Abstract

Many psychophysical studies of the ability of the human observer to detect a signal superimposed upon a uniform background, where both the signal and the background are known exactly, have been reported in the literature. In such cases, the ideal or the Bayesian observer is often used as a mathematical model of human performance since it can be readily calculated and is a good predictor of human performance for the task at hand. If, however, the background is spatially inhomogeneous (lumpy), the ideal observer becomes nonlinear, and its performance becomes difficult to evaluate. Since inhomogeneous backgrounds are commonly encountered in many practical applications, we have investigated the effects of background inhomogeneities on human performance. The task was detection of a two-dimensional Gaussian signal superimposed upon an inhomogeneous background and imaged through a pinhole imaging system. Poisson noise corresponding to a certain exposure time and aperture size was added to the detected image. A six-point rating scale technique was used to measure human performance as a function of the strength of the nonuniformities (lumpiness) in the background, the amount of blur of the imaging system, and the amount of Poisson noise in the image. The results of this study were compared with earlier theoretical predictions by Myers et al. [ J. Opt. Soc. Am. A 7, 1279 ( 1990)] for two observer models: the optimum linear discriminant, also known as the Hotelling observer, and a nonprewhitening matched filter. Although the efficiency of the human observer relative to the Hotelling observer was only approximately 10%, the variation in human performance with respect to varying aperture size and exposure time was well predicted by the Hotelling model. The nonprewhitening model, on the other hand, fails to predict human performance in lumpy backgrounds in this study. In particular, this model predicts that performance will saturate with increasing exposure time and drop precipitously with increasing lumpiness; neither effect is observed with human observers.

© 1992 Optical Society of America

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  35. J. P. Rolland, H. H. Barrett, G. W. Seeley, “Quantitative study of deconvolution and display mappings for long-tailed point-spread functions,” in Medical Imaging III: Image Processing, S. J. Dwyer, R. G. Jost, R. H. Schneider, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1092, 17–21 (1989).
    [Crossref]
  36. K. J. Myers, H. H. Barrett, M. C. Borgstrom, 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]
  37. 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]
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1990 (2)

1989 (3)

Panel on Discriminant Analysis, Classification, and Clustering, “Discriminant analysis and clustering,” Stat. Sci. 4, 34–69 (1989).

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

T. A. White, H. H. Barrett, E. B. Cargill, R. D. Fiete, M. Ker, “The use of the Hotelling trace to optimize collimator performance,”J. Nucl. Med. 30, 892 (A) (1989).

1988 (1)

J. A. Swets, “Measuring the accuracy of diagnosis systems,” Science 240, 1285–1293 (1988).
[Crossref] [PubMed]

1987 (2)

1986 (2)

1985 (3)

P. F. Judy, R. G. Swensson, “Detection of small focal lesions in CT images: effects of reconstruction filters and visual display windows,”B. J. Radiol. 58, 137–145 (1985).
[Crossref]

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

K. J. Myers, H. H. Barrett, M. C. Borgstrom, 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]

1984 (4)

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

Z. H. Gu, S. Lee, “Optical implementation of the Hotelling trace criterion for image classification,” Opt. Eng. 23, 727–731 (1984).
[Crossref]

B. L. Cole, S. E. Jenkins, “The effect of the variability of background elements on the conspicuity of objects,” Vision Res. 24, 261–270 (1984).
[Crossref]

U. E. Ruttimann, R. L. Webber, “A simple model combining quantum noise and anatomical variation in radiographs,” Med. Phys. 11, 50–60 (1984).
[Crossref] [PubMed]

1983 (1)

M. L. Deaton, “Estimation and hypothesis testing in regression in the presence of nonhomogeneous error variances,” Commun. Statist. Simula. Computation 12, 45–66 (1983).
[Crossref]

1982 (1)

B. M. W. Tsui, C. E. Metz, R. N. Beck, “Optimum detector spatial resolution for discriminating between tumor uptake distributions in scintigraphy,” Phys. Med. Biol. 28, 775–788 (1982).
[Crossref]

1981 (1)

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

1979 (1)

K. M. Hanson, “Detectability in computed tomographic images,” Med. Phys. 6, 441–451 (1979).
[Crossref] [PubMed]

1978 (1)

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[Crossref] [PubMed]

1974 (1)

G. Revesz, H. L. Kundel, M. A. Graber, “The influence of structured noise on detection of radiologic abnormalities,” Invest. Radiol. 9, 479–486 (1974).
[Crossref] [PubMed]

1973 (1)

F. L. Engel, “Visual conspicuity and selective background interference in eccentric vision,” Vision Res. 14, 459–471 (1973).
[Crossref]

1971 (1)

1958 (1)

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

Aarsvold, J. N.

