Abstract

Many investigators are currently developing models to predict human performance in detecting a signal embedded in complex backgrounds. A common figure of merit for model performance is d, an index of detectability that can be mathematically related to the proportion correct (Pc) when the responses of the model are Gaussian distributed and statistically independent. However, in many multiple-alternative forced-choice (MAFC) detection tasks, the target appears in one of M different locations within an image. If the image contains slow spatially varying luminance changes (low-pass noise), the pixel luminance values at the possible signal locations are correlated and therefore the model/human responses to the different locations might also be correlated. We investigate the effect of response correlations on model performance and compare different figures of merit for these conditions. Our results show that use of the standard d index of detectability assuming statistical independence can lead to erroneous underestimates of Pc and misleading comparisons of models. We introduce a novel figure of merit dr that takes into account response correlations and can be used to accurately estimate Pc. Furthermore, we show that dr can be readily related to the standard index of detectability d by dr=d/1-r, where r is the correlation between the responses in any MAFC detection task. We illustrate the use of the theory by computing figures of merit for two linear models detecting a signal in one of four locations within medical image backgrounds.

© 2000 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. D. L. Wilson, K. N. Jabri, P. Xue, R. Aufrichtig, “Perceived noise versus display noise in temporally filtered image sequences,” J. Electron. Imaging 5, 490–495 (1996).
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  8. A. E. Burgess, X. Li, C. K. Abbey, “Visual signal detectability with two noise components: anomalous masking effects,” J. Opt. Soc. Am. A 14, 2420–2442 (1997).
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  9. A. J. Ahumada, B. L. Beard, “Object detection in a noisy Scene,” in Human Vision, Visual Processing, and Digital Display VII, B. Rogowitz, J. Allebach, eds., Proc. SPIE2657, 190–199 (1996).
  10. A. J. Ahumada, A. B. Watson, A. M. Rohaly, “Models of human image discrimination predict object detection in natural backgrounds,” in Human Vision, Visual Processing, and Digital Display VI, B. Rogowitz, J. Allebach, eds., Proc. SPIE2411, 355–362 (1995).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. F. O. Bochud, F. R. Verdun, J. F. Valley, C. Hessler, R. Moeckli, “Importance of anatomical noise in mammography,” in Image Perception, H. Kundel, ed., Proc. SPIE3036, 74–80 (1997).
  18. F. O. Bochud, C. K. Abbey, M. P. Eckstein, “Further investigation of the effect of phase spectrum on visual detection in structured backgrounds,” in Image Perception, E. Krupinski, ed., Proc. SPIE3663, 273–281 (1999).
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  20. M. S. Chesters, “Human visual perception and ROC methodology in medical imaging,” Phys. Med. Biol. 37, 1433–1476 (1992).
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  21. A. E. Burgess, “Comparison of receiver operating characteristic and forced choice observer performance measurement methods,” Med. Phys. 22, 643–655 (1995).
    [CrossRef] [PubMed]
  22. A. E. Burgess, “Statistically defined backgrounds: performance of a modified nonprewhitening matched filter model,” J. Opt. Soc. Am. A 11, 1237–1242 (1994).
    [CrossRef]
  23. K. Myers, H. H. Barrett, “Addition of a channel mechanism to the ideal observer model,” J. Opt. Soc. Am. A 4, 2447–2457 (1987).
    [CrossRef] [PubMed]
  24. J. Yao, H. H. Barrett, “Predicting human performance by a channelized Hotelling observer model,” in Mathematical Methods in Medical Imaging, Proc. SPIE1768, 161–168 (1992).
    [CrossRef]
  25. H. H. Barrett, J. Yao, J. P. Rolland, K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. USA 90, 9758–9765 (1993).
    [CrossRef] [PubMed]
  26. C. K. Abbey, H. H. Barrett, “Linear iterative reconstruction algorithms: study of observer performance,” in Proceedings of the 14th International Conference on Information Processing in Medical Imaging, Y. Bizais, C. Barillot, R. Di Paola, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 65–76.
  27. C. K. Abbey, H. H. Barrett, D. W. Wilson, “Observer signal to noise ratios for the ML-EM algorithm,” in Image Perception, H. Kundel, ed., Proc. SPIE2712, 47–58 (1996).
  28. C. K. Abbey, H. H. Barrett, M. P. Eckstein, “Practical issues and methodology in assessment of image quality using model observers,” in The Physics of Medical Imaging, H. Roerhig, ed., Proc. SPIE3032, 182–194 (1997).
  29. A slight modification of this formula applies if the response variances differ.
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    [CrossRef] [PubMed]
  31. A. Van der Schaaf, J. H. Van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
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  32. D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).
  33. In some cases a source of internal noise is added to the model observer’s internal response to degrade its performance to human performance levels. In these cases the internal response of the observer is a composite of the scalar product between the template, the image, and the internal noise.
  34. M. Ishida, K. Doi, L. N. Loo, C. E. Metz, J. L. Lehr, “Digital image processing: effect of detectability of simu-lated low-contrast radiographic patterns,” Radiology 150, 569–575 (1984).
    [PubMed]
  35. M. P. Eckstein, C. A. Abbey, J. S. Whiting, “Human vs model observers in anatomic backgrounds,” in Image Perception, H. Kundel, ed., Proc. SPIE3340, 15–26 (1998).
  36. J. Palmer, “Set-size effects in visual search: the effect of attention is independent of the stimulus for simple tasks,” Vision Res. 34, 1703–1721 (1994).
    [CrossRef] [PubMed]
  37. M. L. Shaw, “Identifying attentional and decision making components in information processing,” in Attention and Performance VII, R. S. Nickerson, ed. (Erlbaum, Hillsdale, N.J., 1980), pp. 277–296.
  38. P. S. Bennett, P. D. Jaye, “Letter localization, not discrimination, is constrained by attention,” Can. J. Exp. Psychol. 49, 460–504 (1995).
    [CrossRef] [PubMed]
  39. M. P. Eckstein, “The lower efficiency for conjunctions is due to noise and not serial attentional processing,” Psychol. Sci. 2, 111–118 (1998).
    [CrossRef]
  40. W. A. Wickelgren, “Unidimensional strength theory and component analysis of noise in absolute and comparative judgments,” J. Math. Psychol. 5, 102–122 (1968).
    [CrossRef]
  41. H. H. Barrett, C. K. Abbey, B. Gallas, M. P. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient structured noise,” in Image Perception, H. Kundel, ed., Proc. SPIE3340, 27–43 (1998).

