Abstract

In 1946 and 1948, three very important papers by Albert Rose [J. Soc. Motion Pict. Eng. 47, 273 (1946); J. Opt. Soc. Am. 38, 196 (1948); L. Marton, ed. (Academic, New York, 1948)] were published on the role that photon fluctuations have in setting fundamental performance limits for both human vision and electronic imaging systems. The papers were important because Rose demonstrated that the performance of imaging devices can be evaluated with an absolute scale (quantum efficiency). The analysis of human visual signal detection used in these papers (developed before the formal theory of signal detectability) was based on an approach that has come to be known as the Rose model. In spite of its simplicity, the Rose model is a very good approximation of a Bayesian ideal observer for the carefully and narrowly defined conditions that Rose considered. This simple model can be used effectively for back-of-the-envelope calculations, but it needs to be used with care because of its limited range of validity. One important conclusion arising from Rose’s investigations is that pixel signal-to-noise ratio is not a good figure of merit for imaging systems or components, even though it is still occasionally used as such by some researchers. In the present study, (1) aspects of signal detection theory are presented, (2) Rose’s model is described and discussed, (3) pixel signal-to-noise ratio is discussed, and (4) progress on modeling human noise-limited performance is summarized. This study is intended to be a tutorial with presentation of the main ideas and provision of references to the (dispersed) technical literature.