H. H. Barrett, J. N. Aarsvold, H. B. Barber, E. B. Cargill, R. D. Fiete, T. S. Hickernell, T. D. Milster, K. J. Myers, D. D. Patton, R. K. Rowe, R. H. Seacat, W. E. Smith, J. M. Woolfenden, “Applications of statistical decision theory in nuclear medicine,” Information Processing in Medical Imaging (Plenum, New York, 1988).

Atkins, F. B.

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[Crossref] [PubMed]

Barber, H. B.

H. H. Barrett, J. N. Aarsvold, H. B. Barber, E. B. Cargill, R. D. Fiete, T. S. Hickernell, T. D. Milster, K. J. Myers, D. D. Patton, R. K. Rowe, R. H. Seacat, W. E. Smith, J. M. Woolfenden, “Applications of statistical decision theory in nuclear medicine,” Information Processing in Medical Imaging (Plenum, New York, 1988).

Barlow, H. B.

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

Barrett, H. H.

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]

K. J. Myers, J. P. Rolland, H. H. Barrett, R. F. Wagner, “Aperture optimization for emission imaging: effect of a spatially varying background,” J. Opt. Soc. Am. A 7, 1279–1293 (1990).
[Crossref] [PubMed]

T. A. White, H. H. Barrett, E. B. Cargill, R. D. Fiete, M. Ker, “The use of the Hotelling trace to optimize collimator performance,”J. Nucl. Med. 30, 892 (A) (1989).

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]

R. D. Fiete, H. H. Barrett, W. E. Smith, K. J. Myers, “The Hotelling trace criterion and its correlation with human observer performance,” J. Opt. Soc. Am. A 4, 945–953 (1987).
[Crossref] [PubMed]

W. E. Smith, H. H. Barrett, “Hotelling trace criterion as a figure of merit for the optimization of imaging systems,” J. Opt. Soc. Am. A 3, 717–725 (1986).
[Crossref]

K. J. Myers, H. H. Barrett, M. C. Borgstrom, 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]

J. P. Rolland, H. H. Barrett, G. W. Seeley, “Quantitative study of deconvolution and display mappings for long-tailed point-spread functions,” in Medical Imaging III: Image Processing, S. J. Dwyer, R. G. Jost, R. H. Schneider, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1092, 17–21 (1989).
[Crossref]

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

H. H. Barrett, J. N. Aarsvold, H. B. Barber, E. B. Cargill, R. D. Fiete, T. S. Hickernell, T. D. Milster, K. J. Myers, D. D. Patton, R. K. Rowe, R. H. Seacat, W. E. Smith, J. M. Woolfenden, “Applications of statistical decision theory in nuclear medicine,” Information Processing in Medical Imaging (Plenum, New York, 1988).

Beck, R. N.

B. M. W. Tsui, C. E. Metz, R. N. Beck, “Optimum detector spatial resolution for discriminating between tumor uptake distributions in scintigraphy,” Phys. Med. Biol. 28, 775–788 (1982).
[Crossref]

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[Crossref] [PubMed]

Birdsall, T. G.

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

Borgstrom, M. C.

Brown, D. G.

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

R. F. Wagner, D. G. Brown, C. E. Metz, “On the multiplex advantage of coded source/aperture photon imaging,” in Digital Radiography, W. R. Brody, ed., Proc. Soc. Photo-Opt. Instrum. Eng.314, 72–76 (1981).
[Crossref]

Burgess, A. E.

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

A. E. Burgess, R. F. Wagner, R. J. Jennings, “Human signal detection performance for noisy medical images,” in Proceedings of the IEEE ComSoc International Workshop on Medical Imaging, IEEE catalog no. 82CH1751-7 (Institute of Electrical and Electronics Engineers, New York, 1982).

Cargill, E. B.

T. A. White, H. H. Barrett, E. B. Cargill, R. D. Fiete, M. Ker, “The use of the Hotelling trace to optimize collimator performance,”J. Nucl. Med. 30, 892 (A) (1989).

