Abstract

Historically, human signal-detection responses have been assumed to be governed by external determinants (nature of the signal, the noise, and the task) and internal determinants. Variability in the internal determinants is commonly attributed to internal noise (often vaguely defined). We present a variety of experimental results that demonstrate observer inconsistency in performing noise-limited visual detection and discrimination tasks with repeated presentation of images. Our results can be interpreted by using a model that includes an internal-noise component that is directly proportional to image noise. This so-called induced internal-noise component dominates when external noise is easily visible. We demonstrate that decision-variable fluctuations lead to this type of internal noise. Given this induced internal-noise proportionality (σi0 = 0.75 ± 0.1), the upper limit to human visual signal-detection efficiency is 64% ± 6%. This limit is consistent with a variety of results presented in earlier papers in this series [ A. E. Burgess and H. Ghandeharian, J. Opt. Soc. Am. A 1, 900, 906 ( 1984); A. Burgess, J. Opt. Soc. Am. A 2, 1498 ( 1985)].

© 1988 Optical Society of America

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  1. N. S. Nagaraja, “Effect of luminance noise on contrast thresholds,” J. Opt. Soc. Am. 54, 950–955 (1964).
    [Crossref]
  2. G. A. Hay, M. S. Chesters, “A model of visual threshold detection,” J. Theor. Biol. 67, 221–240 (1977);“Signal-transfer functions in threshold and suprathreshold vision,” J. Opt. Soc. Am. 62, 990–998 (1972).
    [Crossref] [PubMed]
  3. A. E. Burgess, K. Humphrey, R. F. Wagner, “Detection of bars and discs in quantum noise,” in Application of Optical Instrumentation in Medicine VII, J. Gray, ed., Proc. Soc. Photo-Opt. Instrum. Eng.173, 34–40 (1979).
    [Crossref]
  4. D. Pelli, “Effects of visual noise,” doctoral dissertation (University of Cambridge, Cambridge, 1981).
  5. A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual discrimination,” Science 214, 93–94 (1981).
    [Crossref] [PubMed]
  6. M. Ishida, K. Doi, L.-N. Loo, C. E. Metz, J. L. Lehr, “Digital image processing: effect on detectability of simulated low-contrast radiographic patterns,” Radiology 150, 569–575 (1984).
    [PubMed]
  7. D. G. Pelli, “The spatiotemporal spectrum of the equivalent noise of human vision,” Invest. Ophthalmol. Suppl. 24, 46 (1983).
  8. H. B. Barlow, “Incremental thresholds at low intensities considered as signal/noise discrimination,” J. Physiol. 136, 469–488 (1957).
    [PubMed]
  9. D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
    [Crossref] [PubMed]
  10. W. A. Wickelgren, “Unidimensional strength theory and component analysis of noise in absolute and comparative judgments,” J. Math. Psychol. 5, 102–122 (1968).
    [Crossref]
  11. J. Jastrow, “A critique of psycho-physic methods,” Am. J. Psychol. 1, 271–309 (1888).
    [Crossref]
  12. J. M Cattell, “On errors of observation,” Am. J. Psychol. 5, 285–293 (1983).
    [Crossref]
  13. H. B. Barlow, “Retinal noise and absolute threshold,” J. Opt. Soc. Am. 46, 634–639 (1956).
    [Crossref] [PubMed]
  14. A. T. Welford, Fundamentals of Skill (Methuen, London, 1968).
  15. D. M. Green, “Consistency of auditory detection judgments,” Psychol. Rev. 71, 392–407 (1964).
    [Crossref] [PubMed]
  16. R. A. Siegel, “Internal and external noise in auditory detection,” M. Sc. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1979).
  17. A. Ahumeda, “Detection of tones masked by noise: a comparison of human observers with digital computer simulated energy detectors of varying bandwidths,” Department of Psychology Tech. Rep. 29 (University of California at Los Angeles, Los Angeles, 1967).
