Abstract

We use the classification image technique to investigate the effect of white noise and various correlated Gaussian noise textures (low-pass, high-pass, and band-pass) on observer performance in detection and discrimination tasks. For these tasks, performance is generally enhanced by an observer’s ability to “prewhiten” correlated noise as part of the formation of a decision variable. We find that observer efficiency in these tasks is well represented by the measured classification images and that human observers show strong evidence of adaptation to different correlated noise textures. This adaptation is captured in the frequency weighting of the classification images.

© 2007 Optical Society of America

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References

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  1. A. P. Pentland, "Fractal-based description of natural scenes," IEEE Trans. Pattern Anal. Mach. Intell. 6, 661-673 (1984).
    [CrossRef]
  2. G. J. Burton and I. R. Moorhead, "Color and spatial structure in natural scenes," Appl. Opt. 26, 157-70 (1987).
    [CrossRef] [PubMed]
  3. D. J. Field, "Relations between the statistics of natural images and the response properties of cortical cells," J. Opt. Soc. Am. A 4, 2379-2394 (1987).
    [CrossRef] [PubMed]
  4. D. J. Tolhurst, Y. Tadmor, and T. Chao, "Amplitude spectra of natural images," Ophthalmic Physiol. Opt. 12, 229-232 (1992).
    [CrossRef] [PubMed]
  5. D. L. Ruderman and W. Bialek, "Statistics of natural images, scaling in the woods," Phys. Rev. Lett. 73, 814-817 (1994).
    [CrossRef] [PubMed]
  6. A. van der Schaaf and J. H. van Hateren, "Modelling the power spectra of natural images: statistics and information," Vision Res. 36, 2759-2770 (1996).
    [CrossRef] [PubMed]
  7. D. L. Ruderman, "Origins of scaling in natural images," Proc. SPIE 2657, 120-131 (1996).
    [CrossRef]
  8. G. Revesz, H. L. Kundel and M. A. Graber, "The influence of structured noise on the detection of radiologic abnormalities," Am. J. Roentgenol. 9, 479-486 (1974).
  9. H. L. Kundel and G. Revesz, "Lesion conspicuity, structured noise, and film reader error," AJR, Am. J. Roentgenol. 126, 1233-1238 (1976).
  10. H. H. Barrett, "Objective assessment of image quality: effects of quantum noise and object variability," J. Opt. Soc. Am. A 7, 1266-1278 (1990).
    [CrossRef] [PubMed]
  11. H. H. Barrett, S. K. Gordon, and R. S. Hershel, "Statistical limitations in transaxial tomography," Comput. Biol. Med. 6, 307-323 (1976).
    [CrossRef] [PubMed]
  12. S. J. Riederer, N. J. Pelc, and D. A. Chessler, "The noise power spectrum in computed x-ray tomography," Phys. Med. Biol. 23, 446-454 (1978).
    [CrossRef] [PubMed]
  13. H. H. Barrett and W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection, and Processing (Academic, 1981).
  14. 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]
  15. K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton, and G. W. Seeley, "The effect of noise correlation on detectability of disk signals in medical imaging," J. Opt. Soc. Am. A 2, 1752-1759 (1985).
    [CrossRef] [PubMed]
  16. R. D. Fiete, H. H. Barrett, W. E. Smit, and K. J. Myers, "Hotelling trace criterion and its correlation with human-observer performance," J. Opt. Soc. Am. A 4, 945-953 (1987).
    [CrossRef] [PubMed]
  17. 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]
  18. A. E. Burgess, "Statistically defined backgrounds, performance of a modified nonprewhitening observer model," J. Opt. Soc. Am. A 11, 1237-1242 (1994).
    [CrossRef]
  19. 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]
  20. A. E. Burgess, "Visual signal detection with two-component noise: low-pass spectrum effects," J. Opt. Soc. Am. A 16, 694-704 (1999).
    [CrossRef]
  21. 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]
  22. K. J. Myers and H. H. Barrett, "The addition of a channel mechanism to the ideal-observer model," J. Opt. Soc. Am. A 4, 2447-2457 (1987).
    [CrossRef]
  23. 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).
    [CrossRef]
  24. J. A. Solomon, "Channel selection with non-white-noise masks," J. Opt. Soc. Am. A 17, 986-993 (2000).
    [CrossRef]
  25. 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).