H. H. Barrett, J. N. Aarsvold, H. B. Barber, E. B. Cargill, R. D. Fiete, T. S. Hickernell, T. D. Milster, K. J. Myers, D. D. Patton, R. K. Rowe, R. H. Seacat, W. E. Smith, J. M. Woolfenden, “Applications of statistical decision theory in nuclear medicine,” Information Processing in Medical Imaging (Plenum, New York, 1988).

Cole, B. L.

B. L. Cole, S. E. Jenkins, “The effect of the variability of background elements on the conspicuity of objects,” Vision Res. 24, 261–270 (1984).
[Crossref]

Deaton, M. L.

M. L. Deaton, “Estimation and hypothesis testing in regression in the presence of nonhomogeneous error variances,” Commun. Statist. Simula. Computation 12, 45–66 (1983).
[Crossref]

Egan, J. P.

J. P. Egan, Signal Detection Theory and ROC Analysis (Academic, New York, 1975).

Engel, F. L.

F. L. Engel, “Visual conspicuity and selective background interference in eccentric vision,” Vision Res. 14, 459–471 (1973).
[Crossref]

Fiete, R. D.

T. A. White, H. H. Barrett, E. B. Cargill, R. D. Fiete, M. Ker, “The use of the Hotelling trace to optimize collimator performance,”J. Nucl. Med. 30, 892 (A) (1989).

R. D. Fiete, H. H. Barrett, W. E. Smith, K. J. Myers, “The Hotelling trace criterion and its correlation with human observer performance,” J. Opt. Soc. Am. A 4, 945–953 (1987).
[Crossref] [PubMed]

H. H. Barrett, J. N. Aarsvold, H. B. Barber, E. B. Cargill, R. D. Fiete, T. S. Hickernell, T. D. Milster, K. J. Myers, D. D. Patton, R. K. Rowe, R. H. Seacat, W. E. Smith, J. M. Woolfenden, “Applications of statistical decision theory in nuclear medicine,” Information Processing in Medical Imaging (Plenum, New York, 1988).

Fukunaga, K.

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

Ghandeharian, H.

Graber, M. A.

G. Revesz, H. L. Kundel, M. A. Graber, “The influence of structured noise on detection of radiologic abnormalities,” Invest. Radiol. 9, 479–486 (1974).
[Crossref] [PubMed]

Green, D. B.

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

Gu, Z. H.

Z. H. Gu, S. Lee, “Optical implementation of the Hotelling trace criterion for image classification,” Opt. Eng. 23, 727–731 (1984).
[Crossref]

Hanson, K. M.

K. M. Hanson, “Detectability in computed tomographic images,” Med. Phys. 6, 441–451 (1979).
[Crossref] [PubMed]

K. M. Hanson, “Variations in task and the ideal observer,” in Application of Optical Instrumentation in Medicine XI, G. D. Fullerton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.419, 60–67 (1983).

Hickernell, T. S.

H. H. Barrett, J. N. Aarsvold, H. B. Barber, E. B. Cargill, R. D. Fiete, T. S. Hickernell, T. D. Milster, K. J. Myers, D. D. Patton, R. K. Rowe, R. H. Seacat, W. E. Smith, J. M. Woolfenden, “Applications of statistical decision theory in nuclear medicine,” Information Processing in Medical Imaging (Plenum, New York, 1988).

Jenkins, S. E.

B. L. Cole, S. E. Jenkins, “The effect of the variability of background elements on the conspicuity of objects,” Vision Res. 24, 261–270 (1984).
[Crossref]

Jennings, R. J.

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

A. E. Burgess, R. F. Wagner, R. J. Jennings, “Human signal detection performance for noisy medical images,” in Proceedings of the IEEE ComSoc International Workshop on Medical Imaging, IEEE catalog no. 82CH1751-7 (Institute of Electrical and Electronics Engineers, New York, 1982).

Judy, P. F.

P. F. Judy, R. G. Swensson, “Detection of small focal lesions in CT images: effects of reconstruction filters and visual display windows,”B. J. Radiol. 58, 137–145 (1985).
[Crossref]

R. G. Swensson, P. F. Judy, “Background area effects on feature detectability in CT and uncorrelated noise,” presented at the 73rd Annual Meeting of the Radiological Society of North America, Chicago, Ill., 1987.

Ker, M.

