Abstract

Models of human visual detection have been successfully used in computer-generated noise. For these backgrounds, which are generally statistically stationary, model performance can be readily calculated by computing the index of detectability d from the noise power spectrum, the signal profile, and the model template. However, model observers are ultimately needed in more real backgrounds, which may be statistically nonstationary. We investigated different methods to calculate figures of merit for model observers in real backgrounds based on different assumptions about image stationarity. We computed performance of the nonprewhitening matched-filter observer with an eye filter on mammography and coronary angiography for an additive or a multiplicative signal. Performance was measured either by applying the model template to the images or by computing closed-form expressions with various assumptions about image stationarity. Results show first that the structured backgrounds investigated cannot be considered stationary. Second, traditional closed-form expressions of detectability calculated from the noise power spectra with the assumption of background stationarity lead to erroneous estimates of model performance. Third, the most accurate way of measuring model performances is by directly applying the model template on the images or by computing a closed-form expression that does not assume image stationarity.

© 2000 Optical Society of America

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2000 (1)

1999 (3)

1997 (4)

1996 (1)

1995 (1)

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

1994 (3)

1993 (1)

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

1992 (2)

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]

M. S. Chesters, “Human visual perception and ROC methodology in medical imaging,” Phys. Med. Biol. 37, 1433–1476 (1992).
[CrossRef] [PubMed]

1991 (1)

L. Desponds, C. Depeursinge, M. Grecescu, C. Hessler, A. Samiri, J. F. Valley, “Image quality index (IQI) for screen-film mammography,” Phys. Med. Biol. 36, 19–33 (1991).
[CrossRef] [PubMed]

1990 (2)

1987 (1)

1985 (3)

C. Hessler, C. Depeursinge, M. Grecescu, Y. Pochon, S. Raimondi, J. F. Valley, “Objective assessment of mammography systems; Part I: Method,” Radiology 156, 215–219 (1985).
[PubMed]

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 (2)

L. N. D. Loo, K. Doi, C. E. Metz, “A comparison of physical image quality indices and observer performance in the radiographic detection of nylon beads,” Phys. Med. Biol. 29, 837–856 (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]

1982 (1)

P. R. Moran, “A physical statistics theory for detectability of a target signal in noisy images. I. Mathematical background, empirical review, and development of theory,” Med. Phys. 9, 401–413 (1982).
[CrossRef] [PubMed]

1981 (1)

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal determination,” Nature (London) 214, 93–94 (1981).

1979 (1)

R. F. Wagner, D. G. Brown, M. S. Pastel, “Application of information theory to the assessment of computed tomography,” Med. Phys. 6, 83–94 (1979).
[CrossRef] [PubMed]

1975 (1)

B. Julesz, “Experiments in the visual perception of texture,” Sci. Am. 232, 34–43 (1975).
[CrossRef] [PubMed]

1974 (2)

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

R. F. Quick, “A vector-magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
[CrossRef] [PubMed]

Abbey, C. K.

M. P. Eckstein, C. K. Abbey, F. O. Bochud, “Visual signal detection in structured backgrounds. IV. Figures of merit for model performance in multiple-alternative forced-choice detection tasks with correlated responses,” J. Opt. Soc. Am. A 17, 206–217 (2000).
[CrossRef]

A. E. Burgess, X. Li, C. K. Abbey, “Visual signal detectability with two noise components: anomalous masking effects,” J. Opt. Soc. Am. A 14, 2420–2442 (1997).
[CrossRef]

H. H. Barrett, C. K. Abbey, B. Gallas, M. P. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient structured noise,” in Medical Imaging 1998: Image Perception, H. L. Kundel, eds., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

M. P. Eckstein, C. K. Abbey, F. O. Bochud, J. L. Bartroff, J. S. Whiting, “Effect of image compression in model and human observers,” in Medical Imaging 1999: Image Perception and Performance, E. A. Krupinski, ed., Proc. SPIE3663, 243–252 (1999).
[CrossRef]

F. O. Bochud, C. K. Abbey, J. L. Bartroff, D. J. Vodopich, M. P. Eckstein, “Effect of the number of locations in MAFC experiments performed with mammograms,” presented at the Far West Image Perception Conference, Nakoda Lodge, Alberta, Canada, May 20–30, 1999.

