Abstract

Studies have shown that human observers can adapt their detection strategies on the basis of the statistical properties of noisy backgrounds. One common property of such studies is that the backgrounds studied are (or are assumed to be) statistically stationary. Less is known about how humans detect signals in the more complex setting of nonstationary backgrounds. We investigated detection performance in the presence of a globally nonstationary oriented noise background. We controlled for noise-correlation effects by considering a stationary background with a power spectrum matched to the average spectrum of the nonstationary process. Performance of a nonadaptive linear filter that was unable to make use of differences in local statistics yielded constant performance in both the stationary and the nonstationary backgrounds. In contrast, performance of an ideal observer that uses local noise statistics yielded substantially higher (140%) detectability with the nonstationary backgrounds than the stationary ones. Human observers showed significantly higher (33%) detection performance in the nonstationary backgrounds, suggesting that they can adapt their detection mechanisms to the local orientation properties.

© 2006 Optical Society of America

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  1. H. B. Barlow, 'Efficiency of detecting changes of density in random dot patterns,' Vision Res. 18, 637-650 (1978).
  2. A. E. Burgess, R. F. Wagner, R. J. Jennings, and H. B. Barlow, 'Efficiency of human visual signal discrimination,' Science 214, 93-94 (1981).
  3. A. Burgess and H. Ghandeharian, 'Visual signal detection. I. Ability to use phase information,' J. Opt. Soc. Am. A 1, 900-905 (1984).
  4. D. G. Pelli, 'Uncertainty explains many aspects of visual contrast detection and discrimination,' J. Opt. Soc. Am. A 2, 1508-1532 (1985).
  5. 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).
  6. 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).
  7. A. E. Burgess, 'Visual signal detection with two-component noise: low-pass spectrum effects,' J. Opt. Soc. Am. A 16, 694-704 (1999).
  8. M. P. Eckstein, A. J. Ahumada, and A. B. Watson, 'Image discrimination models predict visual detection in natural medical image backgrounds,' in Proc. SPIE 3016, 44-56 (1997).
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  12. M. A. Webster and E. Miyahara, 'Contrast adaptation and the spatial structure of natural images,' J. Opt. Soc. Am. A 14, 2355-2366 (1997).
  13. R. C. Gonzales and R. E. Woods, Digital Image Processing (Prentice Hall, 2001).
  14. W. K. Pratt, Digital Image Processing; PIKS Inside (Wiley, 2001).
  15. Image A from http://www.pixelperfectdigital.com; image B from http://www.nist.gov; image C from http://www.radiologyinfo.org; image D from http://peipa.essex.ac.uk/info/mias.html.
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  17. A. E. Burgess and H. Ghandeharian, 'Visual signal detection. II. Signal-location identification,' J. Opt. Soc. Am. A 1, 906-910 (1984).
  18. A. E. Burgess, 'Statistically defined backgrounds: performance of a modified nonprewhitening observer model,' J. Opt. Soc. Am. A 11, 1237-1242 (1994).
  19. H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, 'Model observers for assessment of image quality,' Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).
  20. R. F. Wagner and K. E. Weaver, 'An assortment of image quality indices for radiographic film-screen combinations--can they be resolved?' in Proc. SPIE 35, 83-84 (1972).
  21. M. P. Eckstein, C. K. Abbey, and F. O. Bochud, 'A practical guide to model observers for visual detection in synthetic and natural noisy images,' in Handbook of Medical Imaging (SPIE, 2000).
  22. F. O. Bochud, C. K. Abbey, and 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).
  23. D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, 1966).
  24. For the NPWE and PW models, the detectability shown in Fig. 6 is transformed from Pc. For the IO with the GNS test image, the detectability is obtained by Eq.(13) to avoid the difficulties of transforming a Pc of value 1 (owing to the high signal contrast) to dmafc (please see Appendix for the comparison between d′ and dmafc in this latter case).
  25. A. E. Burgess and B. Colborne, 'Visual signal detection. IV. Observer inconsistency,' J. Opt. Soc. Am. A 5, 617-627 (1988).
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  27. 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).
  28. M. P. Eckstein, C. K. Abbey, F. O. Bochud, and J. S. Whiting, 'The effect of image compression in model and human observers,' in Proc. SPIE 3663, 243-252 (1999).
  29. F. A. A. Kingdom, D. Keeble, and B. Moulden, 'Sensitivity to orientation modulation in micropattern-based textures,' Vision Res. 35, 79-91 (1994).
  30. 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).
  31. J. Yao and H. H. Barrett, 'Predicting human performance by a channelized Hotelling observer model,' in Proc. SPIE 1768, 161-168 (1992).
  32. M. P. Eckstein and J. S. Whiting, 'Lesion detection in structured noise,' Acad. Radiol. 2, 249-253 (1995).
  33. D. G. Pelli, 'Effects of visual noise,' Ph.D. dissertation (Cambridge University, 1981).
  34. F. O. Bochud, C. K. Abbey, and M. P. Eckstein, 'Further investigation of the effect of phase spectrum on visual detection in structured backgrounds,' in Proc. SPIE 3663, 273-281 (1999).
  35. M. Bath, M. Hakansson, S. Borjesson, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, S. Kheddache, A. Tingberg, and L. G. Mansson, 'Investigation of image components affecting the detection of lung nodules in digital chest radiography,' in Proc. SPIE 5749, 231-242 (2005).
  36. F. O. Bochud, F. R. Verdun, C. Hessler, and J. F. Valley, 'Detectability on radiological images: the effect of the anatomical noise,' in Proc. SPIE 2436, 156-164 (1995).