© 1999 Optical Society of America

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  1. A. Rose, “A unified approach to the performance of photographic film, television pickup tubes and the human eye,” J. Soc. Motion Pict. Eng. 47, 273–294 (1946).
  2. A. Rose, “The sensitivity performance of the human eye on an absolute scale,” J. Opt. Soc. Am. 38, 196–208 (1948).
    [CrossRef] [PubMed]
  3. A. Rose, “Television pickup tubes and the problem of vision,” in Advances in Electronics and Electron Physics, L. Marton, ed. (Academic, New York, 1948), Vol. 1, pp. 131–166.
  4. A. Rose, “Quantum and noise limitations of the visual process,” J. Opt. Soc. Am. 43, 715–716 (1953).
    [CrossRef] [PubMed]
  5. I. Cunningham, R. Shaw, “Signal-to-noise optimization of medical imaging systems,” J. Opt. Soc. Am. A 16, 621–632 (1999).
    [CrossRef]
  6. W. W. Peterson, T. G. Birdsall, W. C. Fox, “The theory of signal detectability,” IRE Trans. Inf. Theory PGIT-4, 171–212 (1954).
    [CrossRef]
  7. D. Van Metter, D. Middleton, “Modern statistical approaches to reception in communication theory,” IRE Trans. Inf. Theory PGIT-4, 119–141 (1954).
    [CrossRef]
  8. P. F. Sharp, C. E. Metz, R. F. Wagner, K. J. Myers, A. E. Burgess, , “Medical imaging: the assessment of image quality” (International Commission on Radiological Units and Measurements, Bethesda, Md., 1996).
  9. 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]
  10. H. H. Barrett, J. L. Denny, R. F. Wagner, K. J. Myers, “Objective assessment of image quality. II. Fisher information, Fourier cross talk, and figures of merit for task performance,” J. Opt. Soc. Am. A 12, 834–852 (1995).
    [CrossRef]
  11. H. H. Barrett, C. K. Abbey, 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]
  12. R. B. Barnes, M. Czerny, “Lasst sich ein Schroteffekt der Photonen mit dem Auge beobachten?” Z. Phys. 79, 436–449 (1932).
    [CrossRef]
  13. S. Hecht, “Quantum relations of vision,” J. Opt. Soc. Am. 32, 42–49 (1942).
    [CrossRef]
  14. H. de Vries, “The quantum character of light and its bearing upon threshold of vision, the differential sensitivity and visual acuity of the eye,” Physica 10, 553–564 (1943).
    [CrossRef]
  15. O. H. Schade, Image Quality: a Comparison of Photographic and Television Systems (RCA Laboratories, Princeton, N.J., 1975).
  16. R. F. Wagner, “Decision theory and the detail signal-to-noise ratio of Otto Schade,” Photograph. Sci. Eng. 22, 41–46 (1977).
  17. R. F. Wagner, “Toward a unified view of radiological imaging systems. Part II: Noisy images,” Med. Phys. 4, 279–296 (1977).
    [CrossRef] [PubMed]
  18. J. W. Coltman, “Fluoroscopic image brightening by electronic means,” Radiology 51, 359–366 (1948).
    [PubMed]
  19. R. E. Sturm, R. H. Morgan, “Screen intensification systems and their limitations,” Am. J. Roentgenol. 62, 617–634 (1949).
  20. D. O. North, “Analysis of the factors which determine signal–noise discrimination in pulsed carrier systems,” (1943),reprinted in Proc. IRE 51, 1016–1028 (1963).
    [CrossRef]
  21. N. Wiener, The Extrapolation, Interpolation, and Smoothing of Stationary Time Series (Wiley, New York, 1960).
  22. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991).
  23. K. R. Castleman, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1996).
  24. J. L. Harris, “Resolving power and decision theory,” J. Opt. Soc. Am. 54, 606–611 (1964).
    [CrossRef]
  25. J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, New York, 1986).
  26. R. A. Fisher, Statistical Methods for Research Workers (Oliver and Boyd, Edinburgh, 1925).
  27. J. Neyman, E. S. Pearson, “On the problem of the most efficient tests of statistical hypotheses,” Philos. Trans. R. Soc. London Ser. A 231, 289 (1933).
    [CrossRef]
  28. A. Wald, Sequential Decision Functions (Wiley, New York, 1950).
  29. J. A. Swets, Signal Detection and Recognition by Human Observers (Wiley, New York, 1964).
  30. D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).
  31. H. L. Van Trees, Detection, Estimation and Modulation Theory (Wiley, New York, 1968), Vols. 1–3.
  32. C. W. Helstrom, Elements of Signal Detection and Estimation (Prentice-Hall PTR, Englewood Cliffs, N.J., 1995).
  33. K. Fukunaga, Introduction to Statistical Pattern Recognition (Academic, New York, 1972).
  34. C. E. Metz, “ROC methodology in radiological imaging,” Invest. Radiol. 21, 720–732 (1986).
    [CrossRef] [PubMed]
  35. C. E. Metz, “Some practical issues of experimental design and data analysis in radiological ROC studies,” Invest. Radiol. 24, 234–245 (1989).
    [CrossRef] [PubMed]
  36. D. G. Brown, M. F. Insana, M. Tapiovaars, “Detection performance of the ideal decision function and its MacLaurin expansion,” J. Acoust. Soc. Am. 97, 379–398 (1995).
    [CrossRef] [PubMed]
  37. A. E. Burgess, “Comparison of receiver operating characteristic and forced choice observer performance measurement methods,” Med. Phys. 22, 643–655 (1995).
    [CrossRef] [PubMed]
  38. J. A. Swets, BBN Technologies, Cambridge, Mass. 02138 and Brigham and Women’s Hospital, Boston, Mass. 02115 (personal communication, 1998).
  39. W. P. Tanner, T. G. Birdsall, “Definitions of d′ and η as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
    [CrossRef]
  40. A. Rose, “The relative sensitivities of television pickup tubes, photographic film and the human eye,” Proc. IRE 30, 293–300 (1942).
    [CrossRef]
  41. O. Schade, “Electro-optical characteristics of television systems,” RCA Rev. 9, 5–37 (1948).
  42. N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, Cambridge, UK, 1991).
  43. A. E. Burgess, H. Ghandeharian, “Visual signal detection. II. Signal location identification,” J. Opt. Soc. Am. A 1, 906–910 (1984).
    [CrossRef] [PubMed]
  44. 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]
  45. A. E. Burgess, B. Colborne, “Visual signal detection. IV. Observer inconsistency,” J. Opt. Soc. Am. A 5, 617–627 (1988).
    [CrossRef] [PubMed]
  46. S. Daly, “The visual differences predictor: an algorithm for the assessment of image fidelity,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT, Cambridge, Mass., 1993).
  47. A. B. Watson, ed., Digital Images and Human Vision (MIT, Cambridge, Mass., 1993).
  48. H. L. Kundel, “Images, image quality, and observer performance,” Radiology 132, 265–271 (1979).
    [PubMed]
  49. R. F. Wagner, D. G. Brown, “Unified SNR analysis of medical imaging systems,” Phys. Med. Biol. 30, 489–518 (1985).
    [CrossRef]
  50. A. Rose, Vision—Human and Electronic (Plenum, New York, 1973).
  51. D. G. Pelli, “The quantum efficiency of vision,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, Cambridge, UK, 1990), pp. 3–24.
  52. T. E. Cohn, ed., Visual Detection, Vol. 3 of Collected Works in Optics (Optical Society of America, Washington, D.C., 1993).
  53. H. B. Barlow, “The efficiency of detecting changes in density in random dot patterns,” Vision Res. 18, 637–650 (1977).
    [CrossRef]
  54. A. E. Burgess, H. B. Barlow, “The efficiency of numerosity discrimination in random dot images,” Vision Res. 23, 811–819 (1983).
    [CrossRef]
  55. A. E. Burgess, R. J. Jennings, R. F. Wagner, H. B. Barlow, “Efficiency of human visual discrimination,” Science 214, 93–94 (1981).
    [CrossRef] [PubMed]
  56. A. E. Burgess, H. Ghandeharian, “Visual signal detection. I. Ability to use phase information,” J. Opt. Soc. Am. A 1, 900–905 (1984).
    [CrossRef] [PubMed]
  57. D. G. Pelli, “Uncertainty explains many aspects of visual contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1508–1530 (1985).
    [CrossRef] [PubMed]
  58. D. A. Kersten, “Spatial summation in visual noise,” Vision Res. 24, 1977–1990 (1983).
    [CrossRef]
  59. R. Nasanen, H. Kukkonen, J. Ravamo, “Spatial integration of band-pass filtered patterns in noise,” Vision Res. 33, 903–911 (1993).
    [CrossRef] [PubMed]
  60. J. Rovamo, J. Mustonen, R. Nasanen, “Modeling contrast sensitivity as a function of retinal illuminance and grating area,” Vision Res. 34, 1301–1314 (1994).
    [CrossRef] [PubMed]
  61. D. Kersten, “Statistical efficiency for the detection of visual noise,” Vision Res. 27, 1029–1040 (1986).
    [CrossRef]
  62. M. Pavel, G. Sperling, T. Reidl, A. Vanderbeek, “Limits of visual communication: the effect of signal-to-noise ratio on the intelligibility of American Sign Language,” J. Opt. Soc. Am. A 4, 2355–2365 (1987).
    [CrossRef] [PubMed]
  63. B. S. Tjan, G. E. Legge, W. L. Braje, D. Kersten, “Human efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3069 (1995).
    [CrossRef] [PubMed]
  64. T. Kumar, P. Zhou, D. A. Glaser, “Comparison of human performance with algorithms for estimating fractal dimension of fractional Brownian statistics,” J. Opt. Soc. Am. A 10, 1136–1146 (1993).
    [CrossRef] [PubMed]
  65. K. J. Myers, M. C. Borgstrom, H. H. Barrett, D. D. Patton, G. W. Seeley, “Effect of noise correlation on detectability of disk signals in medical imaging,” J. Opt. Soc. Am. A 2, 1752–1759 (1985).
    [CrossRef] [PubMed]
  66. K. J. Myers, H. H. Barrett, “Addition of a channel mechanism to the ideal-observer model,” J. Opt. Soc. Am. A 4, 2447–2457 (1987).
    [CrossRef] [PubMed]
  67. J. P. Rolland, H. H. Barrett, “Effect of random background inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A 9, 649–658 (1992).
    [CrossRef] [PubMed]
  68. A. E. Burgess, X. Li, C. K. Abbey, “Nodule detection in two component noise: toward patient structure,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 2–13 (1997).
    [CrossRef]
  69. A. E. Burgess, “Visual signal detection with two-component noise: low-pass spectrum effects,” J. Opt. Soc. Am. A 16, 694–704 (1999).
    [CrossRef]
  70. K. H. Hanson, “Variations in task and the ideal observer,” in Application of Optical Instrumentation in Medicine XI: Medical Image Production, Processing, Display and Archiving, R. H. Schneider, S. J. Dwyer, eds., Proc. SPIE419, 60–67 (1983).
    [CrossRef]
  71. H. H. Barrett, J. P. Rolland, J. Yao, K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. USA 90, 9758–9765 (1993).
    [CrossRef] [PubMed]
  72. T. W. Anderson, Introduction to Multivariate Statistical Analysis, 2nd ed. (Wiley, New York, 1984).
  73. J. P. Cobb, R. E. Moss, “The four variables of visual threshold,” J. Franklin Inst. 205, 831 (1928).
    [CrossRef]
  74. D. H. Kelly, “Retinal inhomogeneity. I. Spatiotemporal contrast sensitivity,” J. Opt. Soc. Am. A 1, 107–113 (1984).
    [CrossRef] [PubMed]
  75. J. S. Whiting, E. Carterette, D. Honig, N. Eigler, “Observer performance in dynamic displays: effect of frame rate on visual signal detection in noisy images,” in Medical Imaging 1991: Image Perception, H. L. Kundel, Proc. SPIE1453, 165–176 (1991).
    [CrossRef]
  76. M. P. Eckstein, J. S. Whiting, J. P. Thomas, “Detection and discrimination of moving signals in Gaussian uncorrelated noise,” in Medical Imaging 1996: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 9–25 (1996).
    [CrossRef]
  77. P. Xue, D. L. Wilson, “Pulsed fluoroscopy detectability from interspersed adaptive forced-choice measurements,” Med. Phys. 23, 1833–1843 (1996).
    [CrossRef] [PubMed]
  78. M. J. Tapiovaara, “Efficiency of low-contrast detail detectability in fluoroscopic imaging,” Med. Phys. 24, 655–664 (1997).
    [CrossRef] [PubMed]
  79. R. Aufrichtig, C. W. Thomas, P. Xue, D. L. Wilson, “Model for perception of pulsed fluoroscopy image sequences,” J. Opt. Soc. Am. A 13, 3167–3176 (1994).
    [CrossRef]
  80. D. L. Wilson, P. Xue, K. N. Jabri, R. Aufrichtig, “Perceived noise versus display noise in temporally filtered image sequences,” J. Electron. Imaging 5, 490–495 (1996).
    [CrossRef]
  81. M. P. Eckstein, J. S. Whiting, J. P. Thomas, “Role of knowledge in human visual temporal integration in spatiotemporal noise,” J. Opt. Soc. Am. A 13, 1960–1968 (1996).
    [CrossRef]