T. A. White, H. H. Barrett, E. B. Cargill, R. D. Fiete, M. Ker, “The use of the Hotelling trace to optimize collimator performance,”J. Nucl. Med. 30, 892 (A) (1989).

Kundel, H. L.

G. Revesz, H. L. Kundel, M. A. Graber, “The influence of structured noise on detection of radiologic abnormalities,” Invest. Radiol. 9, 479–486 (1974).
[Crossref] [PubMed]

Lee, S.

Z. H. Gu, S. Lee, “Optical implementation of the Hotelling trace criterion for image classification,” Opt. Eng. 23, 727–731 (1984).
[Crossref]

Metz, C. E.

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

C. E. Metz, “ROC methodology in radiologic imaging,” Invest. Radiol. 21, 720–733 (1986).
[Crossref] [PubMed]

B. M. W. Tsui, C. E. Metz, R. N. Beck, “Optimum detector spatial resolution for discriminating between tumor uptake distributions in scintigraphy,” Phys. Med. Biol. 28, 775–788 (1982).
[Crossref]

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[Crossref] [PubMed]

R. F. Wagner, D. G. Brown, C. E. Metz, “On the multiplex advantage of coded source/aperture photon imaging,” in Digital Radiography, W. R. Brody, ed., Proc. Soc. Photo-Opt. Instrum. Eng.314, 72–76 (1981).
[Crossref]

Milster, T. D.

H. H. Barrett, J. N. Aarsvold, H. B. Barber, E. B. Cargill, R. D. Fiete, T. S. Hickernell, T. D. Milster, K. J. Myers, D. D. Patton, R. K. Rowe, R. H. Seacat, W. E. Smith, J. M. Woolfenden, “Applications of statistical decision theory in nuclear medicine,” Information Processing in Medical Imaging (Plenum, New York, 1988).

Myers, K. J.

Nachmias, J.

Patton, D. D.

K. J. Myers, H. H. Barrett, M. C. Borgstrom, 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]

H. H. Barrett, J. N. Aarsvold, H. B. Barber, E. B. Cargill, R. D. Fiete, T. S. Hickernell, T. D. Milster, K. J. Myers, D. D. Patton, R. K. Rowe, R. H. Seacat, W. E. Smith, J. M. Woolfenden, “Applications of statistical decision theory in nuclear medicine,” Information Processing in Medical Imaging (Plenum, New York, 1988).

Revesz, G.

G. Revesz, H. L. Kundel, M. A. Graber, “The influence of structured noise on detection of radiologic abnormalities,” Invest. Radiol. 9, 479–486 (1974).
[Crossref] [PubMed]

Robson, J.

Rolland, J. P.

K. J. Myers, J. P. Rolland, H. H. Barrett, R. F. Wagner, “Aperture optimization for emission imaging: effect of a spatially varying background,” J. Opt. Soc. Am. A 7, 1279–1293 (1990).
[Crossref] [PubMed]

J. P. Rolland, “Factors influencing lesion detection in medical imaging,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1990).

J. P. Rolland, H. H. Barrett, G. W. Seeley, “Quantitative study of deconvolution and display mappings for long-tailed point-spread functions,” in Medical Imaging III: Image Processing, S. J. Dwyer, R. G. Jost, R. H. Schneider, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1092, 17–21 (1989).
[Crossref]

Rowe, R. K.

H. H. Barrett, J. N. Aarsvold, H. B. Barber, E. B. Cargill, R. D. Fiete, T. S. Hickernell, T. D. Milster, K. J. Myers, D. D. Patton, R. K. Rowe, R. H. Seacat, W. E. Smith, J. M. Woolfenden, “Applications of statistical decision theory in nuclear medicine,” Information Processing in Medical Imaging (Plenum, New York, 1988).

Ruttimann, U. E.

U. E. Ruttimann, R. L. Webber, “A simple model combining quantum noise and anatomical variation in radiographs,” Med. Phys. 11, 50–60 (1984).
[Crossref] [PubMed]

Sachs, M.

Seacat, R. H.

H. H. Barrett, J. N. Aarsvold, H. B. Barber, E. B. Cargill, R. D. Fiete, T. S. Hickernell, T. D. Milster, K. J. Myers, D. D. Patton, R. K. Rowe, R. H. Seacat, W. E. Smith, J. M. Woolfenden, “Applications of statistical decision theory in nuclear medicine,” Information Processing in Medical Imaging (Plenum, New York, 1988).