2000 (1)

1998 (1)

M. P. Eckstein, “The lower efficiency for conjunctions is due to noise and not serial attentional processing,” Psychol. Sci. 2, 111–118 (1998).
[CrossRef]

1997 (4)

1996 (4)

M. P. Eckstein, J. S. Whiting, “Visual signal detection in structured backgrounds. I. Effect of number of possible locations and signal contrast,” J. Opt. Soc. Am. A 13, 1777–1787 (1996).
[CrossRef]

M. P. Eckstein, J. S. Whiting, J. P. Thomas, “Role of knowledge in human visual temporal integration in spatiotemporal noise,” J. Opt. Soc. Am. A 13, 1960–1968 (1996).
[CrossRef]

D. L. Wilson, K. N. Jabri, P. Xue, R. Aufrichtig, “Perceived noise versus display noise in temporally filtered image sequences,” J. Electron. Imaging 5, 490–495 (1996).
[CrossRef]

A. Van der Schaaf, J. H. Van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759–2770 (1996).
[CrossRef] [PubMed]

1995 (2)

A. E. Burgess, “Comparison of receiver operating characteristic and forced choice observer performance measurement methods,” Med. Phys. 22, 643–655 (1995).
[CrossRef] [PubMed]

P. S. Bennett, P. D. Jaye, “Letter localization, not discrimination, is constrained by attention,” Can. J. Exp. Psychol. 49, 460–504 (1995).
[CrossRef] [PubMed]

1994 (2)

J. Palmer, “Set-size effects in visual search: the effect of attention is independent of the stimulus for simple tasks,” Vision Res. 34, 1703–1721 (1994).
[CrossRef] [PubMed]