F. O. Bochud, C. K. Abbey, M. P. Eckstein, “Further investigation of the effect of phase spectrum on visual detection in structured backgrounds,” in Medical Imaging 1999: Image Perception and Performance, E. A. Krupinski, ed., Proc. SPIE3663, 273–281 (1999).
[CrossRef]

M. P. Eckstein, C. K. Abbey, J. S. Whiting, “Human vs model observers in anatomic backgrounds,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 15–26 (1998).

Ahumada, A. J.

M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Visual signal detection in structured backgrounds. II. Effects of contrast gain control, background variations, and white noise,” J. Opt. Soc. Am. A 14, 2406–2419 (1997).
[CrossRef]

M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Image discrimination models predict signal detection in natural medical image backgrounds,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 44–56 (1997).
[CrossRef]

A. J. Ahumada, B. L. Beard, “Object detection in a noisy scene,” in Human Vision and Electronic Imaging, B. E. Rogowitz, J. P. Allebach, eds., Proc. SPIE2657, 190–199 (1996).
[CrossRef]

Barlow, H. B.

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal determination,” Nature (London) 214, 93–94 (1981).

Barrett, H. H.

Bartroff, J. L.

M. P. Eckstein, C. K. Abbey, F. O. Bochud, J. L. Bartroff, J. S. Whiting, “Effect of image compression in model and human observers,” in Medical Imaging 1999: Image Perception and Performance, E. A. Krupinski, ed., Proc. SPIE3663, 243–252 (1999).
[CrossRef]

F. O. Bochud, C. K. Abbey, J. L. Bartroff, D. J. Vodopich, M. P. Eckstein, “Effect of the number of locations in MAFC experiments performed with mammograms,” presented at the Far West Image Perception Conference, Nakoda Lodge, Alberta, Canada, May 20–30, 1999.

Beard, B. L.

A. J. Ahumada, B. L. Beard, “Object detection in a noisy scene,” in Human Vision and Electronic Imaging, B. E. Rogowitz, J. P. Allebach, eds., Proc. SPIE2657, 190–199 (1996).
[CrossRef]

Bochud, F. O.

M. P. Eckstein, C. K. Abbey, F. O. Bochud, “Visual signal detection in structured backgrounds. IV. Figures of merit for model performance in multiple-alternative forced-choice detection tasks with correlated responses,” J. Opt. Soc. Am. A 17, 206–217 (2000).
[CrossRef]

F. O. Bochud, J. F. Valley, F. R. Verdun, C. Hessler, P. Schnyder, “Estimation of the noisy component of anatomical backgrounds,” Med. Phys. 26, 1365–1370 (1999).
[CrossRef] [PubMed]

M. P. Eckstein, C. K. Abbey, F. O. Bochud, J. L. Bartroff, J. S. Whiting, “Effect of image compression in model and human observers,” in Medical Imaging 1999: Image Perception and Performance, E. A. Krupinski, ed., Proc. SPIE3663, 243–252 (1999).
[CrossRef]

F. O. Bochud, C. K. Abbey, J. L. Bartroff, D. J. Vodopich, M. P. Eckstein, “Effect of the number of locations in MAFC experiments performed with mammograms,” presented at the Far West Image Perception Conference, Nakoda Lodge, Alberta, Canada, May 20–30, 1999.