Seeley, G. W.

K. J. Myers, H. H. Barrett, M. C. Borgstrom, 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]

J. P. Rolland, H. H. Barrett, G. W. Seeley, “Quantitative study of deconvolution and display mappings for long-tailed point-spread functions,” in Medical Imaging III: Image Processing, S. J. Dwyer, R. G. Jost, R. H. Schneider, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1092, 17–21 (1989).
[Crossref]

Smith, W. E.

R. D. Fiete, H. H. Barrett, W. E. Smith, K. J. Myers, “The Hotelling trace criterion and its correlation with human observer performance,” J. Opt. Soc. Am. A 4, 945–953 (1987).
[Crossref] [PubMed]

W. E. Smith, H. H. Barrett, “Hotelling trace criterion as a figure of merit for the optimization of imaging systems,” J. Opt. Soc. Am. A 3, 717–725 (1986).
[Crossref]

H. H. Barrett, J. N. Aarsvold, H. B. Barber, E. B. Cargill, R. D. Fiete, T. S. Hickernell, T. D. Milster, K. J. Myers, D. D. Patton, R. K. Rowe, R. H. Seacat, W. E. Smith, J. M. Woolfenden, “Applications of statistical decision theory in nuclear medicine,” Information Processing in Medical Imaging (Plenum, New York, 1988).

Starr, S. J.

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[Crossref] [PubMed]

Swensson, R. G.

P. F. Judy, R. G. Swensson, “Detection of small focal lesions in CT images: effects of reconstruction filters and visual display windows,”B. J. Radiol. 58, 137–145 (1985).
[Crossref]

R. G. Swensson, P. F. Judy, “Background area effects on feature detectability in CT and uncorrelated noise,” presented at the 73rd Annual Meeting of the Radiological Society of North America, Chicago, Ill., 1987.

Swets, J. A.

J. A. Swets, “Measuring the accuracy of diagnosis systems,” Science 240, 1285–1293 (1988).
[Crossref] [PubMed]

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

Swindell, W.

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

Tanner, W. P.

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

Tsui, B. M. W.

B. M. W. Tsui, C. E. Metz, R. N. Beck, “Optimum detector spatial resolution for discriminating between tumor uptake distributions in scintigraphy,” Phys. Med. Biol. 28, 775–788 (1982).
[Crossref]

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[Crossref] [PubMed]

Van Trees, H. L.

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

Wagner, R. F.

K. J. Myers, J. P. Rolland, H. H. Barrett, R. F. Wagner, “Aperture optimization for emission imaging: effect of a spatially varying background,” J. Opt. Soc. Am. A 7, 1279–1293 (1990).
[Crossref] [PubMed]

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

A. E. Burgess, R. F. Wagner, R. J. Jennings, “Human signal detection performance for noisy medical images,” in Proceedings of the IEEE ComSoc International Workshop on Medical Imaging, IEEE catalog no. 82CH1751-7 (Institute of Electrical and Electronics Engineers, New York, 1982).

R. F. Wagner, D. G. Brown, C. E. Metz, “On the multiplex advantage of coded source/aperture photon imaging,” in Digital Radiography, W. R. Brody, ed., Proc. Soc. Photo-Opt. Instrum. Eng.314, 72–76 (1981).
[Crossref]

Webber, R. L.

U. E. Ruttimann, R. L. Webber, “A simple model combining quantum noise and anatomical variation in radiographs,” Med. Phys. 11, 50–60 (1984).
[Crossref] [PubMed]

White, T. A.

T. A. White, H. H. Barrett, E. B. Cargill, R. D. Fiete, M. Ker, “The use of the Hotelling trace to optimize collimator performance,”J. Nucl. Med. 30, 892 (A) (1989).

Woolfenden, J. M.

H. H. Barrett, J. N. Aarsvold, H. B. Barber, E. B. Cargill, R. D. Fiete, T. S. Hickernell, T. D. Milster, K. J. Myers, D. D. Patton, R. K. Rowe, R. H. Seacat, W. E. Smith, J. M. Woolfenden, “Applications of statistical decision theory in nuclear medicine,” Information Processing in Medical Imaging (Plenum, New York, 1988).