2005 (1)

M. Bath, M. Hakansson, S. Borjesson, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, S. Kheddache, A. Tingberg, and L. G. Mansson, 'Investigation of image components affecting the detection of lung nodules in digital chest radiography,' in Proc. SPIE 5749, 231-242 (2005).

2004 (1)

Y. Zhang, B. T. Pham, and M. P. Eckstein, 'Evaluation of JPEG 2000 encoder options: human and model observer detection of variable signals in X-ray coronary angiograms,' IEEE Trans. Med. Imaging 23, 613-632 (2004).

2003 (1)

2001 (2)

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).

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).

2000 (1)

1999 (3)

A. E. Burgess, 'Visual signal detection with two-component noise: low-pass spectrum effects,' J. Opt. Soc. Am. A 16, 694-704 (1999).

M. P. Eckstein, C. K. Abbey, F. O. Bochud, and J. S. Whiting, 'The effect of image compression in model and human observers,' in Proc. SPIE 3663, 243-252 (1999).

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, 'Further investigation of the effect of phase spectrum on visual detection in structured backgrounds,' in Proc. SPIE 3663, 273-281 (1999).

1997 (4)

1995 (2)

M. P. Eckstein and J. S. Whiting, 'Lesion detection in structured noise,' Acad. Radiol. 2, 249-253 (1995).

F. O. Bochud, F. R. Verdun, C. Hessler, and J. F. Valley, 'Detectability on radiological images: the effect of the anatomical noise,' in Proc. SPIE 2436, 156-164 (1995).

1994 (2)

F. A. A. Kingdom, D. Keeble, and B. Moulden, 'Sensitivity to orientation modulation in micropattern-based textures,' Vision Res. 35, 79-91 (1994).

A. E. Burgess, 'Statistically defined backgrounds: performance of a modified nonprewhitening observer model,' J. Opt. Soc. Am. A 11, 1237-1242 (1994).

1993 (1)

H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, 'Model observers for assessment of image quality,' Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).

1992 (2)

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).

J. Yao and H. H. Barrett, 'Predicting human performance by a channelized Hotelling observer model,' in Proc. SPIE 1768, 161-168 (1992).

1988 (1)

1987 (1)

1985 (2)

1984 (2)

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).

1978 (1)

H. B. Barlow, 'Efficiency of detecting changes of density in random dot patterns,' Vision Res. 18, 637-650 (1978).

1972 (1)

R. F. Wagner and K. E. Weaver, 'An assortment of image quality indices for radiographic film-screen combinations--can they be resolved?' in Proc. SPIE 35, 83-84 (1972).

Abbey, C. K.

Ahumada, A. J.