    [CrossRef]
  26. 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]
  27. A. J. Ahumada and J. Lovell, "Stimulus features in signal detection," J. Acoust. Soc. Am. 49, 1751-1756 (1971).
    [CrossRef]
  28. A. J. Ahumada, R. Marken, and A. Sandusky, "Time and frequency analyses of auditory signal detection." J. Acoust. Soc. Am. 57, 385-390 (1975).
    [CrossRef]
  29. A. J. Ahumada, "Perceptual classification images from Vernier acuity masked by noise," Perception 25, ECVP Abstract Suppl. (1996).
  30. B. L. Beard and A. J. Ahumada, "A technique to extract relevant image features for visual tasks," Proc. SPIE 3299, 79-85 (1998).
    [CrossRef]
  31. D. Q. Nykamp and D. L. Ringach, "Full identification of a linear-nonlinear system via cross-correlation analysis," J. Vision 2, 1-11 (2002).
    [CrossRef]
  32. C. K. Abbey and M. P. Eckstein, "Classification image analysis, Estimation and statistical inference for two-alternative forced-choice experiments," J. Vision 2, 66-78 (2002).
    [CrossRef]
  33. R. F. Murray, P. J. Bennett, and A. B. Sekuler, "Optimal methods for calculating classification images, weighted sums," J. Vision 2, 79-104 (2002).
    [CrossRef]
  34. C. K. Abbey and M. P. Eckstein, "Optimal shifted estimates of human-observer templates in two-alternative forced-choice experiments," IEEE Trans. Med. Imaging 21, 429-440 (2002).
    [CrossRef] [PubMed]
  35. A. E. Burgess and H. Ghandeharian, "Visual signal detection II. Signal location identification," J. Opt. Soc. Am. A 1, 906-910 (1984).
    [CrossRef] [PubMed]
  36. C. K. Abbey and M. P. Eckstein, "Estimates of human-observer templates for simple detection tasks in correlated noise," Proc. SPIE 3981, 70-77 (2000).
    [CrossRef]
  37. R. F. Murray, P. J. Bennett, and A. B. Sekuler, "Classification images predict absolute efficiency," J. Vision 5, 139-149 (2005).
    [CrossRef]
  38. D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, 1966).
  39. C. K. Abbey and M. P. Eckstein, "Classification images for detection, contrast discrimination, and identification tasks with a common ideal observer," J. Vision 6, 335-355 (2006).
    [CrossRef]
  40. W. P. Tanner and T. G. Birdsall, "Definitions of d′ and η as psychophysical measures," J. Acoust. Soc. Am. 30, 922-928 (1958).
    [CrossRef]
  41. 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]
  42. D. G. Pelli, "Effects of visual noise," Doctoral dissertation (Cambridge University, Cambridge (1981).
  43. F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. (London) 197, 551-566 (1968).
  44. C. Blakemore and F. W. Campbell, "On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images," J. Physiol. (London) 203, 237-260 (1969).
  45. C. F. Stromeyer, III and S. A. Klein, "Spatial frequency channels in human vision as asymmetric (edge) mechanisms," Vision Res. 14, 1409-1420 (1974).
    [CrossRef] [PubMed]
  46. S. A. Klein, "Measuring, estimating, and understanding the psychometric function: a commentary," Percept. Psychophys. 63, 1421-1455 (2001).
    [CrossRef]
  47. A. J. Ahumada, "Putting the visual system noise back in the picture," J. Opt. Soc. Am. A 4, 2372-2378 (1987).
    [CrossRef] [PubMed]
  48. P. Neri and D. J. Heeger, "Spatiotemporal mechanisms for detecting and identifying image features in human vision," Nat. Neurosci. 5, 812-816 (2002).
    [PubMed]
  49. B. S. Tjan and A. S. Nandy, "Classification images with uncertainty," J. Vision 6, 387-413 (2006).
    [CrossRef]
  50. C. K. Abbey, M. P. Eckstein, and F. O. Bochud, "Estimation of human-observer templates for 2 alternative forced choice tasks," Proc. SPIE 3663, 284-295 (1999).
    [CrossRef]
  51. C. K. Abbey and M. P. Eckstein, "Classification images of bandpass mechanisms across noise spectral density," J. Vision 6, 116 (abstract) (2006).
    [CrossRef]
  52. A. H. Baydush and C. E. Floyd, "Improved image quality in digital mammography with image processing," Med. Phys. 27, 1503-1508 (2000).
    [CrossRef] [PubMed]
  53. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 1988).
  54. Note that Murray describe cross correlation with the template of the ideal observer. This is correct only for the white-noise case they considered.