  18. M. F. Spiegel, D. M. Green, “Two procedures for estimating internal noise,” J. Acoust. Soc. Am. 70, 69–73 (1981).
    [Crossref] [PubMed]
  19. A. E. Burgess, “Detection and identification efficiency: an update,” in Application of Optical Instrumentation in Medicine XIII: Medical Image Production, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.535, 50–56 (1985);“On observer internal noise,” in Application of Optical Instrumentation in Medicine XIV: Medical Imaging, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 626, 208–213 (1986).
    [Crossref]
  20. R. F. Wagner, D. G. Brown, M. S. Pastel, “The application of information theory to the assessment of computed tomography,” Med. Phys. 6, 441–451 (1979).
  21. G. E. Legge, D. Kersten, A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. A 4, 381–404 (1987).
  22. A. E. Burgess, H. Ghandeharian, “Visual signal detection.I. Ability to use phase information,” J. Opt. Soc. Am. A 1, 900–905 (1984).
    [Crossref] [PubMed]
  23. A. E. Burgess, H. Ghandeharian, “Visual signal detection.II. Signal-location identification,” J. Opt. Soc. Am. A 1, 906–910 (1984).
    [Crossref] [PubMed]
  24. A. Burgess, “Visual signal detection. III. On Bayesian use of prior knowledge and cross correlation,” J. Opt. Soc. Am. A 2, 1498–1507 (1985).
    [Crossref] [PubMed]
  25. P. Elliot, “Forced choice tables,” in Signal Detection and Recognition by Human Observers, J. A. Swets, ed. (Wiley, New York, 1964), App. 1, pp. 679–684.
  26. T. E. Hanna, R. H. Gilkey, D. E. Robinson, “Evaluation of methods of estimating internal noise,” University of Indiana, Bloomington, Indiana 47401 (personal communication, 1979);R. H. Gilkey, A. S. Frank, D. E. Robinson, “Estimates of internal noise,” J. Acoust. Soc. Am. 64, S36(A) (1978);“Estimates of the ratio of external to internal noise obtained using repeatable samples of noise,” 69, S23(A) (1981).
    [Crossref]
  27. J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
    [Crossref] [PubMed]
  28. D. G. Pelli, “Uncertainty explains many aspects of visual contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1508–1532 (1985).
    [Crossref] [PubMed]
  29. J. M. Foley, G. E. Legge, “Contrast detection and nearthreshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
    [Crossref]
  30. H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1971), Part III, pp. 8–55.
  31. G. W. Wilcox, “Inter-observer agreement and models of monaural auditory processing in detection tasks,” doctoral dissertation (University of Michigan, Ann Arbor, Mich., 1968).
  32. T. G. Birdsall, “Detection of a signal specified exactly with a noisy stored reference signal,” J. Acoust. Soc. Am. 32, 1038–1045 (1960).
    [Crossref]
  33. H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1971), Part I, pp. 335–349.
  34. W. E. Smith, H. H. Barrett, “Hotelling trace criterion as a figure of merit for the optimization of imaging systems,” J. Opt. Soc. Am A 3, 717–725 (1986).
    [Crossref]
  35. H. H. Barrett, K. J. Myers, R. F. Wagner, “Beyond signal-detection theory,” in Application of Optical Instrumentation in Medicine XIV: Medical Imaging, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.626, 231–239 (1986).
  36. R. D. Fiete, H. H. Barrett, W. E. Smith, K. J. Myers, “Hotelling trace criterion and its correlation with human-observer performance,” J. Opt. Soc. Am. A 4, 945–953 (1987).
    [Crossref] [PubMed]
  37. R. F. Wagner, H. H. Barrett, “Quadratic tasks and the ideal observer,” in Medical Imaging, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.767, 306–309 (1987).
  38. F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186, 558–578 (1966).
    [PubMed]