M. P. Eckstein, A. J. Ahumada, and 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).

M. P. Eckstein, A. J. Ahumada, and A. B. Watson, 'Image discrimination models predict visual detection in natural medical image backgrounds,' in Proc. SPIE 3016, 44-56 (1997).

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).

H. B. Barlow, 'Efficiency of detecting changes of density in random dot patterns,' Vision Res. 18, 637-650 (1978).

Barrett, H. H.

Bartroff, J. L.

Bath, M.

M. Bath, M. Hakansson, S. Borjesson, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, S. Kheddache, A. Tingberg, and L. G. Mansson, 'Investigation of image components affecting the detection of lung nodules in digital chest radiography,' in Proc. SPIE 5749, 231-242 (2005).

Bochud, F. O.

M. Bath, M. Hakansson, S. Borjesson, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, S. Kheddache, A. Tingberg, and L. G. Mansson, 'Investigation of image components affecting the detection of lung nodules in digital chest radiography,' in Proc. SPIE 5749, 231-242 (2005).

M. P. Eckstein, J. L. Bartroff, C. K. Abbey, J. S. Whiting, and F. O. Bochud, 'Automated computer evaluation and optimization of image compression of x-ray coronary angiograms for signal known exactly detection tasks,' Opt. Express 11, 460-475 (2003).

F. O. Bochud, C. K. Abbey, and 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).

M. P. Eckstein, C. K. Abbey, F. O. Bochud, and J. S. Whiting, 'The effect of image compression in model and human observers,' in Proc. SPIE 3663, 243-252 (1999).

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, 'Further investigation of the effect of phase spectrum on visual detection in structured backgrounds,' in Proc. SPIE 3663, 273-281 (1999).

F. O. Bochud, F. R. Verdun, C. Hessler, and J. F. Valley, 'Detectability on radiological images: the effect of the anatomical noise,' in Proc. SPIE 2436, 156-164 (1995).

M. P. Eckstein, C. K. Abbey, and F. O. Bochud, 'A practical guide to model observers for visual detection in synthetic and natural noisy images,' in Handbook of Medical Imaging (SPIE, 2000).

Borgstrom, M. C.

Borjesson, S.

M. Bath, M. Hakansson, S. Borjesson, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, S. Kheddache, A. Tingberg, and L. G. Mansson, 'Investigation of image components affecting the detection of lung nodules in digital chest radiography,' in Proc. SPIE 5749, 231-242 (2005).

Burgess, A.

Burgess, A. E.

Colborne, B.

Eckstein, M. P.

Y. Zhang, B. T. Pham, and M. P. Eckstein, 'Evaluation of JPEG 2000 encoder options: human and model observer detection of variable signals in X-ray coronary angiograms,' IEEE Trans. Med. Imaging 23, 613-632 (2004).

M. P. Eckstein, J. L. Bartroff, C. K. Abbey, J. S. Whiting, and F. O. Bochud, 'Automated computer evaluation and optimization of image compression of x-ray coronary angiograms for signal known exactly detection tasks,' Opt. Express 11, 460-475 (2003).

F. O. Bochud, C. K. Abbey, and 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).

M. P. Eckstein, C. K. Abbey, F. O. Bochud, and J. S. Whiting, 'The effect of image compression in model and human observers,' in Proc. SPIE 3663, 243-252 (1999).

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, 'Further investigation of the effect of phase spectrum on visual detection in structured backgrounds,' in Proc. SPIE 3663, 273-281 (1999).

M. P. Eckstein, A. J. Ahumada, and 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).

M. P. Eckstein, A. J. Ahumada, and A. B. Watson, 'Image discrimination models predict visual detection in natural medical image backgrounds,' in Proc. SPIE 3016, 44-56 (1997).

M. P. Eckstein and J. S. Whiting, 'Lesion detection in structured noise,' Acad. Radiol. 2, 249-253 (1995).

M. P. Eckstein, C. K. Abbey, and F. O. Bochud, 'A practical guide to model observers for visual detection in synthetic and natural noisy images,' in Handbook of Medical Imaging (SPIE, 2000).

Ghandeharian, H.

Gonzales, R. C.