1999 (2)

1998 (1)

1997 (1)

M. J. Tapiovaara, “Efficiency of low-contrast detail detectability in fluoroscopic imaging,” Med. Phys. 24, 655–664 (1997).
[CrossRef] [PubMed]

1996 (3)

P. Xue, D. L. Wilson, “Pulsed fluoroscopy detectability from interspersed adaptive forced-choice measurements,” Med. Phys. 23, 1833–1843 (1996).
[CrossRef] [PubMed]

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

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

1995 (4)

H. H. Barrett, J. L. Denny, R. F. Wagner, K. J. Myers, “Objective assessment of image quality. II. Fisher information, Fourier cross talk, and figures of merit for task performance,” J. Opt. Soc. Am. A 12, 834–852 (1995).
[CrossRef]

B. S. Tjan, G. E. Legge, W. L. Braje, D. Kersten, “Human efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3069 (1995).
[CrossRef] [PubMed]

D. G. Brown, M. F. Insana, M. Tapiovaars, “Detection performance of the ideal decision function and its MacLaurin expansion,” J. Acoust. Soc. Am. 97, 379–398 (1995).
[CrossRef] [PubMed]

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

1994 (2)

R. Aufrichtig, C. W. Thomas, P. Xue, D. L. Wilson, “Model for perception of pulsed fluoroscopy image sequences,” J. Opt. Soc. Am. A 13, 3167–3176 (1994).
[CrossRef]

J. Rovamo, J. Mustonen, R. Nasanen, “Modeling contrast sensitivity as a function of retinal illuminance and grating area,” Vision Res. 34, 1301–1314 (1994).
[CrossRef] [PubMed]

1993 (3)

R. Nasanen, H. Kukkonen, J. Ravamo, “Spatial integration of band-pass filtered patterns in noise,” Vision Res. 33, 903–911 (1993).
[CrossRef] [PubMed]

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

T. Kumar, P. Zhou, D. A. Glaser, “Comparison of human performance with algorithms for estimating fractal dimension of fractional Brownian statistics,” J. Opt. Soc. Am. A 10, 1136–1146 (1993).
[CrossRef] [PubMed]

1992 (1)

1990 (1)

1989 (1)

C. E. Metz, “Some practical issues of experimental design and data analysis in radiological ROC studies,” Invest. Radiol. 24, 234–245 (1989).
[CrossRef] [PubMed]

1988 (1)

1987 (2)

1986 (2)

C. E. Metz, “ROC methodology in radiological imaging,” Invest. Radiol. 21, 720–732 (1986).
[CrossRef] [PubMed]

D. Kersten, “Statistical efficiency for the detection of visual noise,” Vision Res. 27, 1029–1040 (1986).
[CrossRef]

1985 (4)

1984 (3)

1983 (2)

A. E. Burgess, H. B. Barlow, “The efficiency of numerosity discrimination in random dot images,” Vision Res. 23, 811–819 (1983).
[CrossRef]

D. A. Kersten, “Spatial summation in visual noise,” Vision Res. 24, 1977–1990 (1983).
[CrossRef]

1981 (1)

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

1979 (1)

H. L. Kundel, “Images, image quality, and observer performance,” Radiology 132, 265–271 (1979).
[PubMed]

1977 (3)

R. F. Wagner, “Decision theory and the detail signal-to-noise ratio of Otto Schade,” Photograph. Sci. Eng. 22, 41–46 (1977).

R. F. Wagner, “Toward a unified view of radiological imaging systems. Part II: Noisy images,” Med. Phys. 4, 279–296 (1977).
[CrossRef] [PubMed]

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

1964 (1)

1958 (1)

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

1954 (2)

W. W. Peterson, T. G. Birdsall, W. C. Fox, “The theory of signal detectability,” IRE Trans. Inf. Theory PGIT-4, 171–212 (1954).
[CrossRef]

D. Van Metter, D. Middleton, “Modern statistical approaches to reception in communication theory,” IRE Trans. Inf. Theory PGIT-4, 119–141 (1954).
[CrossRef]

1953 (1)

1949 (1)

R. E. Sturm, R. H. Morgan, “Screen intensification systems and their limitations,” Am. J. Roentgenol. 62, 617–634 (1949).

1948 (3)

J. W. Coltman, “Fluoroscopic image brightening by electronic means,” Radiology 51, 359–366 (1948).
[PubMed]

O. Schade, “Electro-optical characteristics of television systems,” RCA Rev. 9, 5–37 (1948).

A. Rose, “The sensitivity performance of the human eye on an absolute scale,” J. Opt. Soc. Am. 38, 196–208 (1948).
[CrossRef] [PubMed]

1946 (1)

A. Rose, “A unified approach to the performance of photographic film, television pickup tubes and the human eye,” J. Soc. Motion Pict. Eng. 47, 273–294 (1946).

1943 (1)

H. de Vries, “The quantum character of light and its bearing upon threshold of vision, the differential sensitivity and visual acuity of the eye,” Physica 10, 553–564 (1943).
[CrossRef]

1942 (2)

A. Rose, “The relative sensitivities of television pickup tubes, photographic film and the human eye,” Proc. IRE 30, 293–300 (1942).
[CrossRef]

S. Hecht, “Quantum relations of vision,” J. Opt. Soc. Am. 32, 42–49 (1942).
[CrossRef]

1933 (1)

J. Neyman, E. S. Pearson, “On the problem of the most efficient tests of statistical hypotheses,” Philos. Trans. R. Soc. London Ser. A 231, 289 (1933).
[CrossRef]

1932 (1)

R. B. Barnes, M. Czerny, “Lasst sich ein Schroteffekt der Photonen mit dem Auge beobachten?” Z. Phys. 79, 436–449 (1932).
[CrossRef]

1928 (1)

J. P. Cobb, R. E. Moss, “The four variables of visual threshold,” J. Franklin Inst. 205, 831 (1928).
[CrossRef]

Abbey, C. K.