1987 (2)

1986 (1)

W. E. Smith, H. H. Barrett, “Hotelling trace criterion as a figure of merit for the optimization of imaging systems,” J. Opt. Soc. Am A 3, 717–725 (1986).
[Crossref]

1985 (2)

1984 (3)

1983 (3)

D. G. Pelli, “The spatiotemporal spectrum of the equivalent noise of human vision,” Invest. Ophthalmol. Suppl. 24, 46 (1983).

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[Crossref] [PubMed]

J. M Cattell, “On errors of observation,” Am. J. Psychol. 5, 285–293 (1983).
[Crossref]

1981 (3)

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

J. M. Foley, G. E. Legge, “Contrast detection and nearthreshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
[Crossref]

M. F. Spiegel, D. M. Green, “Two procedures for estimating internal noise,” J. Acoust. Soc. Am. 70, 69–73 (1981).
[Crossref] [PubMed]

1979 (1)

R. F. Wagner, D. G. Brown, M. S. Pastel, “The application of information theory to the assessment of computed tomography,” Med. Phys. 6, 441–451 (1979).

1977 (1)

G. A. Hay, M. S. Chesters, “A model of visual threshold detection,” J. Theor. Biol. 67, 221–240 (1977);“Signal-transfer functions in threshold and suprathreshold vision,” J. Opt. Soc. Am. 62, 990–998 (1972).
[Crossref] [PubMed]

1974 (1)

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[Crossref] [PubMed]

1968 (1)

W. A. Wickelgren, “Unidimensional strength theory and component analysis of noise in absolute and comparative judgments,” J. Math. Psychol. 5, 102–122 (1968).
[Crossref]

1966 (1)

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186, 558–578 (1966).
[PubMed]

1964 (2)

D. M. Green, “Consistency of auditory detection judgments,” Psychol. Rev. 71, 392–407 (1964).
[Crossref] [PubMed]

N. S. Nagaraja, “Effect of luminance noise on contrast thresholds,” J. Opt. Soc. Am. 54, 950–955 (1964).
[Crossref]

1960 (1)

T. G. Birdsall, “Detection of a signal specified exactly with a noisy stored reference signal,” J. Acoust. Soc. Am. 32, 1038–1045 (1960).
[Crossref]

1957 (1)

H. B. Barlow, “Incremental thresholds at low intensities considered as signal/noise discrimination,” J. Physiol. 136, 469–488 (1957).
[PubMed]

1956 (1)

1888 (1)

J. Jastrow, “A critique of psycho-physic methods,” Am. J. Psychol. 1, 271–309 (1888).
[Crossref]

Ahumeda, A.

A. Ahumeda, “Detection of tones masked by noise: a comparison of human observers with digital computer simulated energy detectors of varying bandwidths,” Department of Psychology Tech. Rep. 29 (University of California at Los Angeles, Los Angeles, 1967).

Barlow, H. B.

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

H. B. Barlow, “Incremental thresholds at low intensities considered as signal/noise discrimination,” J. Physiol. 136, 469–488 (1957).
[PubMed]

H. B. Barlow, “Retinal noise and absolute threshold,” J. Opt. Soc. Am. 46, 634–639 (1956).
[Crossref] [PubMed]

Barrett, H. H.

R. D. Fiete, H. H. Barrett, W. E. Smith, K. J. Myers, “Hotelling trace criterion and its correlation with human-observer performance,” J. Opt. Soc. Am. A 4, 945–953 (1987).
[Crossref] [PubMed]

W. E. Smith, H. H. Barrett, “Hotelling trace criterion as a figure of merit for the optimization of imaging systems,” J. Opt. Soc. Am A 3, 717–725 (1986).
[Crossref]

H. H. Barrett, K. J. Myers, R. F. Wagner, “Beyond signal-detection theory,” in Application of Optical Instrumentation in Medicine XIV: Medical Imaging, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.626, 231–239 (1986).

R. F. Wagner, H. H. Barrett, “Quadratic tasks and the ideal observer,” in Medical Imaging, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.767, 306–309 (1987).

Birdsall, T. G.

T. G. Birdsall, “Detection of a signal specified exactly with a noisy stored reference signal,” J. Acoust. Soc. Am. 32, 1038–1045 (1960).
[Crossref]

Brown, D. G.

R. F. Wagner, D. G. Brown, M. S. Pastel, “The application of information theory to the assessment of computed tomography,” Med. Phys. 6, 441–451 (1979).

Burgess, A.

Burgess, A. E.

G. E. Legge, D. Kersten, A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. A 4, 381–404 (1987).

A. E. Burgess, H. Ghandeharian, “Visual signal detection.I. Ability to use phase information,” J. Opt. Soc. Am. A 1, 900–905 (1984).
[Crossref] [PubMed]

A. E. Burgess, H. Ghandeharian, “Visual signal detection.II. Signal-location identification,” J. Opt. Soc. Am. A 1, 906–910 (1984).
[Crossref] [PubMed]

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

A. E. Burgess, K. Humphrey, R. F. Wagner, “Detection of bars and discs in quantum noise,” in Application of Optical Instrumentation in Medicine VII, J. Gray, ed., Proc. Soc. Photo-Opt. Instrum. Eng.173, 34–40 (1979).
[Crossref]

A. E. Burgess, “Detection and identification efficiency: an update,” in Application of Optical Instrumentation in Medicine XIII: Medical Image Production, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.535, 50–56 (1985);“On observer internal noise,” in Application of Optical Instrumentation in Medicine XIV: Medical Imaging, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 626, 208–213 (1986).
[Crossref]

Campbell, F. W.