2006 (3)

C. K. Abbey and M. P. Eckstein, "Classification images for detection, contrast discrimination, and identification tasks with a common ideal observer," J. Vision 6, 335-355 (2006).
[CrossRef]

B. S. Tjan and A. S. Nandy, "Classification images with uncertainty," J. Vision 6, 387-413 (2006).
[CrossRef]

C. K. Abbey and M. P. Eckstein, "Classification images of bandpass mechanisms across noise spectral density," J. Vision 6, 116 (abstract) (2006).
[CrossRef]

2005 (1)

R. F. Murray, P. J. Bennett, and A. B. Sekuler, "Classification images predict absolute efficiency," J. Vision 5, 139-149 (2005).
[CrossRef]

2002 (5)

P. Neri and D. J. Heeger, "Spatiotemporal mechanisms for detecting and identifying image features in human vision," Nat. Neurosci. 5, 812-816 (2002).
[PubMed]

D. Q. Nykamp and D. L. Ringach, "Full identification of a linear-nonlinear system via cross-correlation analysis," J. Vision 2, 1-11 (2002).
[CrossRef]

C. K. Abbey and M. P. Eckstein, "Classification image analysis, Estimation and statistical inference for two-alternative forced-choice experiments," J. Vision 2, 66-78 (2002).
[CrossRef]

R. F. Murray, P. J. Bennett, and A. B. Sekuler, "Optimal methods for calculating classification images, weighted sums," J. Vision 2, 79-104 (2002).
[CrossRef]

C. K. Abbey and M. P. Eckstein, "Optimal shifted estimates of human-observer templates in two-alternative forced-choice experiments," IEEE Trans. Med. Imaging 21, 429-440 (2002).
[CrossRef] [PubMed]

2001 (3)

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]

S. A. Klein, "Measuring, estimating, and understanding the psychometric function: a commentary," Percept. Psychophys. 63, 1421-1455 (2001).
[CrossRef]

2000 (4)

A. H. Baydush and C. E. Floyd, "Improved image quality in digital mammography with image processing," Med. Phys. 27, 1503-1508 (2000).
[CrossRef] [PubMed]

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).
[CrossRef]

J. A. Solomon, "Channel selection with non-white-noise masks," J. Opt. Soc. Am. A 17, 986-993 (2000).
[CrossRef]

C. K. Abbey and M. P. Eckstein, "Estimates of human-observer templates for simple detection tasks in correlated noise," Proc. SPIE 3981, 70-77 (2000).
[CrossRef]

1999 (2)

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

C. K. Abbey, M. P. Eckstein, and F. O. Bochud, "Estimation of human-observer templates for 2 alternative forced choice tasks," Proc. SPIE 3663, 284-295 (1999).
[CrossRef]

1998 (1)

B. L. Beard and A. J. Ahumada, "A technique to extract relevant image features for visual tasks," Proc. SPIE 3299, 79-85 (1998).
[CrossRef]

1997 (2)

1996 (2)

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

D. L. Ruderman, "Origins of scaling in natural images," Proc. SPIE 2657, 120-131 (1996).
[CrossRef]

1994 (2)

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

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

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).
[CrossRef]

1992 (2)

1990 (1)

1987 (5)

1985 (1)

1984 (2)

A. P. Pentland, "Fractal-based description of natural scenes," IEEE Trans. Pattern Anal. Mach. Intell. 6, 661-673 (1984).
[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]

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]

1978 (1)

S. J. Riederer, N. J. Pelc, and D. A. Chessler, "The noise power spectrum in computed x-ray tomography," Phys. Med. Biol. 23, 446-454 (1978).
[CrossRef] [PubMed]

1976 (2)

H. H. Barrett, S. K. Gordon, and R. S. Hershel, "Statistical limitations in transaxial tomography," Comput. Biol. Med. 6, 307-323 (1976).
[CrossRef] [PubMed]

H. L. Kundel and G. Revesz, "Lesion conspicuity, structured noise, and film reader error," AJR, Am. J. Roentgenol. 126, 1233-1238 (1976).