R. C. Gonzales and R. E. Woods, Digital Image Processing (Prentice Hall, 2001).

Green, D. M.

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

Hakansson, M.

M. Bath, M. Hakansson, S. Borjesson, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, S. Kheddache, A. Tingberg, and L. G. Mansson, 'Investigation of image components affecting the detection of lung nodules in digital chest radiography,' in Proc. SPIE 5749, 231-242 (2005).

Hessler, C.

F. O. Bochud, F. R. Verdun, C. Hessler, and J. F. Valley, 'Detectability on radiological images: the effect of the anatomical noise,' in Proc. SPIE 2436, 156-164 (1995).

Hoeschen, C.

M. Bath, M. Hakansson, S. Borjesson, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, S. Kheddache, A. Tingberg, and L. G. Mansson, 'Investigation of image components affecting the detection of lung nodules in digital chest radiography,' in Proc. SPIE 5749, 231-242 (2005).

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).

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).

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).

Keeble, D.

F. A. A. Kingdom, D. Keeble, and B. Moulden, 'Sensitivity to orientation modulation in micropattern-based textures,' Vision Res. 35, 79-91 (1994).

Kheddache, S.

M. Bath, M. Hakansson, S. Borjesson, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, S. Kheddache, A. Tingberg, and L. G. Mansson, 'Investigation of image components affecting the detection of lung nodules in digital chest radiography,' in Proc. SPIE 5749, 231-242 (2005).

Kingdom, F. A. A.

F. A. A. Kingdom, D. Keeble, and B. Moulden, 'Sensitivity to orientation modulation in micropattern-based textures,' Vision Res. 35, 79-91 (1994).

Li, X.

Mansson, L. G.

M. Bath, M. Hakansson, S. Borjesson, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, S. Kheddache, A. Tingberg, and L. G. Mansson, 'Investigation of image components affecting the detection of lung nodules in digital chest radiography,' in Proc. SPIE 5749, 231-242 (2005).

Miyahara, E.

Moulden, B.

F. A. A. Kingdom, D. Keeble, and B. Moulden, 'Sensitivity to orientation modulation in micropattern-based textures,' Vision Res. 35, 79-91 (1994).

Myers, K. J.

Patton, D. D.

Pelli, D. G.

Pham, B. T.

Y. Zhang, B. T. Pham, and M. P. Eckstein, 'Evaluation of JPEG 2000 encoder options: human and model observer detection of variable signals in X-ray coronary angiograms,' IEEE Trans. Med. Imaging 23, 613-632 (2004).

Pratt, W. K.

W. K. Pratt, Digital Image Processing; PIKS Inside (Wiley, 2001).

Rolland, J. P.

H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, 'Model observers for assessment of image quality,' Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).

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).

Seeley, G. W.

Swets, J. A.

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

Tingberg, A.

M. Bath, M. Hakansson, S. Borjesson, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, S. Kheddache, A. Tingberg, and L. G. Mansson, 'Investigation of image components affecting the detection of lung nodules in digital chest radiography,' in Proc. SPIE 5749, 231-242 (2005).

Tischenko, O.

M. Bath, M. Hakansson, S. Borjesson, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, S. Kheddache, A. Tingberg, and L. G. Mansson, 'Investigation of image components affecting the detection of lung nodules in digital chest radiography,' in Proc. SPIE 5749, 231-242 (2005).

Ullman, G.

M. Bath, M. Hakansson, S. Borjesson, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, S. Kheddache, A. Tingberg, and L. G. Mansson, 'Investigation of image components affecting the detection of lung nodules in digital chest radiography,' in Proc. SPIE 5749, 231-242 (2005).

Valley, J. F.

F. O. Bochud, F. R. Verdun, C. Hessler, and J. F. Valley, 'Detectability on radiological images: the effect of the anatomical noise,' in Proc. SPIE 2436, 156-164 (1995).

Verdun, F. R.

M. Bath, M. Hakansson, S. Borjesson, C. Hoeschen, O. Tischenko, F. O. Bochud, F. R. Verdun, G. Ullman, S. Kheddache, A. Tingberg, and L. G. Mansson, 'Investigation of image components affecting the detection of lung nodules in digital chest radiography,' in Proc. SPIE 5749, 231-242 (2005).

