C. E.

S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiology 116, 533–538 (1975).
[PubMed]

Starr, S. J.

S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiology 116, 533–538 (1975).
[PubMed]

Swensson, R. G.

R. G. Swensson, P. F. Judy, “Detection of noisy visual targets: models for the effects of spatial uncertainty and signal-to-noise ratio,” Percept. Psychophys. 29, 521–534 (1981).
[CrossRef] [PubMed]

Tanner, W. P.

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and η as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

VanderLugt, A.

Wagner, R. F.

A. E. Burgess, R. F. Wagner, R. J. J. Jennings, “Statistical efficiency: a measure of human visual signal detection performance,” J. Appl. Photogr. Eng. 8, 76–78 (1982).

Weber, D. L.

D. M. Green, D. L. Weber, “Detection of temporally uncertain signals,” J. Acoust. Soc. Am. 67, 1304–1311 (1980).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Acoust. Soc. Am. (2)

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and η as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

D. M. Green, D. L. Weber, “Detection of temporally uncertain signals,” J. Acoust. Soc. Am. 67, 1304–1311 (1980).
[CrossRef] [PubMed]

J. Appl. Photogr. Eng. (1)

A. E. Burgess, R. F. Wagner, R. J. J. Jennings, “Statistical efficiency: a measure of human visual signal detection performance,” J. Appl. Photogr. Eng. 8, 76–78 (1982).

J. Opt. Soc. Am. (1)

Percept. Psychophys. (1)

R. G. Swensson, P. F. Judy, “Detection of noisy visual targets: models for the effects of spatial uncertainty and signal-to-noise ratio,” Percept. Psychophys. 29, 521–534 (1981).
[CrossRef] [PubMed]

Photogr. Sci. Eng. (1)

R. P. Chambers, J. S. Courtney-Pratt, “Experiments on the detection of visual signals in noise using computer-generated signals,” Photogr. Sci. Eng. 13, 286–298 (1969).

Radiology (1)

S. J. Starr, C. E. Metz, L. B. Lusted, D. J. Goodenough, “Visual detection and localization of radiographic images,” Radiology 116, 533–538 (1975).
[PubMed]

Other (1)

P. Elliott, “Forced Choice Tables (Appendix 1),” in Signal Detection and Recognition by Human Observers, J. A. Swets, ed. (Wiley, New York, 1964), pp. 679–684.

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Figures (7)

Fig. 1
Fig. 1

(a) Sample display of the MAFC signal localization task. Sixteen signals are presented here (rather than one) to illustrate the variable signal visibility because of the added visual noise. A noiseless copy of the signal is shown in the upper-right-hand corner. The SNR is 6.3, and the signal just above the cursor (cross) has a normalized cross correlation equal to 8.31. Note that the SNR is the ensemble average of normalized cross-correlation values. (b) Example display for M = 98 with signal-location bars present. There is one disk signal somewhere in the two square noise fields. The observer selects the most probable location. The bars define two sets of square grid lines that identify boundaries of disk-signal-location alternatives. In this example, the signal is in the location above the cursor (cross). Reference copies of the disk signal are shown above the noise fields.

Fig. 2
Fig. 2

Percentage of correct localization responses for the disk signal as a function of SNR for two observers and five values of M. The solid lines are for a MAP observer operating at 50% statistical efficiency.

Fig. 3
Fig. 3

The results of Fig. 2 (observer BC) have been transformed into a detectability index plot (dM as a function of SNR). The best-fit line has a slope of 0.74 and an ordinate intercept of 0.26 in SNR units.

Fig. 4
Fig. 4

Detectability index plot for observer AB for disk data given in Fig. 2. The best-fit line slope is 0.75, and the intercept is 0.26 in SNR units. The fact that the data fall on a common line (within experimental error) indicates that results from one value of M can be used to predict performance for all values of M.

Fig. 5
Fig. 5

Variation in threshold SNR (defined for 90% correct detection) as a function of the value of M for the disk signal. The two human observers required about 2 times higher SNR than the ideal observer performing the same detection task.

Fig. 6
Fig. 6

The detectability index plot (dM versus SNR) for the square signal with M ranging from 2 to 1800.

Fig. 7
Fig. 7

Detectability index plot for the two-cycle sine wave with M ranging from 2 to 72. Note the increased value of the intercept of the best-fit line.

Equations (2)

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- f i ( x , y ) f j ( x , y ) = 0.
P ( C ) = - d x P S N ( x ) [ - d y P N ( y ) ] M - 1 .

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