A. E. Burgess, “Statistically defined backgrounds: performance of a modified nonprewhitening matched filter model,” J. Opt. Soc. Am. A 11, 1237–1242 (1994).
[CrossRef]

1993 (1)

H. H. Barrett, J. Yao, J. P. Rolland, K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. USA 90, 9758–9765 (1993).
[CrossRef] [PubMed]

1992 (2)

J. P. Rolland, H. H. Barrett, “Effect of random inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A 9, 649–658 (1992).
[CrossRef] [PubMed]

M. S. Chesters, “Human visual perception and ROC methodology in medical imaging,” Phys. Med. Biol. 37, 1433–1476 (1992).
[CrossRef] [PubMed]

1987 (1)

1985 (1)

1984 (2)

A. E. Burgess, H. Ghandeharian, “Visual signal detection. II. Signal location identification,” J. Opt. Soc. Am. A 1, 900–905 (1984).
[CrossRef] [PubMed]

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

1981 (2)

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

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

Abbey, C. A.

M. P. Eckstein, C. A. Abbey, J. S. Whiting, “Human vs model observers in anatomic backgrounds,” in Image Perception, H. Kundel, ed., Proc. SPIE3340, 15–26 (1998).

Abbey, C. K.

F. O. Bochud, C. K. Abbey, M. P. Eckstein, “Visual signal detection in structured backgrounds. III. Calculation of figures of merit for model observers in statistically nonstationary backgrounds,” J. Opt. Soc. Am. A 17, 193–205 (2000).
[CrossRef]

A. E. Burgess, X. Li, C. K. Abbey, “Visual signal detectability with two noise components: anomalous masking effects,” J. Opt. Soc. Am. A 14, 2420–2442 (1997).
[CrossRef]

F. O. Bochud, C. K. Abbey, M. P. Eckstein, “Further investigation of the effect of phase spectrum on visual detection in structured backgrounds,” in Image Perception, E. Krupinski, ed., Proc. SPIE3663, 273–281 (1999).

C. K. Abbey, H. H. Barrett, “Linear iterative reconstruction algorithms: study of observer performance,” in Proceedings of the 14th International Conference on Information Processing in Medical Imaging, Y. Bizais, C. Barillot, R. Di Paola, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 65–76.

C. K. Abbey, H. H. Barrett, D. W. Wilson, “Observer signal to noise ratios for the ML-EM algorithm,” in Image Perception, H. Kundel, ed., Proc. SPIE2712, 47–58 (1996).

C. K. Abbey, H. H. Barrett, M. P. Eckstein, “Practical issues and methodology in assessment of image quality using model observers,” in The Physics of Medical Imaging, H. Roerhig, ed., Proc. SPIE3032, 182–194 (1997).

H. H. Barrett, C. K. Abbey, B. Gallas, M. P. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient structured noise,” in Image Perception, H. Kundel, ed., Proc. SPIE3340, 27–43 (1998).

Ahumada, A. J.

M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Visual signal detection in structured backgrounds. II. Effects of contrast gain control, background variations, and white noise,” J. Opt. Soc. Am. A 14, 2406–2419 (1997).
[CrossRef]

A. M. Rohaly, A. J. Ahumada, A. B. Watson, “Object detection in natural backgrounds predicted by discrimination performance and models,” Vision Res. 37, 3225–3235 (1997).
[CrossRef]

A. J. Ahumada, A. B. Watson, A. M. Rohaly, “Models of human image discrimination predict object detection in natural backgrounds,” in Human Vision, Visual Processing, and Digital Display VI, B. Rogowitz, J. Allebach, eds., Proc. SPIE2411, 355–362 (1995).
[CrossRef]

A. J. Ahumada, B. L. Beard, “Object detection in a noisy Scene,” in Human Vision, Visual Processing, and Digital Display VII, B. Rogowitz, J. Allebach, eds., Proc. SPIE2657, 190–199 (1996).

M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Image discrimination models predict signal detection in natural medical image backgrounds,” in Human Vision, Visual Processing, and Digital Display VIII, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 44–56 (1997).

Aufrichtig, R.