H. H. Barrett, C. K. Abbey, 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, C. K. Abbey, “Nodule detection in two component noise: toward patient structure,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 2–13 (1997).
[CrossRef]

Anderson, T. W.

T. W. Anderson, Introduction to Multivariate Statistical Analysis, 2nd ed. (Wiley, New York, 1984).

Aufrichtig, R.

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

R. Aufrichtig, C. W. Thomas, P. Xue, D. L. Wilson, “Model for perception of pulsed fluoroscopy image sequences,” J. Opt. Soc. Am. A 13, 3167–3176 (1994).
[CrossRef]

Barlow, H. B.

A. E. Burgess, H. B. Barlow, “The efficiency of numerosity discrimination in random dot images,” Vision Res. 23, 811–819 (1983).
[CrossRef]

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

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

Barnes, R. B.

R. B. Barnes, M. Czerny, “Lasst sich ein Schroteffekt der Photonen mit dem Auge beobachten?” Z. Phys. 79, 436–449 (1932).
[CrossRef]

Barrett, H. H.

Bendat, J. S.

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, New York, 1986).

Birdsall, T. G.

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

W. W. Peterson, T. G. Birdsall, W. C. Fox, “The theory of signal detectability,” IRE Trans. Inf. Theory PGIT-4, 171–212 (1954).
[CrossRef]

Borgstrom, M. C.

Braje, W. L.

B. S. Tjan, G. E. Legge, W. L. Braje, D. Kersten, “Human efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3069 (1995).
[CrossRef] [PubMed]

Brown, D. G.

D. G. Brown, M. F. Insana, M. Tapiovaars, “Detection performance of the ideal decision function and its MacLaurin expansion,” J. Acoust. Soc. Am. 97, 379–398 (1995).
[CrossRef] [PubMed]

R. F. Wagner, D. G. Brown, “Unified SNR analysis of medical imaging systems,” Phys. Med. Biol. 30, 489–518 (1985).
[CrossRef]

Burgess, A. E.

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

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

A. E. Burgess, B. Colborne, “Visual signal detection. IV. Observer inconsistency,” J. Opt. Soc. Am. A 5, 617–627 (1988).
[CrossRef] [PubMed]

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]

A. E. Burgess, H. Ghandeharian, “Visual signal detection. I. Ability to use phase information,” J. Opt. Soc. Am. A 1, 900–905 (1984).
[CrossRef] [PubMed]

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

A. E. Burgess, H. B. Barlow, “The efficiency of numerosity discrimination in random dot images,” Vision Res. 23, 811–819 (1983).
[CrossRef]

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

P. F. Sharp, C. E. Metz, R. F. Wagner, K. J. Myers, A. E. Burgess, , “Medical imaging: the assessment of image quality” (International Commission on Radiological Units and Measurements, Bethesda, Md., 1996).

A. E. Burgess, X. Li, C. K. Abbey, “Nodule detection in two component noise: toward patient structure,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 2–13 (1997).
[CrossRef]

Carterette, E.

J. S. Whiting, E. Carterette, D. Honig, N. Eigler, “Observer performance in dynamic displays: effect of frame rate on visual signal detection in noisy images,” in Medical Imaging 1991: Image Perception, H. L. Kundel, Proc. SPIE1453, 165–176 (1991).
[CrossRef]

Castleman, K. R.

K. R. Castleman, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1996).

Clarkson, E.

Cobb, J. P.

J. P. Cobb, R. E. Moss, “The four variables of visual threshold,” J. Franklin Inst. 205, 831 (1928).
[CrossRef]

Colborne, B.

Coltman, J. W.

J. W. Coltman, “Fluoroscopic image brightening by electronic means,” Radiology 51, 359–366 (1948).
[PubMed]

Creelman, C. D.

N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, Cambridge, UK, 1991).

Cunningham, I.

Czerny, M.

R. B. Barnes, M. Czerny, “Lasst sich ein Schroteffekt der Photonen mit dem Auge beobachten?” Z. Phys. 79, 436–449 (1932).
[CrossRef]

Daly, S.

S. Daly, “The visual differences predictor: an algorithm for the assessment of image fidelity,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT, Cambridge, Mass., 1993).

de Vries, H.

H. de Vries, “The quantum character of light and its bearing upon threshold of vision, the differential sensitivity and visual acuity of the eye,” Physica 10, 553–564 (1943).
[CrossRef]

Denny, J. L.

Eckstein, M. P.

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

M. P. Eckstein, J. S. Whiting, J. P. Thomas, “Detection and discrimination of moving signals in Gaussian uncorrelated noise,” in Medical Imaging 1996: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 9–25 (1996).
[CrossRef]

Eigler, N.

J. S. Whiting, E. Carterette, D. Honig, N. Eigler, “Observer performance in dynamic displays: effect of frame rate on visual signal detection in noisy images,” in Medical Imaging 1991: Image Perception, H. L. Kundel, Proc. SPIE1453, 165–176 (1991).
[CrossRef]

Fisher, R. A.

R. A. Fisher, Statistical Methods for Research Workers (Oliver and Boyd, Edinburgh, 1925).

Fox, W. C.

W. W. Peterson, T. G. Birdsall, W. C. Fox, “The theory of signal detectability,” IRE Trans. Inf. Theory PGIT-4, 171–212 (1954).
[CrossRef]

Fukunaga, K.

K. Fukunaga, Introduction to Statistical Pattern Recognition (Academic, New York, 1972).

Ghandeharian, H.

Glaser, D. A.

Green, D. M.

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

Hanson, K. H.

K. H. Hanson, “Variations in task and the ideal observer,” in Application of Optical Instrumentation in Medicine XI: Medical Image Production, Processing, Display and Archiving, R. H. Schneider, S. J. Dwyer, eds., Proc. SPIE419, 60–67 (1983).
[CrossRef]

Harris, J. L.

Hecht, S.

Helstrom, C. W.

C. W. Helstrom, Elements of Signal Detection and Estimation (Prentice-Hall PTR, Englewood Cliffs, N.J., 1995).

Honig, D.

J. S. Whiting, E. Carterette, D. Honig, N. Eigler, “Observer performance in dynamic displays: effect of frame rate on visual signal detection in noisy images,” in Medical Imaging 1991: Image Perception, H. L. Kundel, Proc. SPIE1453, 165–176 (1991).
[CrossRef]

Insana, M. F.