F. O. Bochud, C. K. Abbey, M. P. Eckstein, “Further investigation of the effect of phase spectrum on visual detection in structured backgrounds,” in Medical Imaging 1999: Image Perception and Performance, E. A. Krupinski, ed., Proc. SPIE3663, 273–281 (1999).
[CrossRef]

F. O. Bochud, F. R. Verdun, C. Hessler, J. F. Valley, “Detectability on radiological images: the effect of the anatomical noise,” in Medical Imaging 1995: Image Perception, H. L. Kundel, ed., Proc. SPIE2436, 156–164 (1995).
[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, M. S. Pastel, “Application of information theory to the assessment of computed tomography,” Med. Phys. 6, 83–94 (1979).
[CrossRef] [PubMed]

Burgess, A. E.

Chan, K. H.

S. E. Seltzer, P. F. Judy, R. G. Swensson, K. H. Chan, R. D. Nawfel, “Flattening of the contrast-detail curve for large lesions on liver CT images,” Med. Phys. 21, 1547–1555 (1994).
[CrossRef] [PubMed]

Chesters, M. S.

M. S. Chesters, “Human visual perception and ROC methodology in medical imaging,” Phys. Med. Biol. 37, 1433–1476 (1992).
[CrossRef] [PubMed]

Clarkson, E.

J. P. Rolland, A. Goon, E. Clarkson, L. Yu, “Synthesis of biomedical tissue,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 85–90 (1998).
[CrossRef]

Dainty, J. C.

J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974).

Depeursinge, C.

L. Desponds, C. Depeursinge, M. Grecescu, C. Hessler, A. Samiri, J. F. Valley, “Image quality index (IQI) for screen-film mammography,” Phys. Med. Biol. 36, 19–33 (1991).
[CrossRef] [PubMed]

C. Hessler, C. Depeursinge, M. Grecescu, Y. Pochon, S. Raimondi, J. F. Valley, “Objective assessment of mammography systems; Part I: Method,” Radiology 156, 215–219 (1985).
[PubMed]

Desponds, L.

L. Desponds, C. Depeursinge, M. Grecescu, C. Hessler, A. Samiri, J. F. Valley, “Image quality index (IQI) for screen-film mammography,” Phys. Med. Biol. 36, 19–33 (1991).
[CrossRef] [PubMed]

Doi, K.

L. N. D. Loo, K. Doi, C. E. Metz, “A comparison of physical image quality indices and observer performance in the radiographic detection of nylon beads,” Phys. Med. Biol. 29, 837–856 (1984).
[CrossRef] [PubMed]

Eckstein, M. P.

M. P. Eckstein, C. K. Abbey, F. O. Bochud, “Visual signal detection in structured backgrounds. IV. Figures of merit for model performance in multiple-alternative forced-choice detection tasks with correlated responses,” J. Opt. Soc. Am. A 17, 206–217 (2000).
[CrossRef]

M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Visual signal detection in structured backgrounds. II. Effects of contrast gain control, background variations, and white noise,” J. Opt. Soc. Am. A 14, 2406–2419 (1997).
[CrossRef]

M. P. Eckstein, J. S. Whiting, “Visual signal detection in structured backgrounds. I. Effect of number of possible spatial locations and signal contrast,” J. Opt. Soc. Am. A 13, 1777–1787 (1996).
[CrossRef]

F. O. Bochud, C. K. Abbey, J. L. Bartroff, D. J. Vodopich, M. P. Eckstein, “Effect of the number of locations in MAFC experiments performed with mammograms,” presented at the Far West Image Perception Conference, Nakoda Lodge, Alberta, Canada, May 20–30, 1999.

M. P. Eckstein, C. K. Abbey, J. S. Whiting, “Human vs model observers in anatomic backgrounds,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 15–26 (1998).

F. O. Bochud, C. K. Abbey, M. P. Eckstein, “Further investigation of the effect of phase spectrum on visual detection in structured backgrounds,” in Medical Imaging 1999: Image Perception and Performance, E. A. Krupinski, ed., Proc. SPIE3663, 273–281 (1999).
[CrossRef]

H. H. Barrett, C. K. Abbey, B. Gallas, M. P. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient structured noise,” in Medical Imaging 1998: Image Perception, H. L. Kundel, eds., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Image discrimination models predict signal detection in natural medical image backgrounds,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 44–56 (1997).
[CrossRef]

M. P. Eckstein, C. K. Abbey, F. O. Bochud, J. L. Bartroff, J. S. Whiting, “Effect of image compression in model and human observers,” in Medical Imaging 1999: Image Perception and Performance, E. A. Krupinski, ed., Proc. SPIE3663, 243–252 (1999).
[CrossRef]

Foley, J. M.