D. L. Wilson, K. N. Jabri, P. Xue, R. Aufrichtig, “Perceived noise versus display noise in temporally filtered image sequences,” J. Electron. Imaging 5, 490–495 (1996).
[CrossRef]

Barlow, H. B.

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

Barrett, H. H.

H. H. Barrett, J. Yao, J. P. Rolland, K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. USA 90, 9758–9765 (1993).
[CrossRef] [PubMed]

J. P. Rolland, H. H. Barrett, “Effect of random inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A 9, 649–658 (1992).
[CrossRef] [PubMed]

K. Myers, H. H. Barrett, “Addition of a channel mechanism to the ideal observer model,” J. Opt. Soc. Am. A 4, 2447–2457 (1987).
[CrossRef] [PubMed]

K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton, G. W. Seeley, “Effect of noise correlation on detectability of disk signals in medical imaging,” J. Opt. Soc. Am. A 2, 1752–1759 (1985).
[CrossRef] [PubMed]

C. K. Abbey, H. H. Barrett, “Linear iterative reconstruction algorithms: study of observer performance,” in Proceedings of the 14th International Conference on Information Processing in Medical Imaging, Y. Bizais, C. Barillot, R. Di Paola, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 65–76.

J. Yao, H. H. Barrett, “Predicting human performance by a channelized Hotelling observer model,” in Mathematical Methods in Medical Imaging, Proc. SPIE1768, 161–168 (1992).
[CrossRef]

H. H. Barrett, C. K. Abbey, B. Gallas, M. P. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient structured noise,” in Image Perception, H. Kundel, ed., Proc. SPIE3340, 27–43 (1998).

C. K. Abbey, H. H. Barrett, M. P. Eckstein, “Practical issues and methodology in assessment of image quality using model observers,” in The Physics of Medical Imaging, H. Roerhig, ed., Proc. SPIE3032, 182–194 (1997).

C. K. Abbey, H. H. Barrett, D. W. Wilson, “Observer signal to noise ratios for the ML-EM algorithm,” in Image Perception, H. Kundel, ed., Proc. SPIE2712, 47–58 (1996).

Beard, B. L.

A. J. Ahumada, B. L. Beard, “Object detection in a noisy Scene,” in Human Vision, Visual Processing, and Digital Display VII, B. Rogowitz, J. Allebach, eds., Proc. SPIE2657, 190–199 (1996).

Bennett, P. S.

P. S. Bennett, P. D. Jaye, “Letter localization, not discrimination, is constrained by attention,” Can. J. Exp. Psychol. 49, 460–504 (1995).
[CrossRef] [PubMed]

Bochud, F. O.

F. O. Bochud, C. K. Abbey, M. P. Eckstein, “Visual signal detection in structured backgrounds. III. Calculation of figures of merit for model observers in statistically nonstationary backgrounds,” J. Opt. Soc. Am. A 17, 193–205 (2000).
[CrossRef]

F. O. Bochud, F. R. Verdun, J. F. Valley, C. Hessler, R. Moeckli, “Importance of anatomical noise in mammography,” in Image Perception, H. Kundel, ed., Proc. SPIE3036, 74–80 (1997).

F. O. Bochud, C. K. Abbey, M. P. Eckstein, “Further investigation of the effect of phase spectrum on visual detection in structured backgrounds,” in Image Perception, E. Krupinski, ed., Proc. SPIE3663, 273–281 (1999).

Borgstrom, M. C.

Borthwick, R.

A. B. Watson, M. Taylor, R. Borthwick, “Image quality and entropy masking,” in Human Vision, Visual Processing, and Digital Display VIII, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 2–12 (1997).

Brady, N.

N. Brady, “Spatial scale interactions and image statistics,” Perception 26, 1089–1100 (1997).
[CrossRef] [PubMed]

Burgess, A. E.

Chesters, M. S.

M. S. Chesters, “Human visual perception and ROC methodology in medical imaging,” Phys. Med. Biol. 37, 1433–1476 (1992).
[CrossRef] [PubMed]

Doi, K.

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

Eckstein, M. P.