D. G. Brown, M. F. Insana, M. Tapiovaars, “Detection performance of the ideal decision function and its MacLaurin expansion,” J. Acoust. Soc. Am. 97, 379–398 (1995).
[CrossRef] [PubMed]

Jabri, K. N.

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

Jennings, R. J.

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

Kelly, D. H.

Kersten, D.

B. S. Tjan, G. E. Legge, W. L. Braje, D. Kersten, “Human efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3069 (1995).
[CrossRef] [PubMed]

D. Kersten, “Statistical efficiency for the detection of visual noise,” Vision Res. 27, 1029–1040 (1986).
[CrossRef]

Kersten, D. A.

D. A. Kersten, “Spatial summation in visual noise,” Vision Res. 24, 1977–1990 (1983).
[CrossRef]

Kukkonen, H.

R. Nasanen, H. Kukkonen, J. Ravamo, “Spatial integration of band-pass filtered patterns in noise,” Vision Res. 33, 903–911 (1993).
[CrossRef] [PubMed]

Kumar, T.

Kundel, H. L.

H. L. Kundel, “Images, image quality, and observer performance,” Radiology 132, 265–271 (1979).
[PubMed]

Legge, G. E.

B. S. Tjan, G. E. Legge, W. L. Braje, D. Kersten, “Human efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3069 (1995).
[CrossRef] [PubMed]

Li, X.

A. E. Burgess, X. Li, C. K. Abbey, “Nodule detection in two component noise: toward patient structure,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 2–13 (1997).
[CrossRef]

Macmillan, N. A.

N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, Cambridge, UK, 1991).

Metz, C. E.

C. E. Metz, “Some practical issues of experimental design and data analysis in radiological ROC studies,” Invest. Radiol. 24, 234–245 (1989).
[CrossRef] [PubMed]

C. E. Metz, “ROC methodology in radiological imaging,” Invest. Radiol. 21, 720–732 (1986).
[CrossRef] [PubMed]

P. F. Sharp, C. E. Metz, R. F. Wagner, K. J. Myers, A. E. Burgess, , “Medical imaging: the assessment of image quality” (International Commission on Radiological Units and Measurements, Bethesda, Md., 1996).

Middleton, D.

D. Van Metter, D. Middleton, “Modern statistical approaches to reception in communication theory,” IRE Trans. Inf. Theory PGIT-4, 119–141 (1954).
[CrossRef]

Morgan, R. H.

R. E. Sturm, R. H. Morgan, “Screen intensification systems and their limitations,” Am. J. Roentgenol. 62, 617–634 (1949).

Moss, R. E.

J. P. Cobb, R. E. Moss, “The four variables of visual threshold,” J. Franklin Inst. 205, 831 (1928).
[CrossRef]

Mustonen, J.

J. Rovamo, J. Mustonen, R. Nasanen, “Modeling contrast sensitivity as a function of retinal illuminance and grating area,” Vision Res. 34, 1301–1314 (1994).
[CrossRef] [PubMed]

Myers, K. J.

Nasanen, R.

J. Rovamo, J. Mustonen, R. Nasanen, “Modeling contrast sensitivity as a function of retinal illuminance and grating area,” Vision Res. 34, 1301–1314 (1994).
[CrossRef] [PubMed]

R. Nasanen, H. Kukkonen, J. Ravamo, “Spatial integration of band-pass filtered patterns in noise,” Vision Res. 33, 903–911 (1993).
[CrossRef] [PubMed]

Neyman, J.

J. Neyman, E. S. Pearson, “On the problem of the most efficient tests of statistical hypotheses,” Philos. Trans. R. Soc. London Ser. A 231, 289 (1933).
[CrossRef]

North, D. O.

D. O. North, “Analysis of the factors which determine signal–noise discrimination in pulsed carrier systems,” (1943),reprinted in Proc. IRE 51, 1016–1028 (1963).
[CrossRef]

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991).

Patton, D. D.

Pavel, M.

Pearson, E. S.

J. Neyman, E. S. Pearson, “On the problem of the most efficient tests of statistical hypotheses,” Philos. Trans. R. Soc. London Ser. A 231, 289 (1933).
[CrossRef]

Pelli, D. G.

D. G. Pelli, “Uncertainty explains many aspects of visual contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1508–1530 (1985).
[CrossRef] [PubMed]

D. G. Pelli, “The quantum efficiency of vision,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, Cambridge, UK, 1990), pp. 3–24.

Peterson, W. W.

W. W. Peterson, T. G. Birdsall, W. C. Fox, “The theory of signal detectability,” IRE Trans. Inf. Theory PGIT-4, 171–212 (1954).
[CrossRef]

Piersol, A. G.

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, New York, 1986).

Ravamo, J.

R. Nasanen, H. Kukkonen, J. Ravamo, “Spatial integration of band-pass filtered patterns in noise,” Vision Res. 33, 903–911 (1993).
[CrossRef] [PubMed]

Reidl, T.

Rolland, J. P.

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

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

Rose, A.

A. Rose, “Quantum and noise limitations of the visual process,” J. Opt. Soc. Am. 43, 715–716 (1953).
[CrossRef] [PubMed]

A. Rose, “The sensitivity performance of the human eye on an absolute scale,” J. Opt. Soc. Am. 38, 196–208 (1948).
[CrossRef] [PubMed]

A. Rose, “A unified approach to the performance of photographic film, television pickup tubes and the human eye,” J. Soc. Motion Pict. Eng. 47, 273–294 (1946).

A. Rose, “The relative sensitivities of television pickup tubes, photographic film and the human eye,” Proc. IRE 30, 293–300 (1942).
[CrossRef]

A. Rose, Vision—Human and Electronic (Plenum, New York, 1973).

A. Rose, “Television pickup tubes and the problem of vision,” in Advances in Electronics and Electron Physics, L. Marton, ed. (Academic, New York, 1948), Vol. 1, pp. 131–166.

Rovamo, J.

J. Rovamo, J. Mustonen, R. Nasanen, “Modeling contrast sensitivity as a function of retinal illuminance and grating area,” Vision Res. 34, 1301–1314 (1994).
[CrossRef] [PubMed]

Schade, O.

O. Schade, “Electro-optical characteristics of television systems,” RCA Rev. 9, 5–37 (1948).

Schade, O. H.

O. H. Schade, Image Quality: a Comparison of Photographic and Television Systems (RCA Laboratories, Princeton, N.J., 1975).

Seeley, G. W.

Sharp, P. F.

P. F. Sharp, C. E. Metz, R. F. Wagner, K. J. Myers, A. E. Burgess, , “Medical imaging: the assessment of image quality” (International Commission on Radiological Units and Measurements, Bethesda, Md., 1996).

Shaw, R.

Sperling, G.

Sturm, R. E.

