Abstract

A previous study [J. Opt. Soc. Am. A 22, 3 (2005)] has shown that human efficiency for detecting a Gaussian signal at a known location in non-Gaussian distributed lumpy backgrounds is approximately 4%. This human efficiency is much less than the reported 40% efficiency that has been documented for Gaussian-distributed lumpy backgrounds [J. Opt. Soc. Am. A 16, 694 (1999) and J. Opt. Soc. Am. A 18, 473 (2001) ]. We conducted a psychophysical study with a number of changes, specifically in display-device calibration and data scaling, from the design of the aforementioned study. Human efficiency relative to the ideal observer was found again to be approximately 5%. Our variance analysis indicates that neither scaling nor display made a statistically significant difference in human performance for the task. We conclude that the non-Gaussian distributed lumpy background is a major factor in our low human-efficiency results.

© 2007 Optical Society of America

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References

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  1. H. L. Van Trees, Detection, Estimation, and Modulation Theory Part I (Academic, 1968).
  2. M. A. Kupinski, J. W. Hoppin, E. Clarkson, and H. H. Barrett, "Ideal-observer computation in medical imaging with use of Markov-chain Monte Carlo techniques," J. Opt. Soc. Am. A 20, 430-438 (2003).
    [CrossRef]
  3. S. Park, M. A. Kupinski, E. Clarkson, and H. H. Barrett, "Ideal-observer performance under signal and background uncertainty," in Information Processing in Medical Imaging, Vol. 2732 in Lecture Notes in Computer Science, C. J. Taylor and J. A. Noble, eds. (Springer-Verlag, 2003) pp. 342-353.
  4. H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, 2004).
  5. B. D. Gallas and H. H. Barrett, "Validating the use of channels to estimate the ideal linear observer," J. Opt. Soc. Am. A 20, 1725-1738 (2003).
    [CrossRef]
  6. D. H. Hubel and T. N. Wiesel, "Receptive fields, binocular interaction and functional architecture in the cat's visual cortex," J. Physiol. (London) 160, 106-154 (1962).
  7. J. G. Robson, "Spatial and temporal contrast sensitivity functions of the visual system," J. Opt. Soc. Am. 56, 1141-1142 (1966).
    [CrossRef]
  8. C. K. Abbey and H. H. Barrett, "Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability," J. Opt. Soc. Am. A 18, 473-488 (2001).
    [CrossRef]
  9. H. H. Barrett, J. Yao, J. P. Holland, and K. J. Myers, "Model observers for assessment of image quality," Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).
    [CrossRef] [PubMed]
  10. A. E. Burgess, X. Li, and C. K. Abbey, "Visual signal detectability with two noise components: anomalous masking effects," J. Opt. Soc. Am. A 14, 2420-2442 (1997).
    [CrossRef]
  11. A. E. Burgess, "Visual signal detectability with two-component noise: low-pass spectrum effects," J. Opt. Soc. Am. A 16, 694-704 (1999).
    [CrossRef]
  12. A. E. Burgess, F. L. Jacobson, and P. F. Judy, "Human observer detection experiments with mammograms and power-law noise," Med. Phys. 28, 419-437 (2001).
    [CrossRef] [PubMed]
  13. F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Search for lesions in mammograms: statistical characterization of observer responses," Med. Phys. 31, 24-36 (2004).
    [CrossRef] [PubMed]
  14. S. Park, E. Clarkson, M. A. Kupinski, and H. H. Barrett, "Efficiency of the human observer detecting random signals in random backgrounds," J. Opt. Soc. Am. A 22, 3-16 (2005).
    [CrossRef]
  15. S. Park, E. Clarkson, M. A. Kupinski, and H. H. Barrett, "Efficiency of human and model observers for signal-detection tasks in non-Gaussian distributed lumpy backgrounds," Proc. SPIE 5749, 138-149 (2005).
    [CrossRef]
  16. J. P. Rolland and H. H. Barrett, "Effect of random background inhomogeneity on observer detection performance," J. Opt. Soc. Am. A 9, 649-658 (1992).
    [CrossRef] [PubMed]
  17. B. D. Gallas, "One-shot estimate of MRMC variance: AUC," Acad. Radiol. 13, 353-362 (2006).
    [CrossRef] [PubMed]
  18. D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, 1966).
  19. H. H. Barrett, C. K. Abbey, and E. Clarkson, "Objective assessment of image quality III: ROC metrics, ideal observers, and likelihood-generating functions," J. Opt. Soc. Am. A 15, 1520-1535 (1998).
    [CrossRef]
  20. A. E. Burgess, R. F. Wagner, R. J. Jennings, and H. B. Barlow, "Efficiency of human visual signal discrimination," Science 214, 93-94 (1981).
    [CrossRef] [PubMed]
  21. W. P. Tanner and T. G. Birdsall, "Definitions of d? and ? as psychophysical measures," J. Acoust. Soc. Am. 30, 922-928 (1958).
    [CrossRef]
  22. A. E. Burgess, "The Rose model, revisited," J. Opt. Soc. Am. A 16, 633-646 (1999).
    [CrossRef]
  23. A. Badano and M. J. Flynn, "Method for measuring veiling glare in high performance display devices," Appl. Opt. 13, 2059-2066 (2000).
  24. A. Badano and D. H. Fifadara, "Comparison of Fourier-optics, telescopic, and goniometric methods for measuring angular emissions from medical liquid-crystal displays," Appl. Opt. 26, 4999-5005 (2004).
    [CrossRef]
  25. F. A. Wichmann and N. J. Hill, "The psychometric function: I. Fitting, sampling, and goodness of fit," Percept. Psychophys. 63, 1314-1329 (2001).
    [CrossRef]
  26. F. A. Wichmann and N. J. Hill, "The psychometric function: II. Bootstrap-based confidence intervals and sampling," Percept. Psychophys. 63, 1314-1329 (2001).
    [CrossRef]
  27. F. Shen and E. Clarkson, "Using Fisher information to approximate ideal-observer performance on detection tasks for lumpy-background images," J. Opt. Soc. Am. A 23, 2406-2414 (2006).
    [CrossRef]