B. J. Radiol. (1)

P. F. Judy, R. G. Swensson, “Detection of small focal lesions in CT images: effects of reconstruction filters and visual display windows,”B. J. Radiol. 58, 137–145 (1985).
[Crossref]

Commun. Statist. Simula. Computation (1)

M. L. Deaton, “Estimation and hypothesis testing in regression in the presence of nonhomogeneous error variances,” Commun. Statist. Simula. Computation 12, 45–66 (1983).
[Crossref]

Invest. Radiol. (3)

C. E. Metz, “ROC methodology in radiologic imaging,” Invest. Radiol. 21, 720–733 (1986).
[Crossref] [PubMed]

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

G. Revesz, H. L. Kundel, M. A. Graber, “The influence of structured noise on detection of radiologic abnormalities,” Invest. Radiol. 9, 479–486 (1974).
[Crossref] [PubMed]

J. Acoust. Soc. Am. (1)

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

J. Nucl. Med. (1)

T. A. White, H. H. Barrett, E. B. Cargill, R. D. Fiete, M. Ker, “The use of the Hotelling trace to optimize collimator performance,”J. Nucl. Med. 30, 892 (A) (1989).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

Med. Phys. (2)

U. E. Ruttimann, R. L. Webber, “A simple model combining quantum noise and anatomical variation in radiographs,” Med. Phys. 11, 50–60 (1984).
[Crossref] [PubMed]

K. M. Hanson, “Detectability in computed tomographic images,” Med. Phys. 6, 441–451 (1979).
[Crossref] [PubMed]

Opt. Eng. (1)

Z. H. Gu, S. Lee, “Optical implementation of the Hotelling trace criterion for image classification,” Opt. Eng. 23, 727–731 (1984).
[Crossref]

Phys. Med. Biol. (3)

B. M. W. Tsui, C. E. Metz, R. N. Beck, “Optimum detector spatial resolution for discriminating between tumor uptake distributions in scintigraphy,” Phys. Med. Biol. 28, 775–788 (1982).
[Crossref]

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

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[Crossref] [PubMed]

Science (2)

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

J. A. Swets, “Measuring the accuracy of diagnosis systems,” Science 240, 1285–1293 (1988).
[Crossref] [PubMed]

Stat. Sci. (1)

Panel on Discriminant Analysis, Classification, and Clustering, “Discriminant analysis and clustering,” Stat. Sci. 4, 34–69 (1989).

Vision Res. (2)

F. L. Engel, “Visual conspicuity and selective background interference in eccentric vision,” Vision Res. 14, 459–471 (1973).
[Crossref]

B. L. Cole, S. E. Jenkins, “The effect of the variability of background elements on the conspicuity of objects,” Vision Res. 24, 261–270 (1984).
[Crossref]

Other (12)

R. G. Swensson, P. F. Judy, “Background area effects on feature detectability in CT and uncorrelated noise,” presented at the 73rd Annual Meeting of the Radiological Society of North America, Chicago, Ill., 1987.

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

A. E. Burgess, R. F. Wagner, R. J. Jennings, “Human signal detection performance for noisy medical images,” in Proceedings of the IEEE ComSoc International Workshop on Medical Imaging, IEEE catalog no. 82CH1751-7 (Institute of Electrical and Electronics Engineers, New York, 1982).

K. M. Hanson, “Variations in task and the ideal observer,” in Application of Optical Instrumentation in Medicine XI, G. D. Fullerton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.419, 60–67 (1983).

H. H. Barrett, J. N. Aarsvold, H. B. Barber, E. B. Cargill, R. D. Fiete, T. S. Hickernell, T. D. Milster, K. J. Myers, D. D. Patton, R. K. Rowe, R. H. Seacat, W. E. Smith, J. M. Woolfenden, “Applications of statistical decision theory in nuclear medicine,” Information Processing in Medical Imaging (Plenum, New York, 1988).

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

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

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

J. P. Egan, Signal Detection Theory and ROC Analysis (Academic, New York, 1975).

R. F. Wagner, D. G. Brown, C. E. Metz, “On the multiplex advantage of coded source/aperture photon imaging,” in Digital Radiography, W. R. Brody, ed., Proc. Soc. Photo-Opt. Instrum. Eng.314, 72–76 (1981).
[Crossref]

J. P. Rolland, “Factors influencing lesion detection in medical imaging,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1990).