R. E. Sturm, R. H. Morgan, “Screen intensification systems and their limitations,” Am. J. Roentgenol. 62, 617–634 (1949).

Swets, J. A.

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

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

J. A. Swets, BBN Technologies, Cambridge, Mass. 02138 and Brigham and Women’s Hospital, Boston, Mass. 02115 (personal communication, 1998).

Tanner, W. P.

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

Tapiovaara, M. J.

M. J. Tapiovaara, “Efficiency of low-contrast detail detectability in fluoroscopic imaging,” Med. Phys. 24, 655–664 (1997).
[CrossRef] [PubMed]

Tapiovaars, M.

D. G. Brown, M. F. Insana, M. Tapiovaars, “Detection performance of the ideal decision function and its MacLaurin expansion,” J. Acoust. Soc. Am. 97, 379–398 (1995).
[CrossRef] [PubMed]

Thomas, C. W.

R. Aufrichtig, C. W. Thomas, P. Xue, D. L. Wilson, “Model for perception of pulsed fluoroscopy image sequences,” J. Opt. Soc. Am. A 13, 3167–3176 (1994).
[CrossRef]

Thomas, J. P.

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

M. P. Eckstein, J. S. Whiting, J. P. Thomas, “Detection and discrimination of moving signals in Gaussian uncorrelated noise,” in Medical Imaging 1996: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 9–25 (1996).
[CrossRef]

Tjan, B. S.

B. S. Tjan, G. E. Legge, W. L. Braje, D. Kersten, “Human efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3069 (1995).
[CrossRef] [PubMed]

Van Metter, D.

D. Van Metter, D. Middleton, “Modern statistical approaches to reception in communication theory,” IRE Trans. Inf. Theory PGIT-4, 119–141 (1954).
[CrossRef]

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation and Modulation Theory (Wiley, New York, 1968), Vols. 1–3.

Vanderbeek, A.

Wagner, R. F.

H. H. Barrett, J. L. Denny, R. F. Wagner, K. J. Myers, “Objective assessment of image quality. II. Fisher information, Fourier cross talk, and figures of merit for task performance,” J. Opt. Soc. Am. A 12, 834–852 (1995).
[CrossRef]

R. F. Wagner, D. G. Brown, “Unified SNR analysis of medical imaging systems,” Phys. Med. Biol. 30, 489–518 (1985).
[CrossRef]

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

R. F. Wagner, “Decision theory and the detail signal-to-noise ratio of Otto Schade,” Photograph. Sci. Eng. 22, 41–46 (1977).

R. F. Wagner, “Toward a unified view of radiological imaging systems. Part II: Noisy images,” Med. Phys. 4, 279–296 (1977).
[CrossRef] [PubMed]

P. F. Sharp, C. E. Metz, R. F. Wagner, K. J. Myers, A. E. Burgess, , “Medical imaging: the assessment of image quality” (International Commission on Radiological Units and Measurements, Bethesda, Md., 1996).

Wald, A.

A. Wald, Sequential Decision Functions (Wiley, New York, 1950).

Whiting, J. S.

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

J. S. Whiting, E. Carterette, D. Honig, N. Eigler, “Observer performance in dynamic displays: effect of frame rate on visual signal detection in noisy images,” in Medical Imaging 1991: Image Perception, H. L. Kundel, Proc. SPIE1453, 165–176 (1991).
[CrossRef]

M. P. Eckstein, J. S. Whiting, J. P. Thomas, “Detection and discrimination of moving signals in Gaussian uncorrelated noise,” in Medical Imaging 1996: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 9–25 (1996).
[CrossRef]

Wiener, N.

N. Wiener, The Extrapolation, Interpolation, and Smoothing of Stationary Time Series (Wiley, New York, 1960).

Wilson, D. L.

P. Xue, D. L. Wilson, “Pulsed fluoroscopy detectability from interspersed adaptive forced-choice measurements,” Med. Phys. 23, 1833–1843 (1996).
[CrossRef] [PubMed]

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

R. Aufrichtig, C. W. Thomas, P. Xue, D. L. Wilson, “Model for perception of pulsed fluoroscopy image sequences,” J. Opt. Soc. Am. A 13, 3167–3176 (1994).
[CrossRef]

Xue, P.

P. Xue, D. L. Wilson, “Pulsed fluoroscopy detectability from interspersed adaptive forced-choice measurements,” Med. Phys. 23, 1833–1843 (1996).
[CrossRef] [PubMed]

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

R. Aufrichtig, C. W. Thomas, P. Xue, D. L. Wilson, “Model for perception of pulsed fluoroscopy image sequences,” J. Opt. Soc. Am. A 13, 3167–3176 (1994).
[CrossRef]

Yao, J.

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

Zhou, P.

Am. J. Roentgenol. (1)

R. E. Sturm, R. H. Morgan, “Screen intensification systems and their limitations,” Am. J. Roentgenol. 62, 617–634 (1949).

Invest. Radiol. (2)

C. E. Metz, “ROC methodology in radiological imaging,” Invest. Radiol. 21, 720–732 (1986).
[CrossRef] [PubMed]

C. E. Metz, “Some practical issues of experimental design and data analysis in radiological ROC studies,” Invest. Radiol. 24, 234–245 (1989).
[CrossRef] [PubMed]

IRE Trans. Inf. Theory (2)

W. W. Peterson, T. G. Birdsall, W. C. Fox, “The theory of signal detectability,” IRE Trans. Inf. Theory PGIT-4, 171–212 (1954).
[CrossRef]

D. Van Metter, D. Middleton, “Modern statistical approaches to reception in communication theory,” IRE Trans. Inf. Theory PGIT-4, 119–141 (1954).
[CrossRef]

J. Acoust. Soc. Am. (2)

D. G. Brown, M. F. Insana, M. Tapiovaars, “Detection performance of the ideal decision function and its MacLaurin expansion,” J. Acoust. Soc. Am. 97, 379–398 (1995).
[CrossRef] [PubMed]

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

J. Electron. Imaging (1)

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

J. Franklin Inst. (1)

J. P. Cobb, R. E. Moss, “The four variables of visual threshold,” J. Franklin Inst. 205, 831 (1928).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (18)

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

I. Cunningham, R. Shaw, “Signal-to-noise optimization of medical imaging systems,” J. Opt. Soc. Am. A 16, 621–632 (1999).
[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]

D. H. Kelly, “Retinal inhomogeneity. I. Spatiotemporal contrast sensitivity,” J. Opt. Soc. Am. A 1, 107–113 (1984).
[CrossRef] [PubMed]

A. E. Burgess, H. Ghandeharian, “Visual signal detection. I. Ability to use phase information,” J. Opt. Soc. Am. A 1, 900–905 (1984).
[CrossRef] [PubMed]