2006 (2)

2005 (2)

S. Park, E. Clarkson, M. A. Kupinski, and H. H. Barrett, "Efficiency of the human observer detecting random signals in random backgrounds," J. Opt. Soc. Am. A 22, 3-16 (2005).
[CrossRef]

S. Park, E. Clarkson, M. A. Kupinski, and H. H. Barrett, "Efficiency of human and model observers for signal-detection tasks in non-Gaussian distributed lumpy backgrounds," Proc. SPIE 5749, 138-149 (2005).
[CrossRef]

2004 (3)

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Search for lesions in mammograms: statistical characterization of observer responses," Med. Phys. 31, 24-36 (2004).
[CrossRef] [PubMed]

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, 2004).

A. Badano and D. H. Fifadara, "Comparison of Fourier-optics, telescopic, and goniometric methods for measuring angular emissions from medical liquid-crystal displays," Appl. Opt. 26, 4999-5005 (2004).
[CrossRef]

2003 (2)

2001 (4)

C. K. Abbey and H. H. Barrett, "Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability," J. Opt. Soc. Am. A 18, 473-488 (2001).
[CrossRef]

A. E. Burgess, F. L. Jacobson, and P. F. Judy, "Human observer detection experiments with mammograms and power-law noise," Med. Phys. 28, 419-437 (2001).
[CrossRef] [PubMed]

F. A. Wichmann and N. J. Hill, "The psychometric function: I. Fitting, sampling, and goodness of fit," Percept. Psychophys. 63, 1314-1329 (2001).
[CrossRef]

F. A. Wichmann and N. J. Hill, "The psychometric function: II. Bootstrap-based confidence intervals and sampling," Percept. Psychophys. 63, 1314-1329 (2001).
[CrossRef]

2000 (1)

A. Badano and M. J. Flynn, "Method for measuring veiling glare in high performance display devices," Appl. Opt. 13, 2059-2066 (2000).