1975 (1)

A. J. Ahumada, R. Marken, and A. Sandusky, "Time and frequency analyses of auditory signal detection." J. Acoust. Soc. Am. 57, 385-390 (1975).
[CrossRef]

1974 (2)

G. Revesz, H. L. Kundel and M. A. Graber, "The influence of structured noise on the detection of radiologic abnormalities," Am. J. Roentgenol. 9, 479-486 (1974).

C. F. Stromeyer, III and S. A. Klein, "Spatial frequency channels in human vision as asymmetric (edge) mechanisms," Vision Res. 14, 1409-1420 (1974).
[CrossRef] [PubMed]

1971 (1)

A. J. Ahumada and J. Lovell, "Stimulus features in signal detection," J. Acoust. Soc. Am. 49, 1751-1756 (1971).
[CrossRef]

1969 (1)

C. Blakemore and F. W. Campbell, "On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images," J. Physiol. (London) 203, 237-260 (1969).

1968 (1)

F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. (London) 197, 551-566 (1968).

1958 (1)

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

AJR, Am. J. Roentgenol. (1)

H. L. Kundel and G. Revesz, "Lesion conspicuity, structured noise, and film reader error," AJR, Am. J. Roentgenol. 126, 1233-1238 (1976).

Am. J. Roentgenol. (1)

G. Revesz, H. L. Kundel and M. A. Graber, "The influence of structured noise on the detection of radiologic abnormalities," Am. J. Roentgenol. 9, 479-486 (1974).

Appl. Opt. (1)

Comput. Biol. Med. (1)

H. H. Barrett, S. K. Gordon, and R. S. Hershel, "Statistical limitations in transaxial tomography," Comput. Biol. Med. 6, 307-323 (1976).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging (1)

C. K. Abbey and M. P. Eckstein, "Optimal shifted estimates of human-observer templates in two-alternative forced-choice experiments," IEEE Trans. Med. Imaging 21, 429-440 (2002).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

A. P. Pentland, "Fractal-based description of natural scenes," IEEE Trans. Pattern Anal. Mach. Intell. 6, 661-673 (1984).
[CrossRef]

J. Acoust. Soc. Am. (3)

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

A. J. Ahumada and J. Lovell, "Stimulus features in signal detection," J. Acoust. Soc. Am. 49, 1751-1756 (1971).
[CrossRef]

A. J. Ahumada, R. Marken, and A. Sandusky, "Time and frequency analyses of auditory signal detection." J. Acoust. Soc. Am. 57, 385-390 (1975).
[CrossRef]

J. Opt. Soc. Am. A (15)

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

H. H. Barrett, "Objective assessment of image quality: effects of quantum noise and object variability," J. Opt. Soc. Am. A 7, 1266-1278 (1990).
[CrossRef] [PubMed]

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

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

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

A. E. Burgess, "Statistically defined backgrounds, performance of a modified nonprewhitening observer model," J. Opt. Soc. Am. A 11, 1237-1242 (1994).
[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. E. Burgess, "Visual signal detection with two-component noise: low-pass spectrum effects," J. Opt. Soc. Am. A 16, 694-704 (1999).
[CrossRef]

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]

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

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).
[CrossRef]

J. A. Solomon, "Channel selection with non-white-noise masks," J. Opt. Soc. Am. A 17, 986-993 (2000).
[CrossRef]

A. J. Ahumada, "Putting the visual system noise back in the picture," J. Opt. Soc. Am. A 4, 2372-2378 (1987).
[CrossRef] [PubMed]

J. Physiol. (London) (2)

F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. (London) 197, 551-566 (1968).

C. Blakemore and F. W. Campbell, "On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images," J. Physiol. (London) 203, 237-260 (1969).

J. Vision (7)

C. K. Abbey and M. P. Eckstein, "Classification images for detection, contrast discrimination, and identification tasks with a common ideal observer," J. Vision 6, 335-355 (2006).
[CrossRef]

B. S. Tjan and A. S. Nandy, "Classification images with uncertainty," J. Vision 6, 387-413 (2006).
[CrossRef]

C. K. Abbey and M. P. Eckstein, "Classification images of bandpass mechanisms across noise spectral density," J. Vision 6, 116 (abstract) (2006).
[CrossRef]

D. Q. Nykamp and D. L. Ringach, "Full identification of a linear-nonlinear system via cross-correlation analysis," J. Vision 2, 1-11 (2002).
[CrossRef]

C. K. Abbey and M. P. Eckstein, "Classification image analysis, Estimation and statistical inference for two-alternative forced-choice experiments," J. Vision 2, 66-78 (2002).
[CrossRef]