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

H. H. Barrett, C. K. Abbey, 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, “Visual signal detection. III. On Bayesian use of prior knowledge and cross correlation,” J. Opt. Soc. Am. A 2, 1498–1507 (1985).
[CrossRef] [PubMed]

D. G. Pelli, “Uncertainty explains many aspects of visual contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1508–1530 (1985).
[CrossRef] [PubMed]

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

M. Pavel, G. Sperling, T. Reidl, A. Vanderbeek, “Limits of visual communication: the effect of signal-to-noise ratio on the intelligibility of American Sign Language,” J. Opt. Soc. Am. A 4, 2355–2365 (1987).
[CrossRef] [PubMed]

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

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

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

T. Kumar, P. Zhou, D. A. Glaser, “Comparison of human performance with algorithms for estimating fractal dimension of fractional Brownian statistics,” J. Opt. Soc. Am. A 10, 1136–1146 (1993).
[CrossRef] [PubMed]

H. H. Barrett, J. L. Denny, R. F. Wagner, K. J. Myers, “Objective assessment of image quality. II. Fisher information, Fourier cross talk, and figures of merit for task performance,” J. Opt. Soc. Am. A 12, 834–852 (1995).
[CrossRef]

R. Aufrichtig, C. W. Thomas, P. Xue, D. L. Wilson, “Model for perception of pulsed fluoroscopy image sequences,” J. Opt. Soc. Am. A 13, 3167–3176 (1994).
[CrossRef]

J. Soc. Motion Pict. Eng. (1)

A. Rose, “A unified approach to the performance of photographic film, television pickup tubes and the human eye,” J. Soc. Motion Pict. Eng. 47, 273–294 (1946).

Med. Phys. (4)

R. F. Wagner, “Toward a unified view of radiological imaging systems. Part II: Noisy images,” Med. Phys. 4, 279–296 (1977).
[CrossRef] [PubMed]

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

P. Xue, D. L. Wilson, “Pulsed fluoroscopy detectability from interspersed adaptive forced-choice measurements,” Med. Phys. 23, 1833–1843 (1996).
[CrossRef] [PubMed]

M. J. Tapiovaara, “Efficiency of low-contrast detail detectability in fluoroscopic imaging,” Med. Phys. 24, 655–664 (1997).
[CrossRef] [PubMed]

Philos. Trans. R. Soc. London Ser. A (1)

J. Neyman, E. S. Pearson, “On the problem of the most efficient tests of statistical hypotheses,” Philos. Trans. R. Soc. London Ser. A 231, 289 (1933).
[CrossRef]

Photograph. Sci. Eng. (1)

R. F. Wagner, “Decision theory and the detail signal-to-noise ratio of Otto Schade,” Photograph. Sci. Eng. 22, 41–46 (1977).

Phys. Med. Biol. (1)

R. F. Wagner, D. G. Brown, “Unified SNR analysis of medical imaging systems,” Phys. Med. Biol. 30, 489–518 (1985).
[CrossRef]

Physica (1)

H. de Vries, “The quantum character of light and its bearing upon threshold of vision, the differential sensitivity and visual acuity of the eye,” Physica 10, 553–564 (1943).
[CrossRef]

Proc. IRE (1)

A. Rose, “The relative sensitivities of television pickup tubes, photographic film and the human eye,” Proc. IRE 30, 293–300 (1942).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

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

Radiology (2)

H. L. Kundel, “Images, image quality, and observer performance,” Radiology 132, 265–271 (1979).
[PubMed]

J. W. Coltman, “Fluoroscopic image brightening by electronic means,” Radiology 51, 359–366 (1948).
[PubMed]

RCA Rev. (1)

O. Schade, “Electro-optical characteristics of television systems,” RCA Rev. 9, 5–37 (1948).

Science (1)

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

Vision Res. (7)

D. A. Kersten, “Spatial summation in visual noise,” Vision Res. 24, 1977–1990 (1983).
[CrossRef]

R. Nasanen, H. Kukkonen, J. Ravamo, “Spatial integration of band-pass filtered patterns in noise,” Vision Res. 33, 903–911 (1993).
[CrossRef] [PubMed]

J. Rovamo, J. Mustonen, R. Nasanen, “Modeling contrast sensitivity as a function of retinal illuminance and grating area,” Vision Res. 34, 1301–1314 (1994).
[CrossRef] [PubMed]

D. Kersten, “Statistical efficiency for the detection of visual noise,” Vision Res. 27, 1029–1040 (1986).
[CrossRef]

B. S. Tjan, G. E. Legge, W. L. Braje, D. Kersten, “Human efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3069 (1995).
[CrossRef] [PubMed]

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

A. E. Burgess, H. B. Barlow, “The efficiency of numerosity discrimination in random dot images,” Vision Res. 23, 811–819 (1983).
[CrossRef]

Z. Phys. (1)

R. B. Barnes, M. Czerny, “Lasst sich ein Schroteffekt der Photonen mit dem Auge beobachten?” Z. Phys. 79, 436–449 (1932).
[CrossRef]

Other (27)

T. W. Anderson, Introduction to Multivariate Statistical Analysis, 2nd ed. (Wiley, New York, 1984).

K. H. Hanson, “Variations in task and the ideal observer,” in Application of Optical Instrumentation in Medicine XI: Medical Image Production, Processing, Display and Archiving, R. H. Schneider, S. J. Dwyer, eds., Proc. SPIE419, 60–67 (1983).
[CrossRef]

J. S. Whiting, E. Carterette, D. Honig, N. Eigler, “Observer performance in dynamic displays: effect of frame rate on visual signal detection in noisy images,” in Medical Imaging 1991: Image Perception, H. L. Kundel, Proc. SPIE1453, 165–176 (1991).
[CrossRef]

M. P. Eckstein, J. S. Whiting, J. P. Thomas, “Detection and discrimination of moving signals in Gaussian uncorrelated noise,” in Medical Imaging 1996: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 9–25 (1996).
[CrossRef]

A. Rose, Vision—Human and Electronic (Plenum, New York, 1973).

D. G. Pelli, “The quantum efficiency of vision,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, Cambridge, UK, 1990), pp. 3–24.

T. E. Cohn, ed., Visual Detection, Vol. 3 of Collected Works in Optics (Optical Society of America, Washington, D.C., 1993).

N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, Cambridge, UK, 1991).

S. Daly, “The visual differences predictor: an algorithm for the assessment of image fidelity,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT, Cambridge, Mass., 1993).

A. B. Watson, ed., Digital Images and Human Vision (MIT, Cambridge, Mass., 1993).

J. A. Swets, BBN Technologies, Cambridge, Mass. 02138 and Brigham and Women’s Hospital, Boston, Mass. 02115 (personal communication, 1998).

O. H. Schade, Image Quality: a Comparison of Photographic and Television Systems (RCA Laboratories, Princeton, N.J., 1975).