1999 (2)

1998 (1)

1997 (1)

1993 (1)

H. H. Barrett, J. Yao, J. P. Holland, and K. J. Myers, "Model observers for assessment of image quality," Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).
[CrossRef] [PubMed]

1992 (1)

1981 (1)

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

1968 (1)

H. L. Van Trees, Detection, Estimation, and Modulation Theory Part I (Academic, 1968).

1966 (2)

1962 (1)

D. H. Hubel and T. N. Wiesel, "Receptive fields, binocular interaction and functional architecture in the cat's visual cortex," J. Physiol. (London) 160, 106-154 (1962).

1958 (1)

W. P. Tanner and T. G. Birdsall, "Definitions of d? and ? as psychophysical measures," J. Acoust. Soc. Am. 30, 922-928 (1958).
[CrossRef]

Abbey, C. K.

Badano, A.

Barlow, H. B.

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

Barrett, H. H.

S. Park, E. Clarkson, M. A. Kupinski, and H. H. Barrett, "Efficiency of human and model observers for signal-detection tasks in non-Gaussian distributed lumpy backgrounds," Proc. SPIE 5749, 138-149 (2005).
[CrossRef]

S. Park, E. Clarkson, M. A. Kupinski, and H. H. Barrett, "Efficiency of the human observer detecting random signals in random backgrounds," J. Opt. Soc. Am. A 22, 3-16 (2005).
[CrossRef]

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, 2004).

M. A. Kupinski, J. W. Hoppin, E. Clarkson, and H. H. Barrett, "Ideal-observer computation in medical imaging with use of Markov-chain Monte Carlo techniques," J. Opt. Soc. Am. A 20, 430-438 (2003).
[CrossRef]

B. D. Gallas and H. H. Barrett, "Validating the use of channels to estimate the ideal linear observer," J. Opt. Soc. Am. A 20, 1725-1738 (2003).
[CrossRef]

C. K. Abbey and H. H. Barrett, "Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability," J. Opt. Soc. Am. A 18, 473-488 (2001).
[CrossRef]

H. H. Barrett, C. K. Abbey, and E. Clarkson, "Objective assessment of image quality III: ROC metrics, ideal observers, and likelihood-generating functions," J. Opt. Soc. Am. A 15, 1520-1535 (1998).
[CrossRef]

H. H. Barrett, J. Yao, J. P. Holland, and K. J. Myers, "Model observers for assessment of image quality," Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).
[CrossRef] [PubMed]

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

Birdsall, T. G.

W. P. Tanner and T. G. Birdsall, "Definitions of d? and ? as psychophysical measures," J. Acoust. Soc. Am. 30, 922-928 (1958).
[CrossRef]

Bochud, F. O.

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Search for lesions in mammograms: statistical characterization of observer responses," Med. Phys. 31, 24-36 (2004).
[CrossRef] [PubMed]

Burgess, A. E.

Clarkson, E.

Eckstein, M. P.

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Search for lesions in mammograms: statistical characterization of observer responses," Med. Phys. 31, 24-36 (2004).
[CrossRef] [PubMed]

Fifadara, D. H.

Flynn, M. J.

A. Badano and M. J. Flynn, "Method for measuring veiling glare in high performance display devices," Appl. Opt. 13, 2059-2066 (2000).

Gallas, B. D.

Green, D. M.

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

Hill, N. J.

F. A. Wichmann and N. J. Hill, "The psychometric function: I. Fitting, sampling, and goodness of fit," Percept. Psychophys. 63, 1314-1329 (2001).
[CrossRef]

F. A. Wichmann and N. J. Hill, "The psychometric function: II. Bootstrap-based confidence intervals and sampling," Percept. Psychophys. 63, 1314-1329 (2001).
[CrossRef]

Holland, J. P.

H. H. Barrett, J. Yao, J. P. Holland, and K. J. Myers, "Model observers for assessment of image quality," Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).
[CrossRef] [PubMed]

Hoppin, J. W.

Hubel, D. H.

D. H. Hubel and T. N. Wiesel, "Receptive fields, binocular interaction and functional architecture in the cat's visual cortex," J. Physiol. (London) 160, 106-154 (1962).

Jacobson, F. L.