J. P. Rolland, H. H. Barrett, G. W. Seeley, “Quantitative study of deconvolution and display mappings for long-tailed point-spread functions,” in Medical Imaging III: Image Processing, S. J. Dwyer, R. G. Jost, R. H. Schneider, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1092, 17–21 (1989).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

Illustrative images of a signal on various backgrounds. The leftmost column shows Gaussian pinhole (rp = 0.4 rs) images of a Gaussian signal (50% contrast, rs = 5.66 pixels, centered in the object array) superimposed upon lumpy backgrounds with a correlation length of 16.98 pixels for Wf(0) = 0, 1.3 × 105, 8.2 × 105, and 3.3 × 106 counts2/(s2 pixel) from top to bottom. The second column shows the same objects imaged by a Gaussian aperture with rp = 0.8 rs. The third and the fourth columns show the same objects imaged by an aperture size rp equal to 1.6 rs and 3.2 rs respectively. In all the cases the exposure time was set to 1 s.

Fig. 2
Fig. 2

Illustrative images of a signal on various backgrounds and imaged with various exposure times. The top row shows the signal (rs = 5.66 pixels) that is present in the images below the signal. The exposure time increases from left to right with T equal to 1, 3, 10, and 50 s, while the lumpiness increases from top to bottom with Wf(0) equal to 0, 1.3 × 105, and 8.2 × 105 counts2/(s pixel). The contrast of the signal on the background was 10% before imaging.

Fig. 3
Fig. 3

Plot of the measured relative brightness versus the displayed gray levels at the cathode-ray tube screen. The measurements were done with a photodiode–55-mm-camera assembly looking at a 16 × 16 pixel array of gray-level values ranging from 0 to 255. The 16 × 16 pixel array was centered in a 128 × 128-pixel array of gray-level value 128. The display monitor was driven by a PCvision board.

Fig. 4
Fig. 4

Plot of the detectabilities predicted by the Hotelling and the NPW observers for the detection of a low-contrast signal on uniform [Wf(0) = 0] and nonuniform [Wf(0) ≠ 0] backgrounds as a function of the size of the pinhole aperture rp. The width of the signal is 5.66 pixels, and the contrasts of the signal are 19.9%, 16.5%, and 14.1% as the lumpiness increases, since the dc background level is kept constant (3000 counts/(s pixel) as we increase the lumpiness, but the mean background level is a function of both the dc background level and the lumpiness [see Eq. (6)]. The mean numbers of blobs are 0, 50, and 100 as Wf(0) increases, while the strength of the blob b0 is kept constant (2 × 105 counts/s). NPWMF, NPW matched filter.

Fig. 5
Fig. 5

Plot of the detectabilities predicted by the Hotelling and the NPW observers for the detection of a low-contrast signal on uniform [Wf(0) = 0] and nonuniform [Wf(0) ≠ 0] backgrounds as a function of the exposure time T. The width of the signal is 5.66 pixels, and the contrast of the signal is 10% before imaging. As the amount of lumpiness increases, the dc background levels are 250, 230, and 200 counts/(s pixel) such that the mean background level is a constant B = 250 counts/(s pixel). The mean number of blobs is 50, and the strengths of the blobs are 0, 6.55 × 103 and 1.64 × 104 counts/s as Wf(0) increases. NPWMF NPW matched filter.

Fig. 6
Fig. 6

Values of detectabilities obtained from the psychophysical studies for the detection of a low-contrast signal on uniform [Wf(0) = 0] and nonuniform [Wf(0) ≠ 0] backgrounds as a function of the size of the pinhole aperture. The values of the parameters used to generate the computer-simulated images are the same as those given in the caption to Fig. 4. Four values of the size of the pinhole aperture rp relative to the size of the signal rs are chosen in this case: rp/rs. equal to 0.2, 0.8, 1.5, and 3.4. The lines shown are simply the lines connecting the data points.

Fig. 7
Fig. 7

Values of detectabilities obtained from the psychophysical studies for the detection of a low-contrast signa1 on uniform [Wf(0) = 0] and nonuniform [Wf(0) ≠ 0] backgrounds as a function of the exposure time T. The values of the parameters used to generate the computer-simulated images are the same as those given in the caption to Fig. 5. Four values of T are chosen: T equal to 1, 3, 10, 50, and 100 s as shown on the graph.