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186, 558–578 (1966).
[PubMed]

Cattell, J. M

J. M Cattell, “On errors of observation,” Am. J. Psychol. 5, 285–293 (1983).
[Crossref]

Chesters, M. S.

G. A. Hay, M. S. Chesters, “A model of visual threshold detection,” J. Theor. Biol. 67, 221–240 (1977);“Signal-transfer functions in threshold and suprathreshold vision,” J. Opt. Soc. Am. 62, 990–998 (1972).
[Crossref] [PubMed]

Dean, A. F.

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[Crossref] [PubMed]

Doi, K.

M. Ishida, K. Doi, L.-N. Loo, C. E. Metz, J. L. Lehr, “Digital image processing: effect on detectability of simulated low-contrast radiographic patterns,” Radiology 150, 569–575 (1984).
[PubMed]

Elliot, P.

P. Elliot, “Forced choice tables,” in Signal Detection and Recognition by Human Observers, J. A. Swets, ed. (Wiley, New York, 1964), App. 1, pp. 679–684.

Fiete, R. D.

Foley, J. M.

J. M. Foley, G. E. Legge, “Contrast detection and nearthreshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
[Crossref]

Ghandeharian, H.

Gilkey, R. H.

T. E. Hanna, R. H. Gilkey, D. E. Robinson, “Evaluation of methods of estimating internal noise,” University of Indiana, Bloomington, Indiana 47401 (personal communication, 1979);R. H. Gilkey, A. S. Frank, D. E. Robinson, “Estimates of internal noise,” J. Acoust. Soc. Am. 64, S36(A) (1978);“Estimates of the ratio of external to internal noise obtained using repeatable samples of noise,” 69, S23(A) (1981).
[Crossref]

Green, D. M.

M. F. Spiegel, D. M. Green, “Two procedures for estimating internal noise,” J. Acoust. Soc. Am. 70, 69–73 (1981).
[Crossref] [PubMed]

D. M. Green, “Consistency of auditory detection judgments,” Psychol. Rev. 71, 392–407 (1964).
[Crossref] [PubMed]

Gubisch, R. W.

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186, 558–578 (1966).
[PubMed]

Hanna, T. E.

T. E. Hanna, R. H. Gilkey, D. E. Robinson, “Evaluation of methods of estimating internal noise,” University of Indiana, Bloomington, Indiana 47401 (personal communication, 1979);R. H. Gilkey, A. S. Frank, D. E. Robinson, “Estimates of internal noise,” J. Acoust. Soc. Am. 64, S36(A) (1978);“Estimates of the ratio of external to internal noise obtained using repeatable samples of noise,” 69, S23(A) (1981).
[Crossref]

Hay, G. A.

G. A. Hay, M. S. Chesters, “A model of visual threshold detection,” J. Theor. Biol. 67, 221–240 (1977);“Signal-transfer functions in threshold and suprathreshold vision,” J. Opt. Soc. Am. 62, 990–998 (1972).
[Crossref] [PubMed]

Humphrey, K.

A. E. Burgess, K. Humphrey, R. F. Wagner, “Detection of bars and discs in quantum noise,” in Application of Optical Instrumentation in Medicine VII, J. Gray, ed., Proc. Soc. Photo-Opt. Instrum. Eng.173, 34–40 (1979).
[Crossref]

Ishida, M.

M. Ishida, K. Doi, L.-N. Loo, C. E. Metz, J. L. Lehr, “Digital image processing: effect on detectability of simulated low-contrast radiographic patterns,” Radiology 150, 569–575 (1984).
[PubMed]

Jastrow, J.

J. Jastrow, “A critique of psycho-physic methods,” Am. J. Psychol. 1, 271–309 (1888).
[Crossref]

Jennings, R. J.

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

Kersten, D.

G. E. Legge, D. Kersten, A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. A 4, 381–404 (1987).

Legge, G. E.

G. E. Legge, D. Kersten, A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. A 4, 381–404 (1987).

J. M. Foley, G. E. Legge, “Contrast detection and nearthreshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
[Crossref]

Lehr, J. L.

M. Ishida, K. Doi, L.-N. Loo, C. E. Metz, J. L. Lehr, “Digital image processing: effect on detectability of simulated low-contrast radiographic patterns,” Radiology 150, 569–575 (1984).
[PubMed]

Loo, L.-N.