A. E. Burgess, F. L. Jacobson, and P. F. Judy, "Human observer detection experiments with mammograms and power-law noise," Med. Phys. 28, 419-437 (2001).
[CrossRef] [PubMed]

Jennings, R. J.

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

Judy, P. F.

A. E. Burgess, F. L. Jacobson, and P. F. Judy, "Human observer detection experiments with mammograms and power-law noise," Med. Phys. 28, 419-437 (2001).
[CrossRef] [PubMed]

Kupinski, M. A.

Li, X.

Myers, K. J.

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, 2004).

H. H. Barrett, J. Yao, J. P. Holland, and K. J. Myers, "Model observers for assessment of image quality," Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).
[CrossRef] [PubMed]

Park, S.

S. Park, E. Clarkson, M. A. Kupinski, and H. H. Barrett, "Efficiency of human and model observers for signal-detection tasks in non-Gaussian distributed lumpy backgrounds," Proc. SPIE 5749, 138-149 (2005).
[CrossRef]

S. Park, E. Clarkson, M. A. Kupinski, and H. H. Barrett, "Efficiency of the human observer detecting random signals in random backgrounds," J. Opt. Soc. Am. A 22, 3-16 (2005).
[CrossRef]

Robson, J. G.

Rolland, J. P.

Shen, F.

Swets, J. A.

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

Tanner, W. P.

W. P. Tanner and T. G. Birdsall, "Definitions of d? and ? as psychophysical measures," J. Acoust. Soc. Am. 30, 922-928 (1958).
[CrossRef]

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation, and Modulation Theory Part I (Academic, 1968).

Wagner, R. F.

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

Wichmann, F. A.

F. A. Wichmann and N. J. Hill, "The psychometric function: II. Bootstrap-based confidence intervals and sampling," Percept. Psychophys. 63, 1314-1329 (2001).
[CrossRef]

F. A. Wichmann and N. J. Hill, "The psychometric function: I. Fitting, sampling, and goodness of fit," Percept. Psychophys. 63, 1314-1329 (2001).
[CrossRef]

Wiesel, T. N.

D. H. Hubel and T. N. Wiesel, "Receptive fields, binocular interaction and functional architecture in the cat's visual cortex," J. Physiol. (London) 160, 106-154 (1962).

Yao, J.

H. H. Barrett, J. Yao, J. P. Holland, and K. J. Myers, "Model observers for assessment of image quality," Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).
[CrossRef] [PubMed]

Acad. Radiol. (1)

B. D. Gallas, "One-shot estimate of MRMC variance: AUC," Acad. Radiol. 13, 353-362 (2006).
[CrossRef] [PubMed]

Appl. Opt. (2)

J. Acoust. Soc. Am. (1)

W. P. Tanner and T. G. Birdsall, "Definitions of d? and ? as psychophysical measures," J. Acoust. Soc. Am. 30, 922-928 (1958).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (10)

C. K. Abbey and H. H. Barrett, "Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability," J. Opt. Soc. Am. A 18, 473-488 (2001).
[CrossRef]

M. A. Kupinski, J. W. Hoppin, E. Clarkson, and H. H. Barrett, "Ideal-observer computation in medical imaging with use of Markov-chain Monte Carlo techniques," J. Opt. Soc. Am. A 20, 430-438 (2003).
[CrossRef]

B. D. Gallas and H. H. Barrett, "Validating the use of channels to estimate the ideal linear observer," J. Opt. Soc. Am. A 20, 1725-1738 (2003).
[CrossRef]

S. Park, E. Clarkson, M. A. Kupinski, and H. H. Barrett, "Efficiency of the human observer detecting random signals in random backgrounds," J. Opt. Soc. Am. A 22, 3-16 (2005).
[CrossRef]

F. Shen and E. Clarkson, "Using Fisher information to approximate ideal-observer performance on detection tasks for lumpy-background images," J. Opt. Soc. Am. A 23, 2406-2414 (2006).
[CrossRef]