Gallas, B.

H. H. Barrett, C. K. Abbey, B. Gallas, M. P. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient structured noise,” in Medical Imaging 1998: Image Perception, H. L. Kundel, eds., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

Ghandeharian, H.

Goon, A.

J. P. Rolland, A. Goon, E. Clarkson, L. Yu, “Synthesis of biomedical tissue,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 85–90 (1998).
[CrossRef]

Graber, M. A.

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

Grecescu, M.

L. Desponds, C. Depeursinge, M. Grecescu, C. Hessler, A. Samiri, J. F. Valley, “Image quality index (IQI) for screen-film mammography,” Phys. Med. Biol. 36, 19–33 (1991).
[CrossRef] [PubMed]

C. Hessler, C. Depeursinge, M. Grecescu, Y. Pochon, S. Raimondi, J. F. Valley, “Objective assessment of mammography systems; Part I: Method,” Radiology 156, 215–219 (1985).
[PubMed]

Hessler, C.

F. O. Bochud, J. F. Valley, F. R. Verdun, C. Hessler, P. Schnyder, “Estimation of the noisy component of anatomical backgrounds,” Med. Phys. 26, 1365–1370 (1999).
[CrossRef] [PubMed]

L. Desponds, C. Depeursinge, M. Grecescu, C. Hessler, A. Samiri, J. F. Valley, “Image quality index (IQI) for screen-film mammography,” Phys. Med. Biol. 36, 19–33 (1991).
[CrossRef] [PubMed]

C. Hessler, C. Depeursinge, M. Grecescu, Y. Pochon, S. Raimondi, J. F. Valley, “Objective assessment of mammography systems; Part I: Method,” Radiology 156, 215–219 (1985).
[PubMed]

F. O. Bochud, F. R. Verdun, C. Hessler, J. F. Valley, “Detectability on radiological images: the effect of the anatomical noise,” in Medical Imaging 1995: Image Perception, H. L. Kundel, ed., Proc. SPIE2436, 156–164 (1995).
[CrossRef]

Jennings, R. J.

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal determination,” Nature (London) 214, 93–94 (1981).

Judy, P. F.

S. E. Seltzer, P. F. Judy, R. G. Swensson, K. H. Chan, R. D. Nawfel, “Flattening of the contrast-detail curve for large lesions on liver CT images,” Med. Phys. 21, 1547–1555 (1994).
[CrossRef] [PubMed]

P. F. Judy, R. G. Swensson, “Display thresholding of images and observer detection performance,” J. Opt. Soc. Am. A 4, 954–965 (1987).
[CrossRef] [PubMed]

Julesz, B.

B. Julesz, “Experiments in the visual perception of texture,” Sci. Am. 232, 34–43 (1975).
[CrossRef] [PubMed]

Kundel, H. L.

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

Li, X.

Loo, L. N. D.

L. N. D. Loo, K. Doi, C. E. Metz, “A comparison of physical image quality indices and observer performance in the radiographic detection of nylon beads,” Phys. Med. Biol. 29, 837–856 (1984).
[CrossRef] [PubMed]

Metz, C. E.

L. N. D. Loo, K. Doi, C. E. Metz, “A comparison of physical image quality indices and observer performance in the radiographic detection of nylon beads,” Phys. Med. Biol. 29, 837–856 (1984).
[CrossRef] [PubMed]

Miyahara, E.

Moran, P. R.

P. R. Moran, “A physical statistics theory for detectability of a target signal in noisy images. I. Mathematical background, empirical review, and development of theory,” Med. Phys. 9, 401–413 (1982).
[CrossRef] [PubMed]

Myers, K. J.