M. Ishida, K. Doi, L.-N. Loo, C. E. Metz, J. L. Lehr, “Digital image processing: effect on detectability of simulated low-contrast radiographic patterns,” Radiology 150, 569–575 (1984).
[PubMed]

Metz, C. E.

M. Ishida, K. Doi, L.-N. Loo, C. E. Metz, J. L. Lehr, “Digital image processing: effect on detectability of simulated low-contrast radiographic patterns,” Radiology 150, 569–575 (1984).
[PubMed]

Movshon, J. A.

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[Crossref] [PubMed]

Myers, K. J.

R. D. Fiete, H. H. Barrett, W. E. Smith, K. J. Myers, “Hotelling trace criterion and its correlation with human-observer performance,” J. Opt. Soc. Am. A 4, 945–953 (1987).
[Crossref] [PubMed]

H. H. Barrett, K. J. Myers, R. F. Wagner, “Beyond signal-detection theory,” in Application of Optical Instrumentation in Medicine XIV: Medical Imaging, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.626, 231–239 (1986).

Nachmias, J.

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[Crossref] [PubMed]

Nagaraja, N. S.

Pastel, M. S.

R. F. Wagner, D. G. Brown, M. S. Pastel, “The application of information theory to the assessment of computed tomography,” Med. Phys. 6, 441–451 (1979).

Pelli, D.

D. Pelli, “Effects of visual noise,” doctoral dissertation (University of Cambridge, Cambridge, 1981).

Pelli, D. G.

D. G. Pelli, “Uncertainty explains many aspects of visual contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1508–1532 (1985).
[Crossref] [PubMed]

D. G. Pelli, “The spatiotemporal spectrum of the equivalent noise of human vision,” Invest. Ophthalmol. Suppl. 24, 46 (1983).

Robinson, D. E.

T. E. Hanna, R. H. Gilkey, D. E. Robinson, “Evaluation of methods of estimating internal noise,” University of Indiana, Bloomington, Indiana 47401 (personal communication, 1979);R. H. Gilkey, A. S. Frank, D. E. Robinson, “Estimates of internal noise,” J. Acoust. Soc. Am. 64, S36(A) (1978);“Estimates of the ratio of external to internal noise obtained using repeatable samples of noise,” 69, S23(A) (1981).
[Crossref]

Sansbury, R. V.

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[Crossref] [PubMed]

Siegel, R. A.

R. A. Siegel, “Internal and external noise in auditory detection,” M. Sc. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1979).

Smith, W. E.

R. D. Fiete, H. H. Barrett, W. E. Smith, K. J. Myers, “Hotelling trace criterion and its correlation with human-observer performance,” J. Opt. Soc. Am. A 4, 945–953 (1987).
[Crossref] [PubMed]

W. E. Smith, H. H. Barrett, “Hotelling trace criterion as a figure of merit for the optimization of imaging systems,” J. Opt. Soc. Am A 3, 717–725 (1986).
[Crossref]

Spiegel, M. F.

M. F. Spiegel, D. M. Green, “Two procedures for estimating internal noise,” J. Acoust. Soc. Am. 70, 69–73 (1981).
[Crossref] [PubMed]

Tolhurst, D. J.

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[Crossref] [PubMed]

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1971), Part I, pp. 335–349.

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1971), Part III, pp. 8–55.

Wagner, R. F.

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

R. F. Wagner, D. G. Brown, M. S. Pastel, “The application of information theory to the assessment of computed tomography,” Med. Phys. 6, 441–451 (1979).

A. E. Burgess, K. Humphrey, R. F. Wagner, “Detection of bars and discs in quantum noise,” in Application of Optical Instrumentation in Medicine VII, J. Gray, ed., Proc. Soc. Photo-Opt. Instrum. Eng.173, 34–40 (1979).
[Crossref]

H. H. Barrett, K. J. Myers, R. F. Wagner, “Beyond signal-detection theory,” in Application of Optical Instrumentation in Medicine XIV: Medical Imaging, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.626, 231–239 (1986).

R. F. Wagner, H. H. Barrett, “Quadratic tasks and the ideal observer,” in Medical Imaging, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.767, 306–309 (1987).

Welford, A. T.

A. T. Welford, Fundamentals of Skill (Methuen, London, 1968).

Wickelgren, W. A.

