Abstract

Many natural backgrounds have approximately isotropic power spectra of the power-law form, P(f)=Kfβ, where f is radial frequency. For natural scenes and mammograms, the values of the exponent, β, range from 1.5 to 3.5. The ideal observer model predicts that for signals with certain properties and backgrounds that can be treated as random noise, a plot of log (contrast threshold) versus log (signal size) will be linear with slope, m, given by: m=(β2)2. This plot is referred to as a contrast-detail (CD) diagram. It is interesting that this predicts a detection threshold that is independent of signal size for β equal to 2. We present two-alternative forced-choice (2AFC) detection results for human and channelized model observers of a simple signal in filtered noise with exponents from 1.5 to 3.5. The CD diagram results are in good agreement with the prediction of this equation.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  17. R. F. Wagner and K. E. Weaver, "An assortment of image quality indices for radiographic film-screen combinations—can they be resolved?" Proc. SPIE 35, 83-94 (1972).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  25. 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]
  26. J. J. Heine and R. P. Velthuizen, "Spectral analysis of full field digital mammography data," Med. Phys. 29, 647-661 (2002).
    [CrossRef] [PubMed]
  27. D. Chakraborty and H. L. Kundel, "Anomalous nodule visibility effects in mammographic images," Proc. SPIE 4324, 68-76 (2001).
    [CrossRef]
  28. A. E. Burgess, "Evaluation of detection model performance in power-law noise," Proc. SPIE 4324, 123-132 (2001).
    [CrossRef]
  29. J. P. Johnson, J. Lubin, J. S. Nafziger, and D. P. Chakraborty, "Visual discrimination modeling of lesion detectability," Proc. SPIE 4686, 248-255 (2002).
    [CrossRef]
  30. A. E. Burgess and P. F. Judy, "Detection in power-law noise: spectrum exponents and CD diagram slopes," Proc. SPIE 5034, 57-62 (2003).
    [CrossRef]
  31. J. P. Johnson, J. Lubin, J. S. Nafziger, E. A. Krupinski, and H. Roehrig, "Channelized model observer using a visual discrimination model," Proc. SPIE 5749, 199-210 (2005).
    [CrossRef]
  32. J. S. Nafziger, J. P. Johnson, and J. Lubin, "Effects of visual fixation cues on the detectability of simulated breast lesions," Proc. SPIE 5749, 566-571 (2005).
    [CrossRef]
  33. R. D. Fiete, H. H. Barrett, W. E. Smith, and K. J. Myers, "Hotelling trace criterion and its correlation with human-observer performance," J. Opt. Soc. Am. 4, 945-953 (1987).
    [CrossRef]
  34. H. H. Barrett, C. K. Abbey, B. Gallas, and M. P. Eckstein, "Stabilized estimates of Hotelling observer detection performance in patient structured noise," Proc. SPIE 3340, 27-43 (1998).
    [CrossRef]
  35. A. B. Watson and D. Pelli, "QUEST: a Bayesian adaptive psychometric method," Percept. Psychophys. 33, 113-20 (1983).
    [CrossRef] [PubMed]
  36. A. E. Burgess, "Comparison of ROC and forced-choice observer performance measurement methods," Med. Phys. 22, 643-55 (1995).
    [CrossRef] [PubMed]
  37. H. L. Kundel, C. F. Nodine, L. Toto, and S. Lauver, "A circle cue enhances detection of simulated masses on mammographic backgrounds," Proc. SPIE 3032, 81-84 (1997).
    [CrossRef]
  38. P. F. Judy and R. G. Swennson, "Detectability of lesions of various sizes on CT images," Proc. SPIE 535, 38-42 (1985).

2005

J. P. Johnson, J. Lubin, J. S. Nafziger, E. A. Krupinski, and H. Roehrig, "Channelized model observer using a visual discrimination model," Proc. SPIE 5749, 199-210 (2005).
[CrossRef]

J. S. Nafziger, J. P. Johnson, and J. Lubin, "Effects of visual fixation cues on the detectability of simulated breast lesions," Proc. SPIE 5749, 566-571 (2005).
[CrossRef]

2003

A. E. Burgess and P. F. Judy, "Detection in power-law noise: spectrum exponents and CD diagram slopes," Proc. SPIE 5034, 57-62 (2003).
[CrossRef]

2002

J. J. Heine and R. P. Velthuizen, "Spectral analysis of full field digital mammography data," Med. Phys. 29, 647-661 (2002).
[CrossRef] [PubMed]

J. P. Johnson, J. Lubin, J. S. Nafziger, and D. P. Chakraborty, "Visual discrimination modeling of lesion detectability," Proc. SPIE 4686, 248-255 (2002).
[CrossRef]

2001

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]

D. Chakraborty and H. L. Kundel, "Anomalous nodule visibility effects in mammographic images," Proc. SPIE 4324, 68-76 (2001).
[CrossRef]