A. E. Burgess, "The Rose model, revisited," J. Opt. Soc. Am. A 16, 633-646 (1999).
[CrossRef]

A. E. Burgess, "Visual signal detectability with two-component noise: low-pass spectrum effects," J. Opt. Soc. Am. A 16, 694-704 (1999).
[CrossRef]

H. H. Barrett, C. K. Abbey, and E. Clarkson, "Objective assessment of image quality III: ROC metrics, ideal observers, and likelihood-generating functions," J. Opt. Soc. Am. A 15, 1520-1535 (1998).
[CrossRef]

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

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

J. Physiol. (London) (1)

D. H. Hubel and T. N. Wiesel, "Receptive fields, binocular interaction and functional architecture in the cat's visual cortex," J. Physiol. (London) 160, 106-154 (1962).

Med. Phys. (2)

A. E. Burgess, F. L. Jacobson, and P. F. Judy, "Human observer detection experiments with mammograms and power-law noise," Med. Phys. 28, 419-437 (2001).
[CrossRef] [PubMed]

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Search for lesions in mammograms: statistical characterization of observer responses," Med. Phys. 31, 24-36 (2004).
[CrossRef] [PubMed]

Percept. Psychophys. (2)

F. A. Wichmann and N. J. Hill, "The psychometric function: I. Fitting, sampling, and goodness of fit," Percept. Psychophys. 63, 1314-1329 (2001).
[CrossRef]

F. A. Wichmann and N. J. Hill, "The psychometric function: II. Bootstrap-based confidence intervals and sampling," Percept. Psychophys. 63, 1314-1329 (2001).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

H. H. Barrett, J. Yao, J. P. Holland, and K. J. Myers, "Model observers for assessment of image quality," Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).
[CrossRef] [PubMed]

Proc. SPIE (1)

S. Park, E. Clarkson, M. A. Kupinski, and H. H. Barrett, "Efficiency of human and model observers for signal-detection tasks in non-Gaussian distributed lumpy backgrounds," Proc. SPIE 5749, 138-149 (2005).
[CrossRef]

Science (1)

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

Other (4)

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

H. L. Van Trees, Detection, Estimation, and Modulation Theory Part I (Academic, 1968).

S. Park, M. A. Kupinski, E. Clarkson, and H. H. Barrett, "Ideal-observer performance under signal and background uncertainty," in Information Processing in Medical Imaging, Vol. 2732 in Lecture Notes in Computer Science, C. J. Taylor and J. A. Noble, eds. (Springer-Verlag, 2003) pp. 342-353.

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, 2004).

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Figures (12)

Fig. 1
Fig. 1

Histogram of image values from 200 signal-absent lumpy-background images.

Fig. 2
Fig. 2

Detection tasks of 2AFC using two different scaling methods. The top and bottom plots show the tasks using Scalings I and II, respectively. Scalings I and II map image values to displayed pixel values ranging in [0, 255] and [40, 255], respectively.

Fig. 3
Fig. 3

Luminance-response curves used in the prior and current studies.

Fig. 4
Fig. 4

Histograms of displayed pixel values from the 20 × 20 signal-location regions in 200 signal-present lumpy-background images, including the Gaussian-signal image of width 3.04, with Scalings I and II.

Fig. 5
Fig. 5

Plot of the performance of the ten observers. The solid curve connects mean percent correct (PC) values of all the observers with ± 2 standard errors from the PC estimates for the six experiments using six different, increasing signal intensities, a s . The errors are MRMC estimates by the one-shot method. The dashed–dotted curve connects individual PC measurements of the best eight observers. The dashed curve connects the PC measurements of the worst two observers. The worst two observers appear to be outliers of the PC measurements.

Fig. 6
Fig. 6

Fitted psychometric curves with the PCs of the best eight observers for Scalings I and II, compared with a reproduced psychometric curve from the prior study. The mean PCs from the prior and current studies are represented, respectively, by squares and stars. The error bars are ± 2 standard deviations estimated by the one-shot method using the PCs from the current study.

Fig. 7
Fig. 7

Plot shows mean differences between PCs of the best eight observers using Scalings I and II. The errors are ± 2 standard deviations estimated by the one-shot method. This analysis is done for all six experiments using six different, increasing signal intensities. The plot indicates that Scalings I and II do not make a statistically significant difference in human performance.