Nawfel, R. D.

S. E. Seltzer, P. F. Judy, R. G. Swensson, K. H. Chan, R. D. Nawfel, “Flattening of the contrast-detail curve for large lesions on liver CT images,” Med. Phys. 21, 1547–1555 (1994).
[CrossRef] [PubMed]

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 (McGraw-Hill, New York, 1991).

Pastel, M. S.

R. F. Wagner, D. G. Brown, M. S. Pastel, “Application of information theory to the assessment of computed tomography,” Med. Phys. 6, 83–94 (1979).
[CrossRef] [PubMed]

Patton, D. D.

Picinbono, B.

B. Picinbono, Random Signals and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1993).

Pickett, R. M.

J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems: Methods from Signal Detection Theory (Academic, New York, 1982).

Pochon, Y.

C. Hessler, C. Depeursinge, M. Grecescu, Y. Pochon, S. Raimondi, J. F. Valley, “Objective assessment of mammography systems; Part I: Method,” Radiology 156, 215–219 (1985).
[PubMed]

Quick, R. F.

R. F. Quick, “A vector-magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
[CrossRef] [PubMed]

Raimondi, S.

C. Hessler, C. Depeursinge, M. Grecescu, Y. Pochon, S. Raimondi, J. F. Valley, “Objective assessment of mammography systems; Part I: Method,” Radiology 156, 215–219 (1985).
[PubMed]

Revesz, G.

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

Rolland, J. P.

H. H. Barrett, J. Yao, J. P. Rolland, 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]

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

J. P. Rolland, A. Goon, E. Clarkson, L. Yu, “Synthesis of biomedical tissue,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 85–90 (1998).
[CrossRef]

Rose, A.

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

Samiri, A.

L. Desponds, C. Depeursinge, M. Grecescu, C. Hessler, A. Samiri, J. F. Valley, “Image quality index (IQI) for screen-film mammography,” Phys. Med. Biol. 36, 19–33 (1991).
[CrossRef] [PubMed]

Schnyder, P.

F. O. Bochud, J. F. Valley, F. R. Verdun, C. Hessler, P. Schnyder, “Estimation of the noisy component of anatomical backgrounds,” Med. Phys. 26, 1365–1370 (1999).
[CrossRef] [PubMed]

Seeley, G. W.

Seltzer, S. E.

S. E. Seltzer, P. F. Judy, R. G. Swensson, K. H. Chan, R. D. Nawfel, “Flattening of the contrast-detail curve for large lesions on liver CT images,” Med. Phys. 21, 1547–1555 (1994).
[CrossRef] [PubMed]

Shaw, R.

J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974).

Solomon, J.

Swensson, R. G.

S. E. Seltzer, P. F. Judy, R. G. Swensson, K. H. Chan, R. D. Nawfel, “Flattening of the contrast-detail curve for large lesions on liver CT images,” Med. Phys. 21, 1547–1555 (1994).
[CrossRef] [PubMed]

P. F. Judy, R. G. Swensson, “Display thresholding of images and observer detection performance,” J. Opt. Soc. Am. A 4, 954–965 (1987).
[CrossRef] [PubMed]

Swets, J. A.

J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems: Methods from Signal Detection Theory (Academic, New York, 1982).

Valley, J. F.

F. O. Bochud, J. F. Valley, F. R. Verdun, C. Hessler, P. Schnyder, “Estimation of the noisy component of anatomical backgrounds,” Med. Phys. 26, 1365–1370 (1999).
[CrossRef] [PubMed]

L. Desponds, C. Depeursinge, M. Grecescu, C. Hessler, A. Samiri, J. F. Valley, “Image quality index (IQI) for screen-film mammography,” Phys. Med. Biol. 36, 19–33 (1991).
[CrossRef] [PubMed]

C. Hessler, C. Depeursinge, M. Grecescu, Y. Pochon, S. Raimondi, J. F. Valley, “Objective assessment of mammography systems; Part I: Method,” Radiology 156, 215–219 (1985).
[PubMed]

F. O. Bochud, F. R. Verdun, C. Hessler, J. F. Valley, “Detectability on radiological images: the effect of the anatomical noise,” in Medical Imaging 1995: Image Perception, H. L. Kundel, ed., Proc. SPIE2436, 156–164 (1995).
[CrossRef]

Verdun, F. R.