F. O. Bochud, C. K. Abbey, M. P. Eckstein, “Visual signal detection in structured backgrounds. III. Calculation of figures of merit for model observers in statistically nonstationary backgrounds,” J. Opt. Soc. Am. A 17, 193–205 (2000).
[CrossRef]

M. P. Eckstein, “The lower efficiency for conjunctions is due to noise and not serial attentional processing,” Psychol. Sci. 2, 111–118 (1998).
[CrossRef]

M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Visual signal detection in structured backgrounds. II. Effects of contrast gain control, background variations, and white noise,” J. Opt. Soc. Am. A 14, 2406–2419 (1997).
[CrossRef]

M. P. Eckstein, J. S. Whiting, “Visual signal detection in structured backgrounds. I. Effect of number of possible locations and signal contrast,” J. Opt. Soc. Am. A 13, 1777–1787 (1996).
[CrossRef]

M. P. Eckstein, J. S. Whiting, J. P. Thomas, “Role of knowledge in human visual temporal integration in spatiotemporal noise,” J. Opt. Soc. Am. A 13, 1960–1968 (1996).
[CrossRef]

M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Image discrimination models predict signal detection in natural medical image backgrounds,” in Human Vision, Visual Processing, and Digital Display VIII, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 44–56 (1997).

F. O. Bochud, C. K. Abbey, M. P. Eckstein, “Further investigation of the effect of phase spectrum on visual detection in structured backgrounds,” in Image Perception, E. Krupinski, ed., Proc. SPIE3663, 273–281 (1999).

H. H. Barrett, C. K. Abbey, B. Gallas, M. P. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient structured noise,” in Image Perception, H. Kundel, ed., Proc. SPIE3340, 27–43 (1998).

M. P. Eckstein, C. A. Abbey, J. S. Whiting, “Human vs model observers in anatomic backgrounds,” in Image Perception, H. Kundel, ed., Proc. SPIE3340, 15–26 (1998).

C. K. Abbey, H. H. Barrett, M. P. Eckstein, “Practical issues and methodology in assessment of image quality using model observers,” in The Physics of Medical Imaging, H. Roerhig, ed., Proc. SPIE3032, 182–194 (1997).

Gallas, B.

H. H. Barrett, C. K. Abbey, B. Gallas, M. P. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient structured noise,” in Image Perception, H. Kundel, ed., Proc. SPIE3340, 27–43 (1998).

Ghandeharian, H.

Green, D. M.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

Hessler, C.

F. O. Bochud, F. R. Verdun, J. F. Valley, C. Hessler, R. Moeckli, “Importance of anatomical noise in mammography,” in Image Perception, H. Kundel, ed., Proc. SPIE3036, 74–80 (1997).

Ishida, M.

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

Jabri, K. N.

D. L. Wilson, K. N. Jabri, P. Xue, R. Aufrichtig, “Perceived noise versus display noise in temporally filtered image sequences,” J. Electron. Imaging 5, 490–495 (1996).
[CrossRef]

Jaye, P. D.

P. S. Bennett, P. D. Jaye, “Letter localization, not discrimination, is constrained by attention,” Can. J. Exp. Psychol. 49, 460–504 (1995).
[CrossRef] [PubMed]

Jennings, R. J.

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

Judy, P. F.

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

Lehr, J. L.

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

Li, X.

Loo, L. N.

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

Moeckli, R.

F. O. Bochud, F. R. Verdun, J. F. Valley, C. Hessler, R. Moeckli, “Importance of anatomical noise in mammography,” in Image Perception, H. Kundel, ed., Proc. SPIE3036, 74–80 (1997).

Myers, K.

Myers, K. J.

Palmer, J.

J. Palmer, “Set-size effects in visual search: the effect of attention is independent of the stimulus for simple tasks,” Vision Res. 34, 1703–1721 (1994).
[CrossRef] [PubMed]

Patton, D. D.

Rohaly, A. M.

A. M. Rohaly, A. J. Ahumada, A. B. Watson, “Object detection in natural backgrounds predicted by discrimination performance and models,” Vision Res. 37, 3225–3235 (1997).
[CrossRef]

A. J. Ahumada, A. B. Watson, A. M. Rohaly, “Models of human image discrimination predict object detection in natural backgrounds,” in Human Vision, Visual Processing, and Digital Display VI, B. Rogowitz, J. Allebach, eds., Proc. SPIE2411, 355–362 (1995).
[CrossRef]

Rolland, J. P.