A. E. Burgess, "Evaluation of detection model performance in power-law noise," Proc. SPIE 4324, 123-132 (2001).
[CrossRef]

1999

F. O. Bochud, J. F. Valley, F. R. Verdun, C. Hessler, and P. Schnyder, "Estimate of the noisy component of anatomical backgrounds," Med. Phys. 26, 1365-1370 (1999).
[CrossRef] [PubMed]

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

1998

H. H. Barrett, C. K. Abbey, B. Gallas, and M. P. Eckstein, "Stabilized estimates of Hotelling observer detection performance in patient structured noise," Proc. SPIE 3340, 27-43 (1998).
[CrossRef]

1997

1996

B. Zheng, Y.-H. Chang, and D. Gur, "Adaptive computer-aided diagnosis scheme of digitized mammograms," Acad. Radiol. 3, 806-814 (1996).
[CrossRef] [PubMed]

1995

A. E. Burgess, "Comparison of ROC and forced-choice observer performance measurement methods," Med. Phys. 22, 643-55 (1995).
[CrossRef] [PubMed]

1994

D. L. Ruderman and W. Bialek, "Statistics of natural images: scaling in the woods," Phys. Rev. Lett. 73, 814-817 (1994).
[CrossRef]

1992

1989

W. S. Geisler, "Sequential ideal-observer analysis of visual discriminations," Psychol. Rev. 96, 267-314 (1989).
[CrossRef] [PubMed]

1988

1987

1985

1984

1983

A. B. Watson and D. Pelli, "QUEST: a Bayesian adaptive psychometric method," Percept. Psychophys. 33, 113-20 (1983).
[CrossRef] [PubMed]

1981

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

1977

H. B. Barlow, "The efficiency of detecting changes in density in random dot patterns," Vision Res. 18, 637-650 (1977).
[CrossRef]

1973

J. Nachmias and R. V. Sansbury, "Grating contrast: discrimination may be better than detection," Vision Res. 14, 1039-1042 (1973).
[CrossRef]

1972

R. F. Wagner and K. E. Weaver, "An assortment of image quality indices for radiographic film-screen combinations—can they be resolved?" Proc. SPIE 35, 83-94 (1972).

1958

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

Acad. Radiol.

B. Zheng, Y.-H. Chang, and D. Gur, "Adaptive computer-aided diagnosis scheme of digitized mammograms," Acad. Radiol. 3, 806-814 (1996).
[CrossRef] [PubMed]

J. Acoust. Soc. Am.

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

J. Opt. Soc. Am.

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

J. Opt. Soc. Am. A

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

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

M. A. Webster and E. Miyahara, "Contrast adaptation and the spatial structure of natural images," J. Opt. Soc. Am. A 14, 2355-2366 (1997).
[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]

A. J. Ahumada and B. L. Beard, "Image discrimination models predict detection in fixed but not random noise," J. Opt. Soc. Am. A 14, 2471-2478 (1997).
[CrossRef]

A. E. 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]

K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton, and 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]

D. Field, "Relations between the statistics of natural scenes and the response of cortical cells," J. Opt. Soc. Am. A 4, 2379-2394 (1987).
[CrossRef]

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

A. E. Burgess and B. Colborne, "Visual signal detection. IV. Observer inconsistency," J. Opt. Soc. Am. A 5, 617-627 (1988).
[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]

Med. Phys.

A. E. Burgess, "Comparison of ROC and forced-choice observer performance measurement methods," Med. Phys. 22, 643-55 (1995).
[CrossRef] [PubMed]

F. O. Bochud, J. F. Valley, F. R. Verdun, C. Hessler, and P. Schnyder, "Estimate of the noisy component of anatomical backgrounds," Med. Phys. 26, 1365-1370 (1999).
[CrossRef] [PubMed]

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]

J. J. Heine and R. P. Velthuizen, "Spectral analysis of full field digital mammography data," Med. Phys. 29, 647-661 (2002).
[CrossRef] [PubMed]

Percept. Psychophys.

A. B. Watson and D. Pelli, "QUEST: a Bayesian adaptive psychometric method," Percept. Psychophys. 33, 113-20 (1983).
[CrossRef] [PubMed]

Phys. Rev. Lett.

D. L. Ruderman and W. Bialek, "Statistics of natural images: scaling in the woods," Phys. Rev. Lett. 73, 814-817 (1994).
[CrossRef]

Proc. SPIE

H. H. Barrett, C. K. Abbey, B. Gallas, and M. P. Eckstein, "Stabilized estimates of Hotelling observer detection performance in patient structured noise," Proc. SPIE 3340, 27-43 (1998).
[CrossRef]

H. L. Kundel, C. F. Nodine, L. Toto, and S. Lauver, "A circle cue enhances detection of simulated masses on mammographic backgrounds," Proc. SPIE 3032, 81-84 (1997).
[CrossRef]