W. A. Wickelgren, “Unidimensional strength theory and component analysis of noise in absolute and comparative judgments,” J. Math. Psychol. 5, 102–122 (1968).
[Crossref]

Wilcox, G. W.

G. W. Wilcox, “Inter-observer agreement and models of monaural auditory processing in detection tasks,” doctoral dissertation (University of Michigan, Ann Arbor, Mich., 1968).

Am. J. Psychol. (2)

J. Jastrow, “A critique of psycho-physic methods,” Am. J. Psychol. 1, 271–309 (1888).
[Crossref]

J. M Cattell, “On errors of observation,” Am. J. Psychol. 5, 285–293 (1983).
[Crossref]

Invest. Ophthalmol. Suppl. (1)

D. G. Pelli, “The spatiotemporal spectrum of the equivalent noise of human vision,” Invest. Ophthalmol. Suppl. 24, 46 (1983).

J. Acoust. Soc. Am. (2)

M. F. Spiegel, D. M. Green, “Two procedures for estimating internal noise,” J. Acoust. Soc. Am. 70, 69–73 (1981).
[Crossref] [PubMed]

T. G. Birdsall, “Detection of a signal specified exactly with a noisy stored reference signal,” J. Acoust. Soc. Am. 32, 1038–1045 (1960).
[Crossref]

J. Math. Psychol. (1)

W. A. Wickelgren, “Unidimensional strength theory and component analysis of noise in absolute and comparative judgments,” J. Math. Psychol. 5, 102–122 (1968).
[Crossref]

J. Opt. Soc. Am A (1)

W. E. Smith, H. H. Barrett, “Hotelling trace criterion as a figure of merit for the optimization of imaging systems,” J. Opt. Soc. Am A 3, 717–725 (1986).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (6)

J. Physiol. (2)

H. B. Barlow, “Incremental thresholds at low intensities considered as signal/noise discrimination,” J. Physiol. 136, 469–488 (1957).
[PubMed]

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186, 558–578 (1966).
[PubMed]

J. Theor. Biol. (1)

G. A. Hay, M. S. Chesters, “A model of visual threshold detection,” J. Theor. Biol. 67, 221–240 (1977);“Signal-transfer functions in threshold and suprathreshold vision,” J. Opt. Soc. Am. 62, 990–998 (1972).
[Crossref] [PubMed]

Med. Phys. (1)

R. F. Wagner, D. G. Brown, M. S. Pastel, “The application of information theory to the assessment of computed tomography,” Med. Phys. 6, 441–451 (1979).

Psychol. Rev. (1)

D. M. Green, “Consistency of auditory detection judgments,” Psychol. Rev. 71, 392–407 (1964).
[Crossref] [PubMed]

Radiology (1)

M. Ishida, K. Doi, L.-N. Loo, C. E. Metz, J. L. Lehr, “Digital image processing: effect on detectability of simulated low-contrast radiographic patterns,” Radiology 150, 569–575 (1984).
[PubMed]

Science (1)

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

Vision Res. (3)

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[Crossref] [PubMed]

J. M. Foley, G. E. Legge, “Contrast detection and nearthreshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
[Crossref]

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[Crossref] [PubMed]

Other (13)

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1971), Part III, pp. 8–55.

G. W. Wilcox, “Inter-observer agreement and models of monaural auditory processing in detection tasks,” doctoral dissertation (University of Michigan, Ann Arbor, Mich., 1968).

P. Elliot, “Forced choice tables,” in Signal Detection and Recognition by Human Observers, J. A. Swets, ed. (Wiley, New York, 1964), App. 1, pp. 679–684.

T. E. Hanna, R. H. Gilkey, D. E. Robinson, “Evaluation of methods of estimating internal noise,” University of Indiana, Bloomington, Indiana 47401 (personal communication, 1979);R. H. Gilkey, A. S. Frank, D. E. Robinson, “Estimates of internal noise,” J. Acoust. Soc. Am. 64, S36(A) (1978);“Estimates of the ratio of external to internal noise obtained using repeatable samples of noise,” 69, S23(A) (1981).
[Crossref]

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1971), Part I, pp. 335–349.

R. F. Wagner, H. H. Barrett, “Quadratic tasks and the ideal observer,” in Medical Imaging, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.767, 306–309 (1987).

H. H. Barrett, K. J. Myers, R. F. Wagner, “Beyond signal-detection theory,” in Application of Optical Instrumentation in Medicine XIV: Medical Imaging, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.626, 231–239 (1986).