H. H. Barrett, J. Yao, J. P. Rolland, K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. USA 90, 9758–9765 (1993).
[CrossRef] [PubMed]

J. P. Rolland, H. H. Barrett, “Effect of random inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A 9, 649–658 (1992).
[CrossRef] [PubMed]

Seeley, G. W.

Shaw, M. L.

M. L. Shaw, “Identifying attentional and decision making components in information processing,” in Attention and Performance VII, R. S. Nickerson, ed. (Erlbaum, Hillsdale, N.J., 1980), pp. 277–296.

Swensson, R. G.

R. G. Swensson, P. F. Judy, “Detection of noisy visual targets: model for the effects of spatial uncertainty and signal to noise ratio,” Percept. Psychophys. 29, 521–534 (1981).
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Other (17)

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In some cases a source of internal noise is added to the model observer’s internal response to degrade its performance to human performance levels. In these cases the internal response of the observer is a composite of the scalar product between the template, the image, and the internal noise.

M. L. Shaw, “Identifying attentional and decision making components in information processing,” in Attention and Performance VII, R. S. Nickerson, ed. (Erlbaum, Hillsdale, N.J., 1980), pp. 277–296.

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C. K. Abbey, H. H. Barrett, D. W. Wilson, “Observer signal to noise ratios for the ML-EM algorithm,” in Image Perception, H. Kundel, ed., Proc. SPIE2712, 47–58 (1996).

C. K. Abbey, H. H. Barrett, M. P. Eckstein, “Practical issues and methodology in assessment of image quality using model observers,” in The Physics of Medical Imaging, H. Roerhig, ed., Proc. SPIE3032, 182–194 (1997).

A slight modification of this formula applies if the response variances differ.

J. Yao, H. H. Barrett, “Predicting human performance by a channelized Hotelling observer model,” in Mathematical Methods in Medical Imaging, Proc. SPIE1768, 161–168 (1992).
[CrossRef]

A. B. Watson, M. Taylor, R. Borthwick, “Image quality and entropy masking,” in Human Vision, Visual Processing, and Digital Display VIII, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 2–12 (1997).

M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Image discrimination models predict signal detection in natural medical image backgrounds,” in Human Vision, Visual Processing, and Digital Display VIII, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 44–56 (1997).

F. O. Bochud, F. R. Verdun, J. F. Valley, C. Hessler, R. Moeckli, “Importance of anatomical noise in mammography,” in Image Perception, H. Kundel, ed., Proc. SPIE3036, 74–80 (1997).

F. O. Bochud, C. K. Abbey, M. P. Eckstein, “Further investigation of the effect of phase spectrum on visual detection in structured backgrounds,” in Image Perception, E. Krupinski, ed., Proc. SPIE3663, 273–281 (1999).

R. F. Wagner, K. E. Weaver, “An assortment of image quality indices for radiographic film-screen combinations—can they be resolved?” in Application of Optical Instrumentation in Medicine I, P. L. Carson, W. H. Hendee, W. C. Zarnstorff, eds., Proc. SPIE35, 83–94 (1972).
[CrossRef]

A. J. Ahumada, B. L. Beard, “Object detection in a noisy Scene,” in Human Vision, Visual Processing, and Digital Display VII, B. Rogowitz, J. Allebach, eds., Proc. SPIE2657, 190–199 (1996).

A. J. Ahumada, A. B. Watson, A. M. Rohaly, “Models of human image discrimination predict object detection in natural backgrounds,” in Human Vision, Visual Processing, and Digital Display VI, B. Rogowitz, J. Allebach, eds., Proc. SPIE2411, 355–362 (1995).
[CrossRef]

H. H. Barrett, C. K. Abbey, B. Gallas, M. P. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient structured noise,” in Image Perception, H. Kundel, ed., Proc. SPIE3340, 27–43 (1998).