R. F. Murray, P. J. Bennett, and A. B. Sekuler, "Optimal methods for calculating classification images, weighted sums," J. Vision 2, 79-104 (2002).
[CrossRef]

R. F. Murray, P. J. Bennett, and A. B. Sekuler, "Classification images predict absolute efficiency," J. Vision 5, 139-149 (2005).
[CrossRef]

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]

A. H. Baydush and C. E. Floyd, "Improved image quality in digital mammography with image processing," Med. Phys. 27, 1503-1508 (2000).
[CrossRef] [PubMed]

Nat. Neurosci. (1)

P. Neri and D. J. Heeger, "Spatiotemporal mechanisms for detecting and identifying image features in human vision," Nat. Neurosci. 5, 812-816 (2002).
[PubMed]

Ophthalmic Physiol. Opt. (1)

D. J. Tolhurst, Y. Tadmor, and T. Chao, "Amplitude spectra of natural images," Ophthalmic Physiol. Opt. 12, 229-232 (1992).
[CrossRef] [PubMed]

Percept. Psychophys. (1)

S. A. Klein, "Measuring, estimating, and understanding the psychometric function: a commentary," Percept. Psychophys. 63, 1421-1455 (2001).
[CrossRef]

Phys. Med. Biol. (1)

S. J. Riederer, N. J. Pelc, and D. A. Chessler, "The noise power spectrum in computed x-ray tomography," Phys. Med. Biol. 23, 446-454 (1978).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

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

Proc. Natl. Acad. Sci. U.S.A. (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).
[CrossRef]

Proc. SPIE (4)

D. L. Ruderman, "Origins of scaling in natural images," Proc. SPIE 2657, 120-131 (1996).
[CrossRef]

B. L. Beard and A. J. Ahumada, "A technique to extract relevant image features for visual tasks," Proc. SPIE 3299, 79-85 (1998).
[CrossRef]

C. K. Abbey and M. P. Eckstein, "Estimates of human-observer templates for simple detection tasks in correlated noise," Proc. SPIE 3981, 70-77 (2000).
[CrossRef]

C. K. Abbey, M. P. Eckstein, and F. O. Bochud, "Estimation of human-observer templates for 2 alternative forced choice tasks," Proc. SPIE 3663, 284-295 (1999).
[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]

Vision Res. (2)

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

C. F. Stromeyer, III and S. A. Klein, "Spatial frequency channels in human vision as asymmetric (edge) mechanisms," Vision Res. 14, 1409-1420 (1974).
[CrossRef] [PubMed]

Other (6)

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 1988).

Note that Murray describe cross correlation with the template of the ideal observer. This is correct only for the white-noise case they considered.

D. G. Pelli, "Effects of visual noise," Doctoral dissertation (Cambridge University, Cambridge (1981).

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

A. J. Ahumada, "Perceptual classification images from Vernier acuity masked by noise," Perception 25, ECVP Abstract Suppl. (1996).

H. H. Barrett and W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection, and Processing (Academic, 1981).

Cited By

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Figures (9)

Fig. 1
Fig. 1

Signals and Noise. A, Mean (noiseless) target and alternative stimuli (shown at enhanced contrast for visibility). In the detection task the alternative is a uniform intensity field, while the discrimination task involves differentiating a more intense focal Gaussian from one that is less intense and more diffuse. B, Spatial and frequency profiles of the difference signal for the two tasks. C, Examples of the four noise textures used in this work. D, Spatial correlation structure and noise power spectra of the textures. All power spectra are scaled to have RMS contrast of 15%.

Fig. 2
Fig. 2

Ideal observer. A, Ideal-observer template for each experiment. B, and C, Frequency response, given in terms of the radial frequency, of each template. Differences between the templates within each task show the degree of accommodation to the different noise textures.

Fig. 3
Fig. 3

Spatial-frequency plots. Various steps taken to produce spatial frequency plots from classification images. The classification image, A, is windowed to a diameter of 0.6°, B, and then transformed to spatial frequencies via the FFT, C. Both real and imaginary components of the Fourier Transform are shown to illustrate the relative strength of signal in the real component. Radial averages, D, are formed by averaging over all values that fall into a bin defined by its distance from the origin in the spatial-frequency domain.