F. O. Bochud, F. R. Verdun, C. Hessler, and J. F. Valley, 'Detectability on radiological images: the effect of the anatomical noise,' in Proc. SPIE 2436, 156-164 (1995).

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).

R. F. Wagner and K. E. Weaver, 'An assortment of image quality indices for radiographic film-screen combinations--can they be resolved?' in Proc. SPIE 35, 83-84 (1972).

Watson, A. B.

M. P. Eckstein, A. J. Ahumada, and 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).

M. P. Eckstein, A. J. Ahumada, and A. B. Watson, 'Image discrimination models predict visual detection in natural medical image backgrounds,' in Proc. SPIE 3016, 44-56 (1997).

Weaver, K. E.

R. F. Wagner and K. E. Weaver, 'An assortment of image quality indices for radiographic film-screen combinations--can they be resolved?' in Proc. SPIE 35, 83-84 (1972).

Webster, M. A.

Whiting, J. S.

M. P. Eckstein, J. L. Bartroff, C. K. Abbey, J. S. Whiting, and F. O. Bochud, 'Automated computer evaluation and optimization of image compression of x-ray coronary angiograms for signal known exactly detection tasks,' Opt. Express 11, 460-475 (2003).

M. P. Eckstein, C. K. Abbey, F. O. Bochud, and J. S. Whiting, 'The effect of image compression in model and human observers,' in Proc. SPIE 3663, 243-252 (1999).

M. P. Eckstein and J. S. Whiting, 'Lesion detection in structured noise,' Acad. Radiol. 2, 249-253 (1995).

Woods, R. E.

R. C. Gonzales and R. E. Woods, Digital Image Processing (Prentice Hall, 2001).

Yao, J.

H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, 'Model observers for assessment of image quality,' Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).

J. Yao and H. H. Barrett, 'Predicting human performance by a channelized Hotelling observer model,' in Proc. SPIE 1768, 161-168 (1992).

Zhang, Y.

Y. Zhang, B. T. Pham, and M. P. Eckstein, 'Evaluation of JPEG 2000 encoder options: human and model observer detection of variable signals in X-ray coronary angiograms,' IEEE Trans. Med. Imaging 23, 613-632 (2004).

Acad. Radiol. (1)

M. P. Eckstein and J. S. Whiting, 'Lesion detection in structured noise,' Acad. Radiol. 2, 249-253 (1995).

IEEE Trans. Med. Imaging (1)

Y. Zhang, B. T. Pham, and M. P. Eckstein, 'Evaluation of JPEG 2000 encoder options: human and model observer detection of variable signals in X-ray coronary angiograms,' IEEE Trans. Med. Imaging 23, 613-632 (2004).

J. Opt. Soc. Am. A (14)

A. Burgess and H. Ghandeharian, 'Visual signal detection. I. Ability to use phase information,' J. Opt. Soc. Am. A 1, 900-905 (1984).

D. G. Pelli, 'Uncertainty explains many aspects of visual contrast detection and discrimination,' J. Opt. Soc. Am. A 2, 1508-1532 (1985).

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).

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).

A. E. Burgess, 'Visual signal detection with two-component noise: low-pass spectrum effects,' J. Opt. Soc. Am. A 16, 694-704 (1999).

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

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).

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

A. E. Burgess, 'Statistically defined backgrounds: performance of a modified nonprewhitening observer model,' J. Opt. Soc. Am. A 11, 1237-1242 (1994).

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

M. P. Eckstein, A. J. Ahumada, and 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).

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).

F. O. Bochud, C. K. Abbey, and 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).

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).

Med. Phys. (1)

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).

Opt. Express (1)

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

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Science (1)

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For the NPWE and PW models, the detectability shown in Fig. 6 is transformed from Pc. For the IO with the GNS test image, the detectability is obtained by Eq.(13) to avoid the difficulties of transforming a Pc of value 1 (owing to the high signal contrast) to dmafc (please see Appendix for the comparison between d′ and dmafc in this latter case).