A. Rose, “Television pickup tubes and the problem of vision,” in Advances in Electronics and Electron Physics, L. Marton, ed. (Academic, New York, 1948), Vol. 1, pp. 131–166.

P. F. Sharp, C. E. Metz, R. F. Wagner, K. J. Myers, A. E. Burgess, , “Medical imaging: the assessment of image quality” (International Commission on Radiological Units and Measurements, Bethesda, Md., 1996).

A. Wald, Sequential Decision Functions (Wiley, New York, 1950).

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

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

H. L. Van Trees, Detection, Estimation and Modulation Theory (Wiley, New York, 1968), Vols. 1–3.

C. W. Helstrom, Elements of Signal Detection and Estimation (Prentice-Hall PTR, Englewood Cliffs, N.J., 1995).

K. Fukunaga, Introduction to Statistical Pattern Recognition (Academic, New York, 1972).

D. O. North, “Analysis of the factors which determine signal–noise discrimination in pulsed carrier systems,” (1943),reprinted in Proc. IRE 51, 1016–1028 (1963).
[CrossRef]

N. Wiener, The Extrapolation, Interpolation, and Smoothing of Stationary Time Series (Wiley, New York, 1960).

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991).

K. R. Castleman, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1996).

J. S. Bendat, A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley, New York, 1986).

R. A. Fisher, Statistical Methods for Research Workers (Oliver and Boyd, Edinburgh, 1925).

A. E. Burgess, X. Li, C. K. Abbey, “Nodule detection in two component noise: toward patient structure,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 2–13 (1997).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Picture used by Rose,4 of woman with flowers, to demonstrate the maximum amount of information that can be represented with varying numbers of photons. A, 3×103; B, 1.2×104; C, 9.3×105; D, 7.6×105; E, 3.6×105; F, 2.8×107. Each photon is represented as a discrete visible speck. The inherent statistical fluctuations in photon density limit one’s ability to detect or identify features in the original scene.

Fig. 2
Fig. 2

Results for MAFC disk signal location identification experiments.43 The figure shows the SNR required for 90% correct detection performance by the ideal observer and by two human observers as a function of the base 2 logarithm of the number of statistically independent signal locations, M. Human efficiency is constant at 50% (SNR=2 higher than ideal). This illustrates one of the benefits of using efficiency as a summary measure of task performance.

Fig. 3
Fig. 3

Results for a free-response experiment for two human observers as a function of measured XCR’s between signals and image data. A variable number of disk signals with variable SNR were presented at random positions in white-noise images. The observers located as many signals as possible under two decision strategies: lax (low miss rate) and strict (low false-alarm rate), which produced false-alarm rates of 3×10-3 and 2×10-4, respectively. The conditional probability of detection was determined at each quantized XCR value. If one uses a 50% correct detection criterion to define a threshold SNR, then the thresholds are roughly 4 and 5 for the lax and the strict strategies, respectively. With a definition of 90% correct, the thresholds increase to 5 and 6, respectively. These results demonstrate good agreement with Rose’s 1948 estimates from subjective signal detection experiments.

Fig. 4
Fig. 4

Demonstration that pixel SNR (SNRp) is not a good primary measure of image quality. SNRp is defined as the ratio of peak signal amplitude and noise standard deviation, σp, per pixel. This figure also shows that signal appearance is highly variable at low SNR, as is expected, given the statistical nature of the images. A, Signal array of disks (diameters of 4, 5, 6, 16 pixels) with amplitude of 24 gray levels. B, Same signal array with added zero-mean white noise (σp of 24 gray levels), so SNRp=1.0 for all the signals. The Rose model and the ideal observer SNR’s are 3.5, 4.6, 5.7, and 14.4. C, After smoothing of portion B. The low-pass-filtered noise has σp of 8.2 gray levels, so SNRp=2.9 for all the signals. D, After edge enhancement of portion B, resulting in a σp value of 39.6 gray levels and a SNRp value of 0.6. The filtering would have no effect on ideal observer SNR. The Rose model is not a valid method for calculating SNR with filtered images.

Equations (35)

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input:x(t)=s(t)+n(t),
output:y(t)=h(t) * x(t),s0(t)=h(t) * s(t),
n0(t)=h(t) * n(t),
ρ(tm)=s02(tm)n02(tm).
S0(f)=H(f)S(f),
P0(f)=|N0(f)|2=|H(f)|2|N(f)|2=|H(f)|2P(f),
ρ(tm)=s02(tm)n02(tm)=-H(f)S(f)exp(i2πftm)df2-|H(f)|2P(f)exp(i2πftm)df,
ρ(0)=-H(f)S(f)df2-|H(f)|2P(f)df.
-H(f)P(f) S(f)P(f)df2-|H(f)|2|P(f)df- |S(f)|2P(f)df.
ρ(0)|-|H(f)|2P(f)df- |S(f)|2P(f)df-|H(f)|2P(f)df,
ρ(0)- |S(f)|2P(f)df.
Hmax(f)=αS*(f)P(f),
ρmax(0)=- |S(f)|2P(f)df.
P[Hi|x(t)]=P(Hi)P[x(t)|Hi]P[x(t)]=P(Hi)P[x(t)|Hi]iP(Hi)P[x(t)|Hi].
λ[x(t)]=p[x(t)|s]p[x(t)|n].
P(λ>κ|s)=κp{λ[x(t)]|s}dλ[x(t)],
P(λ>κ|n)=κp{λ[x(t)]|n}dλ[x(t)].
p(xm|Hi)=1σ2πexp-(xm-vmi)22σ2,
p({xm}|Hi)=m=1Mp(xm|Hi).
λ[{x(t)}]=1σ2πMm=1M exp-(xm-sm)22σ21σ2πMm=1M exp-(xm)22σ2=m=1M exp-(xm-sm)2+xm22σ2.
Λ=ln(λ[{xm}])=1σ2m=1Mxmsm-m=1Msm2/2
=1N0m=1Mxmsm-E/2.
(d)2=[Λs-Λn]2(1/2)[σΛs2+σΛn2].
η=EiEtd,η2=dtdiE2.
SNRRose=meansignalσNb=ΔNsNb=AΔnsAnb
=CAnb.
Λs-Λn=1N0--{s(x, y)+ns(x, y)-nn(x, y)}t(x, y)dxdy
=aτN0Rdxdy=aτAN0,
σΛs2=σΛn2=1N02--n(x, y)2t(x, y)2dxdy
=τN02Rn(x, y)2dxdy=τ2N0AN02,
SNR2=(d)2=(Λs-Λn)2(1/2)(σΛs2+σΛn2)=τ2a2A2N02τ2AN03
=a2AN0.
C=Δnsnb=aN0,
SNRRose2=C2Anb=aN02AN0=a2AN0=SNR2.
CT=kAnb.

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