A. E. Burgess, K. Humphrey, R. F. Wagner, “Detection of bars and discs in quantum noise,” in Application of Optical Instrumentation in Medicine VII, J. Gray, ed., Proc. Soc. Photo-Opt. Instrum. Eng.173, 34–40 (1979).
[Crossref]

D. Pelli, “Effects of visual noise,” doctoral dissertation (University of Cambridge, Cambridge, 1981).

R. A. Siegel, “Internal and external noise in auditory detection,” M. Sc. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1979).

A. Ahumeda, “Detection of tones masked by noise: a comparison of human observers with digital computer simulated energy detectors of varying bandwidths,” Department of Psychology Tech. Rep. 29 (University of California at Los Angeles, Los Angeles, 1967).

A. E. Burgess, “Detection and identification efficiency: an update,” in Application of Optical Instrumentation in Medicine XIII: Medical Image Production, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.535, 50–56 (1985);“On observer internal noise,” in Application of Optical Instrumentation in Medicine XIV: Medical Imaging, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 626, 208–213 (1986).
[Crossref]

A. T. Welford, Fundamentals of Skill (Methuen, London, 1968).

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Figures (6)

Fig. 1
Fig. 1

(a) Signal-energy difference required for threshold amplitude discrimination (defined as d′ = 1) as a function of noise spectral density for a variety of signals. The straight lines represent three simple models: the ideal observer, an observer with internal noise but otherwise ideal, and an observer with both internal noise and a sampling efficiency of 70%. The signals include an aperiodic two-dimensional Gaussian (f = 0), 4.6- and 9.2-cycle/deg pulse bursts (two-dimensional Gaussian-modulated cosine waves), and 2 cycles of a sine wave. (Figure reproduced from Ref. 5.) (b) Display luminance dependence of the constant component internal noise determined by using curve-fitting methods similar to that employed in (a). The data for Nagaraja, Van Meeteren, and Pelli come from an analysis by Pelli.4 The datum for Ishida6 is our upper-limit estimate from published data. The solid line is a best fit by eye.

Fig. 2
Fig. 2

Covariation of the percentage of correct responses, P(C), and the percentage of agreement, P(A), of decisions made on two passes through a set of images. The solid lines are loci for observers with various ratios of internal-noise/external-noise standard deviation. Extreme observers with no internal noise and overwhelmingly large internal noise would have P(A) values of 1.0 and 0.5, respectively, for the two passes through the image set. The dotted ellipse around one data point represents the 1-standard-deviation region.

Fig. 3
Fig. 3

Observer internal-noise standard deviation, σi as a function of external (image)-noise standard deviation, σ0, in relative units. The 2AFC detection threshold (d′ = 1) for the external noise is about 60 on this scale. The data are for a 2AFC amplitude discrimination of sine waves (4.6 and 9.2 cycles/deg). The circles represent data for noise fields equal to the signal size, and the squares are for noise fields twice as large as the signal. The error bars represent ± 1 standard deviation. Two different measurement techniques were used: two passes through stored image sets and 2AFC trials with identical noise fields. The points labeled low noise were done with low image-noise levels and hence have poor accuracy, even after averaging over two observers. The results for the two observers (CS and RA) agree within experimental error. (Figure reproduced from Ref. 18).

Fig. 4
Fig. 4

(a) Variation of the signal detectability index, d′, as a function of the SNR for a disk signal (▪) and a two-cycle sine wave (● observer CS; (○, observer RA). The experiment was done with a fixed noise amplitude and a variable signal amplitude. The sine-wave results show the usual accelerating nonlinearity of the psychometric function. The disk result is nearly linear. The dotted line represents ideal-observer performance. The error bars represent ±1 standard deviation, (b) Internal-noise/external-noise ratios corresponding to the d′ measurements in (a). The sine-wave results show a decreasing ratio as the SNR increases, whereas the ratio is approximately constant for the disk signal. The solid line is a best fit by eye. The error bar represents ±1 standard deviation.

Fig. 5
Fig. 5

A reanalysis of the data in Fig. 4(a), using the data from Fig. 4(b) and a simple model that attempts to correct for the effect of the internal-noise/external-noise ratio, r, on the psychometric function. If the model is successful, the plot should represent the psychometric function that would be found if internal noise were not present. The near linearity of the corrected data suggests that most of the nonlinearity in Fig. 4(a) and the amplitude dependence of σi0 in Fig. 4(b) have a common origin. The error bars represent ±1 standard deviation.