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Figures (8)

Fig. 1
Fig. 1

Examples of oriented textures.[15] (a) Cracks in a tree trunk, (b) ridges in a finger print, (c) ribs in a chest x ray, (d) glandular tissue and ducts in a mammogram.

Fig. 2
Fig. 2

Local filtering of images. The local filtering approach is used to generate (a) GNS and (b) GS textures. Each panel shows a sample background with four possible signal locations indicated (center of white outlined boxes) and the four corresponding local filters. For the stationary background, all local filters are identical.

Fig. 3
Fig. 3

Orientation transition map generation for the GNS test image. Left image: layout of transition areas. Middle image: orientation map; gray values represent the orientation (from 1 to 180 deg ). Right image: GNS test image sample.

Fig. 4
Fig. 4

Image generation procedure. The procedure for generating (a) nonstationary and (b) stationary images. For each sample image, an initial sample of white noise is generated and then filtered with the local filtering algorithm. A second low-contrast white-noise field is then added to the result. The final step consists of adding the signal profile to one location at random and location cues. The four location cues were superimposed only on the images used in the psychophysical studies.

Fig. 5
Fig. 5

Top: signal as an image (left) and a surface (right). Bottom: model observer templates as images and surfaces for the GNS (column 2) and GS (column 3) test images. Row 1, NPWE templates; row 2, PW templates; row 3, IO templates.

Fig. 6
Fig. 6

Model observer performance (NPWE, PW, IO). Standard errors ranged from 0.001 to 0.020 and are too small to display. Left: comparison within model observers Right: comparison across model observers.

Fig. 7
Fig. 7

Human model observer performance. Top row: human observer performance by session groups for three individual observers (1000 trials per group for observers 1 and 2; 500 trials per group for observer 3). Bottom left: performance across all trials per condition for three different human observers (10,000 trials for observers 1 and 2; 5000 trials for observer 3). Standard errors ranged from 0.011 to 0.020 and are too small to display. Bottom right: comparison of human performance averaged across the three observers and the IO performance with internal noise.

Fig. 8
Fig. 8

Comparison between d and d mafc for the IO with GNS test images.

Tables (1)

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Table 1 Comparison of d mafc and d for the Ideal Observer under Nine Signal Contrasts

Equations (18)

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b ( i , j ) = i , j n ( i , j ) f i , j ( i , j ) .
f i , j ( i , j ) = f ( i i , j j ) .
f ( Δ i , Δ j ) = exp { 1 2 [ ( Δ i σ x ) 2 + ( Δ j σ y ) 2 ] } ,
f i , j ( Δ i , Δ j ) = exp ( 1 2 { [ Δ i cos ( θ i , j ) Δ j sin ( θ i , j ) σ x ] 2 + [ Δ i sin ( θ i , j ) + Δ j cos ( θ i , j ) σ y ] 2 } ) .
f stat ( Δ i , Δ j ) = FFT 1 { [ 1 4 FFT ( f loc 1 ) 2 + 1 4 FFT ( f loc 2 ) 2 + 1 4 FFT ( f loc 3 ) 2 + 1 4 FFT ( f loc 4 ) 2 ] 1 2 } ,
g ( i , j ) = b ( i , j ) + n ( i , j ) + s m ( i , j ) ,
λ i = n = 1 N 2 w i , n g i , n = w i g i , i = 1 , , 4 .
w ̃ NPWE = E ̃ 2 s ̃ ,
E = ρ η exp ( c ρ γ ) ,
w PW = K 1 s ,
K i , j = σ 2 ( f stat , i ) t ( f stat , j ) , 0 i , j < 64 × 64 ,
w IO ̱ loc = K loc 1 s , loc = 1 4 ,
K loc , i , j = σ 2 ( f loc , i ) t ( f loc , j ) , 0 i , j < 64 × 64 ,
d = λ s λ n σ λ ,
Pc ( d mafc , M ) = + ϕ ( x d mafc ) [ Φ ( x ) ] M 1 d x ,
PI = ( ( f d GNS d GS ) 1 ) × 100 .
d 1 = λ s , 1 λ n , 2 σ λ , d 2 = λ s , 1 λ n , 3 σ λ ,
d 3 = λ s , 1 λ n , 4 σ λ .

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