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Figures (7)

Fig. 1
Fig. 1

Left column: Across-image two-alternative forced-choice (2AFC) tasks, where the target appears at a specified (fiduciary cues) location of one of two independent images. Right column: Within-image alternative forced-choice tasks, where the target appears in one of M locations within an image. (a) Gaussian low-pass noise, (b), x-ray coronary angiogram, (c), x-ray mammogram, (d), sky image.

Fig. 2
Fig. 2

Distribution of Gaussian internal responses to signal plus background (right distribution) and background only (left distribution). The index of detectability d is defined as the distance between the centers of the distributions in standard deviation units. The variances of the two distributions are assumed to be equal.

Fig. 3
Fig. 3

Proportion correct (Pc) localizing a target versus d for different response correlations (r). Results are given for 2AFC and 16AFC tasks based on Monte Carlo simulations.

Fig. 4
Fig. 4

dMAFC (transform of Pc assuming statistical independence) versus response correlations for two values of d (2.5 and 1.0). Also plotted is dr, calculated from Eq. (9).

Fig. 5
Fig. 5

Pc localizing a target versus number of possible target locations for different internal response correlations.

Fig. 6
Fig. 6

Sample background of x-ray coronary angiogram used for the 4AFC task. The target is a bright disk that might appear at the horizontal center in one of the four locations within the simulated arterial segments cued with the fiduciary marks.

Fig. 7
Fig. 7

Noise power spectrum of x-ray coronary angiographic images used in this paper. The conversion factor to cycles per pixel is 0.3. For details about the method for noise power spectrum estimation, see Bochud et al.16

Tables (3)

Tables Icon

Table 1 Summary of Figures of Merit for MAFC Tasks

Tables Icon

Table 2 Figures of Merit without Taking into Account Response Correlations

Tables Icon

Table 3 Figures of Merit Taking into Account Response Correlations

Equations (29)

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

Pˆc=1Jj=1Jstep[λs,j-maxi(λb,ij)],
d=λs-λb[12(σs2+σb2)]1/2,
d=wT(gs-gb)[wT12(Ks+Kb)w]1/2,
d=-+-+W(u, v)S(u, v)dudv-+-+|W(u, v)|2N(u, v)dudv1/2,
Pc(d, M)=-+ϕ(x-d)[Φ(x)]M-1 dx,
rm,n=(λn,i-λn)(λm,i-λm)[(λn,i-λn)2]1/2[(λm,i-λm)2]1/2,
rm,n=wTKm,nw(wTKmw)1/2(wTKnw)1/2,
rm,n=-+-+N(u, v)|W(u, v)|2 exp[-2πi(Δxu+Δyv)]dudv-+-+N(u, v)|W(u, v)|21/2 dudv.
dr=11-r1/2d,
dr=wT(gs-gb)(wTKw-wTKs,bw)1/2,
dr=-+-+W(u, v)S(u, v)dudv-+-+|W(u, v)|2N(u, v){1-exp[-2πi(Δxu+Δyv)]}dudv1/2.
λ=x=1Ny=1Nw(x, y)g(x, y),
λ=k=1N2wkgk=wTg,
z=ac+bu,
a=r,b=1-r.
rz=a2 cov(c)+b2 cov(u)a2 var(c)+b2 var(u)=r·1+(1-r)·0r·1+(1-r)·1=r,
dr=λs-λb[12(σs2+σb2-2σsb2)]1/2.
dr=λs-λbσ1-r=d1-r.
λs-λb=wT(gs-gb),
σs2=σb2=wTKw.
σs,b=wTKs,bw,
dr=wT(gs-gb)(wTKw-wTKm,nw)1/2.
λs-λb=-+-+W(u, v)S(u, v)dudv,
σs2=σb2=-+-+|W(u, v)|2N(u, v)dudv.
σs,b=-+-+|W(u, v)|2N(u, v)×exp[-2πi(Δxu+Δyv)]dudv.
dr=-+-+W(u, v)S(u, v)dudv-+-+|W(u, v)|2N(u, v){1-exp[-2πi(Δxu+Δyv)]}dudv1/2.
wxy=FFT-1{|Ek,kSk|2},
E(f)=f1.3 exp(-cf2),
wh=K-1(gs-gb),

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