Fig. 6
Fig. 6

Internal-noise/external-noise ratio for simple 2AFC detection of a variety of signals at a number of noise spectral densities. The signals were sharp-edged disks with diameters of 0.11 deg (8 pixels) and 0.22 deg (16 pixels) and a Gaussian disk with a standard deviation of 0.055 deg (4 pixels). All measurements were made by using SNR’s in the vicinity of 2.25. The results do not show any systemic dependence on the noise spectral density. The average ratio for detection is 0.8, in good agreement with the amplitude discrimination results shown in Fig. 3. The error bars represent ± 1 standard deviation.

Equations (28)

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( d ) 2 = I 2 2 / ( I 3 N 0 + I 4 N 1 ) ,
I 2 = S ( u , υ ) F ( u , υ ) M ( u , υ ) d u d υ ,
I 3 = F 2 ( u , υ ) M 2 ( u , υ ) d u d υ ,
I 4 = G 2 ( u , υ ) d u d υ .
( d ) 2 = e 2 / ( σ 0 2 + σ c 2 ) ,
σ 0 2 = i m i 2 σ p 2 = σ p 2 m i 2 .
P ( A y e ) = p ( y e + y i a > 0 ) p ( y e + y i b > 0 ) + p ( y e + y i a < 0 ) p ( y e + y i b < 0 )
= p ( y i a 2 1 / 2 σ c > y e σ 0 σ c ) p ( y i b 2 1 / 2 σ i > y e σ 0 σ c ) + p ( y i a 2 1 / 2 σ i < y e σ 0 σ c ) p ( y i b 2 1 / 2 σ i < y e σ 0 σ c ) = [ Q ( y e k ) ] 2 + [ 1 Q ( y e k ) ] 2 ,
k = σ 0 / σ c
Q ( x ) = x exp ( t 2 / 2 ) d t ( 2 π ) 1 / 2 .
P ( A ) = P ( A ) y e ) p ( y e ) d y e ,
p ( y e ) = 1 ( 2 π ) 1 / 2 exp [ ( y e d ) 2 / 2 ] .
P ( c ) = Q ( k y e ) p ( y e ) d y e .
σ c σ 0 = [ ( d 1 d 2 ) 2 1 ] 1 / 2 .
Z = ln [ L ( x ) ] = μ α T Q m ( y μ α 2 ) + 1 2 y T ( Q n Q m ) Y ,
y = x μ n , Q m = ( Σ n + Σ s ) 1 , Q n = Σ n 1 .
Z α * = ( μ α + e 2 ) T Q m ( y μ α 2 + e 1 e 2 ) + ½ ( y + e 1 ) T ( Q n Q m ) ( y + e 1 ) + e 3 .
Z a * = 1 λ 2 N 0 ( μ α + e 2 ) T D α [ 2 ( y + e 1 ) ( μ α + e 2 ) ] + λ 2 N 0 ( y + e 1 ) T D α ( y + e 1 ) + e 3 .
( d ) 2 = 2 [ mean 1 ( Z α * ) mean 0 ( Z α * ) ] 2 Var 1 ( Z α * ) + Var 0 ( Z α * ) ,
E 1 ( Z α * ) = λ [ δ ( 1 + k 1 ) N 0 + E s / 2 ] / N 0 + ( 1 λ ) [ R E α / 2 δ N 0 k 2 ] / N 0 ,
Var 0 ( Z α * ) = V 3 + δ k 2 [ 2 ( 1 + k 1 ) + k 2 ] + E α ( 1 + k 1 + k 2 ) / N 0 ,
Var 1 ( Z α * ) = Var 0 ( Z α * ) + ( E s R ) k 2 / N 0 .
( d ) 2 = 2 R 2 / F N 0 ,
F = 2 E α ( 1 + k 1 + k 2 ) + ( E s R ) k 2 + 2 N 0 δ k 2 [ 2 ( 1 + k 1 ) + k 2 ] + 2 N 0 V 3 .
( d ) 2 = E S 2 N 0 E s + N 0 2 V 3 .
( d ) 2 = E s N 0 + k 2 N 0 + δ k 2 N 0 ( 2 + k 2 ) / ( E s / N 0 ) .
( d ) 2 E s 2 N 0 2 δ k 2 ( 2 + k 2 ) .
( d ) 2 = E s N 0 + N 1 .

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