Fig. 8
Fig. 8

Example of the profile of the Hotelling feature operator along a radial axis in the space domain for the detection of a Gaussian signal on one uniform and two nonuniform backgrounds. Lumpiness is equivalent to Wf(0). The mean value of the background is 610 counts/(s pixel). The signal width was 10 pixels, and the background autocorrelation length was 30 pixels.

Equations (30)

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

g ( r ) = κ T f ( r ) * t ( r ) ,
a s g = π κ T a s r p 2 ,             r s g = ( r s 2 + r p 2 ) 1 / 2 .
R f ( r ) = W f ( 0 ) 2 π r b 2 exp ( - r 2 / 2 r b 2 ) ,
W f ( ρ ) = W f ( 0 ) exp ( - 2 π 2 r b 2 ρ 2 ) ,
b ( r ) = [ j = 1 K δ ( r - r j ) ] * [ b 0 π r b 2 exp ( - r 2 r b 2 ) ] = j = 1 K b 0 π r b 2 exp ( - r - r j 2 r b 2 ) ,
W f ( 0 ) = K ¯ A d b 0 2 ,
B ¯ = B 0 + b 0 A d K ¯ .
a b g = π κ T b 0 r p 2 ,             r b g = ( r b 2 + r p 2 ) 1 / 2 ,
B 0 g = π κ T B 0 r p 2 .
d a 2 = [ λ ( g ) 1 - λ ( g ) 0 ] 2 P 0 var ( λ ( g ) 0 ) + P 1 var [ λ ( g ) 1 ] ,
AUC = 1 2 + 1 2 erf ( d a 2 ) ,
J = Tr ( S 2 - 1 S 1 ) .
J = P 1 P 2 d Hot 2 ,
( d Hot ) 2 = d 2 ρ s ˜ ( ρ ) 2 H ˜ ( ρ ) 2 [ B ¯ g + H ˜ ( ρ ) 2 W f ( ρ ) ] ,
( d NPW ) 2 = [ d 2 ρ s ˜ ( ρ ) 2 H ˜ ( ρ ) 2 ] 2 B ¯ g d 2 ρ s ˜ ( ρ ) 2 H ˜ ( ρ ) 2 + d 2 ρ s ˜ ( ρ ) 2 H ˜ ( ρ ) 4 W f ( ρ ) .
b ( r ) = [ i = 1 K δ ( r - r 1 ) ] * y ( r ) ,
y ( r ) = b 0 π r b 2 exp [ - r 2 / ( r b 2 ) ] ,
R f ( r - r ) = [ b ( r ) - b ( r ) f ] [ b ( r ) - b ( r ) f ] f ,
R f = b ( r ) b ( r ) f + b ( r ) f b ( r ) f f - b ( r ) b ( r ) f f - b ( r ) f b ( r ) f ,
R f = b ( r ) b ( r ) f - b ( r ) f b ( r ) f .
R f = R f k k
R f k = b ( r ) b ( r ) f k - b ( r ) f k b ( r ) f k ,
term 2 = b ( r ) f k b ( r ) f k = i = 1 K y ( r - r i ) f k i = 1 K y ( r - r i ) f k = K 2 b 0 2 A d 2 .
b ( r ) b ( r ) f k = i = 1 K [ δ ( r - r i ) * y ( r ) ] j = 1 K [ δ ( r - r j ) * y ( r ) ] f k = i = 1 K y ( r - r i ) j = 1 K y ( r - r j ) f k = d 2 r 1 p r ( r 1 ) d 2 r K p r ( r K ) i = 1 K y ( r - r i ) j = 1 K y ( r - r j ) ,
term 1 ( i = j ) = K A d b 0 2 2 π r b 2 exp [ - r 2 / ( 2 r b 2 ) ] .
term 1 ( i j ) = ( K 2 - K ) b 0 2 A d 2 .
R f k = K A d b 0 2 2 π r b 2 exp [ - r 2 / ( 2 r b 2 ) ] + ( K 2 - K ) b 0 2 A d 2 + K 2 b 0 2 A d 2 .
R f ( r ) = K ¯ A d b 0 2 2 π r b 2 exp [ - r 2 / ( ( 2 r b 2 ) ] .
W f ( ρ ) = K ¯ A d b 0 2 exp ( - 2 π 2 r b 2 ρ 2 ) = W f ( 0 ) exp ( - 2 π 2 r b 2 ρ 2 ) ,
W f ( 0 ) = K ¯ A d b 0 2 .

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