P. F. Judy and R. G. Swennson, "Detectability of lesions of various sizes on CT images," Proc. SPIE 535, 38-42 (1985).

D. Chakraborty and H. L. Kundel, "Anomalous nodule visibility effects in mammographic images," Proc. SPIE 4324, 68-76 (2001).
[CrossRef]

A. E. Burgess, "Evaluation of detection model performance in power-law noise," Proc. SPIE 4324, 123-132 (2001).
[CrossRef]

J. P. Johnson, J. Lubin, J. S. Nafziger, and D. P. Chakraborty, "Visual discrimination modeling of lesion detectability," Proc. SPIE 4686, 248-255 (2002).
[CrossRef]

A. E. Burgess and P. F. Judy, "Detection in power-law noise: spectrum exponents and CD diagram slopes," Proc. SPIE 5034, 57-62 (2003).
[CrossRef]

J. P. Johnson, J. Lubin, J. S. Nafziger, E. A. Krupinski, and H. Roehrig, "Channelized model observer using a visual discrimination model," Proc. SPIE 5749, 199-210 (2005).
[CrossRef]

J. S. Nafziger, J. P. Johnson, and J. Lubin, "Effects of visual fixation cues on the detectability of simulated breast lesions," Proc. SPIE 5749, 566-571 (2005).
[CrossRef]

R. F. Wagner and K. E. Weaver, "An assortment of image quality indices for radiographic film-screen combinations—can they be resolved?" Proc. SPIE 35, 83-94 (1972).

Psychol. Rev.

W. S. Geisler, "Sequential ideal-observer analysis of visual discriminations," Psychol. Rev. 96, 267-314 (1989).
[CrossRef] [PubMed]

Science

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

Vision Res.

J. Nachmias and R. V. Sansbury, "Grating contrast: discrimination may be better than detection," Vision Res. 14, 1039-1042 (1973).
[CrossRef]

H. B. Barlow, "The efficiency of detecting changes in density in random dot patterns," Vision Res. 18, 637-650 (1977).
[CrossRef]

Other

A. Pentland, "Fractal-based descriptions of surfaces," in Natural Computation, W.Richards, ed. (MIT Press, 1988), pp. 279-299.

J. A. Swets, Signal Detection and Recognition by Human Observers (Wiley, 1964).

D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, 1966). (Reprinted by Peninsula, 1988.)

H. B. Barlow, "Three points about lateral inhibition," in Sensory Communications, W.A.Rosenblith, ed. (MIT Press, 1961) pp. 782-786.

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Figures (4)

Fig. 1
Fig. 1

Example image for the 2AFC detection task with a nodule signal diameter of 32   pixels and a power-law noise exponent of 2.0. A high amplitude reference version of the signal is shown above the noise fields. The location reference circles are exaggerated in the manuscript image but are unobtrusive low contrast, concentric bipolar circles on the experimental display monitor.

Fig. 2
Fig. 2

(a)–(e) Examples of power-law noise background images with isotropic power spectrum P ( f ) = 1 f β . Exponents are (a) 1.5, (b) 2.0, (c) 2.5, (d) 3.0, (e) 3.5.

Fig. 3
Fig. 3

(a)–(e) The CD diagram (contrast threshold for d equals 2 versus signal diameter) results for two human observers (symbols), regression fits (dashed lines) to the averages for the two observers and regression fits the FHC model results (solid lines) for five power-law exponents: (a) 1.5, (b) 2.0, (c) 2.5, (d) 3.0, (e) 3.5. The error bars for observer 1 are 95% confidence limits.

Fig. 4
Fig. 4

Summary of estimated average human observer CD slopes as a function of the noise power-law exponent.

Tables (1)

Tables Icon

Table 1 Summary of the CD Diagram Slopes for the Five Power-Law Noise Exponents Used in the Experiments a

Equations (16)

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

efficiency
= Signal energy required by the ideal observer Signal energy required by the human observer
= [ Signal amplitude required by the ideal observer Signal amplitude required by the human observer ] 2 .
efficiency = [ d H d I ] 2 .
P ( f ) = K f β
m = ( β 2 ) 2 .
g ( x , y ) = s ( x x 0 , y y 0 ) + n ( x , y ) + b ( x , y ) .
SNR 2 = ( d ) 2 = 2 π 0 S ( f ) 2 f d f P b ( f ) .
S R ( f ) = α R 2 S ( R f ) .
( d ) 2 = 2 π 0 S R ( f ) 2 f d f P b ( f ) = 2 π α 2 R 4 K 0 S ( f ) 2 f ( 1 + β ) d f .
log ( A t ) = C + m log ( R ) , with m = ( β 2 ) 2 .
s C = T t s ,
( d ) 2 = SNR 2 = s C t K C 1 s C .
s ( r ) = A Rect ( 2 ρ ) [ 1 ρ 2 ] υ ,
B n ( r ) = 2 π a exp ( π r 2 a 2 ) L n ( 2 π r 2 a 2 ) ,
K C = E ( g C E [ g C ] ) ( g C E [ g C ] ) t .

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