Fig. 8
Fig. 8

Human detectability for the best eight observers using Scalings I and II, compared with the human and ideal-observer detectabilities from the prior study. The errors for human performance are ± 2 standard deviations estimated with the PCs from the studies. The errors for the ideal observer are estimated by the one-shot method. The ideal-observer d A curve is available only up to a s = 0.4 , since the ideal-observer AUC approaches one at that point.

Fig. 9
Fig. 9

Plots (a) and (b) show comparisons of human and anthropomorphic CHO (aCHO) detectabilities from the prior and current studies, respectively. The 11% line represents human-efficiency results relative to the aCHO in the literature. SDOG and DDOG, respectively, represent sparse and dense difference-of-Gaussians (DOG) channels. For plot (b), human detectabilities are calculated from the PCs of the best eight observers.

Fig. 10
Fig. 10

Histogram of log 10 of the ratios of the local-lump densities under the signal-absent and signal-present cases.

Fig. 11
Fig. 11

Plots show the mean PC for the best eight observers versus the lump-density ratio of the signal-absent and signal-present lumpy-background images as a function of log 10 (lump-density ratio). The data is for Scaling I. From top to bottom, signal intensity, a s , increases (the first three signal intensities). The PC values above the plots are averaged across all lumpy densities and their errors are ± 2 standard errors of the mean estimate.

Fig. 12
Fig. 12

Plots show the mean PC for the best eight observers versus the lump-density ratio of the signal-absent and signal-present lumpy-background images as a function of log 10 (lump-density ratio). The data is for Scaling I. From top to bottom, signal intensity, a s , increases (the last three signal intensities). The PC values above the plots are averaged across all lumpy densities and their errors are ± 2 standard errors of the mean estimate.

Tables (1)

Tables Icon

Table 1 Human Efficiency Results for a SKE Task from Both the Prior and Current Studies a

Equations (22)

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

g = H f + n ,
g ¯ m = S d r h m ( r ) f ( r ) ,
h m ( r ) = h 2 π w 2 exp [ ( r p m ) ( r p m ) 2 w 2 ] .
pr ( g g ¯ ) = m 1 M exp ( g ¯ m ) g ¯ m g m g m ! .
H 0 : g = H f b + n ,
H 1 : g = H ( f b + f s ) + n .
f b = f b ( r ) = n = 1 N L ( r c n a b , σ b ) ,
L ( r c n a b , σ b ) = a b exp { ( r c n ) ( r c n ) 2 σ b 2 } ,
f s = f s ( r ) = a s exp { ( r c ) ( r c ) 2 σ s 2 } ,
Λ ( g ) = pr ( g H 1 ) pr ( g H 0 ) ,
Λ ( g ) = d θ pr ( g b ( θ ) , H 1 ) pr ( θ ) d θ pr ( g b ( θ ) , H 0 ) pr ( θ ) ,
Λ BKE ( g b ( θ ) ) = pr ( g b ( θ ) , H 1 ) pr ( g b ( θ ) , H 0 ) ,
pr ( θ g , H 0 ) = pr ( g b ( θ ) , H 0 ) pr ( θ ) d θ pr ( g b ( θ ) , H 0 ) pr ( θ ) ,
Λ ( g ) = d θ Λ BKE ( g b ( θ ) ) pr ( θ g , H 0 ) .
Λ ̂ ( g ) = 1 J j = J 0 J Λ BKE [ g b ( θ ( j ) ) ] ,
t v = ( K v 1 v s ) t v ,
K v , 0 = T [ diag ( b ¯ ) + K b ] T t ,
K v , 1 = T [ diag ( b ¯ + s ) + K b ] T t = K v , 0 + T diag ( s ) T t ,
d A 2 erf 1 ( 2 AUC 1 ) ,
e = [ d A ( human ) d A ( model ) ] 2 .
e = [ 1 m ( human ) 1 m ( model ) ] 2 = [ m ( model ) m ( human ) ] 2 ,
p = 225 t 1 g max g min × ( g g min ) + t 1 ,

Metrics