Fig. 4
Fig. 4

2AFC procedure. Each trial commences with a blank screen ( 1000 ms ) followed by the first-interval stimulus ( 500 ms ) , a low-contrast noise field to disrupt any persistence effects ( 1000 ms ) , the second-interval stimulus ( 500 ms ) , and finally another low-contrast noise field with response query (unlimited).

Fig. 5
Fig. 5

Observer efficiency. Subject performance is plotted in terms of efficiency with respect to the ideal observer. Observed values range from 1.6% to 60%.

Fig. 6
Fig. 6

Classification images. Results of the template estimation procedure for each observer in each experiment. The apparent texture in these images is estimation error and has the inverse correlation structure of the noise fields.

Fig. 7
Fig. 7

Three tests of a linear decision variable. A, Psychometric functions ( d versus peak signal contrast) from the detection task in high-pass noise. These data are considered evidence against a linear decision variable when the y-axis intercept of a linear fit is significantly different from zero. This experiment was chosen because subject CH has a nonlinear psychometric function by this criterion. B, Example of the classification image test for nonlinear decision variables. The null hypothesis is that the difference between an estimated template derived from target-only and alternative-only noise fields is zero. This example (subject CH for the detection task in white noise) has also been chosen because the null hypothesis is rejected. C, Template efficiency test for a linear decision variable for all experiments and subjects. The null hypothesis is that absolute efficiency (computed from the subject’s performance) and efficiency predicted from the template by Eq. (16) are equal.

Fig. 8
Fig. 8

Spatial frequency content of classification images in the detection task. Each row shows radial averages in the Fourier domain for each subject along with the frequency content of the difference signal and ideal observer template, the prewhitened matched filter. In the white-noise experiment, only the signal is plotted since the ideal observer is identical to the signal in this case. Error bars represent ± 1 standard error in the radial average.

Fig. 9
Fig. 9

Spatial frequency content of classification images for the discrimination task. Each row shows radial averages in the Fourier domain for each subject for the discrimination task.

Tables (3)

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Table 1 Parameters of Experiments a

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Table 2 Summary of Linearity Tests a

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Table 3 Effect of Noise Correlation a

Equations (25)

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Target : g + = p T + n + ,
Alternative : g = p A + n ,
Σ = F 2 D H Λ F 2 D ,
[ Λ W N ] k k = N W N ,
[ Λ L N ] k k = N L N ( 1 + α 1 + ( ρ k 2 ρ 0 ) 3 ) ,
[ Λ H N ] k k = N H N 1 + α ( 1 + ( ρ k 2 ρ 0 ) 3 ) .
[ Λ B N ] k k = N B N ( 1 + 20 exp ( 1 2 ( ρ k ρ c σ B N ) 2 ) ) .
λ = w t g + ε ,
w NPW = s .
w PW = Σ 1 s .
Δ q j = N T N T 1 ( o j P ̂ C ) Σ 1 Δ n j ,
Δ q j n , ε = e ( d 2 ) 2 π ( w t Σ w + σ ε 2 ) w .
d = w t s w t Σ w + σ ε 2 .
P C = Φ ( d 2 ) .
Δ q ̂ = 1 N T j = 1 N T Δ q j .
η = ( d Obs d IO ) 2 .
d IO = s t Σ 1 s .
η ̂ Pred = π e 1 2 ( d ̂ ) 2 ( ( s t Δ q ̂ d IO ) 2 2 P ̂ C ( 1 P ̂ C ) N T ) ,
Σ CI = 2 P C ( 1 P C ) N T Σ 1 ,
s t Δ q ̂ ( s t μ CI , s t Σ CI s ) .
s t Δ q ̂ ( e ( d Obs 2 ) 2 π ( w t Σ w + σ ε 2 ) s t w , 2 P C ( 1 P C ) N T s t Σ 1 s ) .
s t Δ q ̂ d IO ( e ( d Obs 2 ) 2 π d Obs d IO , 2 P C ( 1 P C ) N T ) .
( s t Δ q ̂ d IO ) 2 = e 2 ( d Obs 2 ) 2 π η + 2 P C ( 1 P C ) N T ,
η = π e ( d Obs ) 2 2 ( ( s t Δ q ̂ d IO ) 2 2 P C ( 1 P C ) N T ) ,
η ̂ = π e ( d ̂ Obs ) 2 2 ( ( s t Δ q ̂ d IO ) 2 2 P ̂ C ( 1 P ̂ C ) N T ) .

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