F. O. Bochud, J. F. Valley, F. R. Verdun, C. Hessler, P. Schnyder, “Estimation of the noisy component of anatomical backgrounds,” Med. Phys. 26, 1365–1370 (1999).
[CrossRef] [PubMed]

F. O. Bochud, F. R. Verdun, C. Hessler, J. F. Valley, “Detectability on radiological images: the effect of the anatomical noise,” in Medical Imaging 1995: Image Perception, H. L. Kundel, ed., Proc. SPIE2436, 156–164 (1995).
[CrossRef]

Vodopich, D. J.

F. O. Bochud, C. K. Abbey, J. L. Bartroff, D. J. Vodopich, M. P. Eckstein, “Effect of the number of locations in MAFC experiments performed with mammograms,” presented at the Far West Image Perception Conference, Nakoda Lodge, Alberta, Canada, May 20–30, 1999.

Wagner, R. F.

K. J. Myers, J. P. Rolland, H. H. Barrett, R. F. Wagner, “Aperture optimization for emission imaging: effect of 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 signal determination,” Nature (London) 214, 93–94 (1981).

R. F. Wagner, D. G. Brown, M. S. Pastel, “Application of information theory to the assessment of computed tomography,” Med. Phys. 6, 83–94 (1979).
[CrossRef] [PubMed]

Watson, A. B.

A. B. Watson, J. Solomon, “A model of contrast gain control in human vision,” J. Opt. Soc. Am. A 14, 2379–2391 (1997).
[CrossRef]

M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Visual signal detection in structured backgrounds. II. Effects of contrast gain control, background variations, and white noise,” J. Opt. Soc. Am. A 14, 2406–2419 (1997).
[CrossRef]

M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Image discrimination models predict signal detection in natural medical image backgrounds,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 44–56 (1997).
[CrossRef]

Webster, M. A.

Whiting, J. S.

M. P. Eckstein, J. S. Whiting, “Visual signal detection in structured backgrounds. I. Effect of number of possible spatial locations and signal contrast,” J. Opt. Soc. Am. A 13, 1777–1787 (1996).
[CrossRef]

M. P. Eckstein, C. K. Abbey, J. S. Whiting, “Human vs model observers in anatomic backgrounds,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 15–26 (1998).

M. P. Eckstein, C. K. Abbey, F. O. Bochud, J. L. Bartroff, J. S. Whiting, “Effect of image compression in model and human observers,” in Medical Imaging 1999: Image Perception and Performance, E. A. Krupinski, ed., Proc. SPIE3663, 243–252 (1999).
[CrossRef]

Yao, J.

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

Yu, L.

J. P. Rolland, A. Goon, E. Clarkson, L. Yu, “Synthesis of biomedical tissue,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 85–90 (1998).
[CrossRef]

Am. J. Roentgenol. (1)

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

J. Opt. Soc. Am. A (16)

A. E. Burgess, “The Rose model, revisited,” J. Opt. Soc. Am. A 16, 633–646 (1999).
[CrossRef]

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

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

J. M. Foley, “Human luminance pattern-vision mechanisms: masking experiments require a new model,” J. Opt. Soc. Am. A 11, 1710–1719 (1994).
[CrossRef]

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

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

A. B. Watson, J. Solomon, “A model of contrast gain control in human vision,” J. Opt. Soc. Am. A 14, 2379–2391 (1997).
[CrossRef]

M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Visual signal detection in structured backgrounds. II. Effects of contrast gain control, background variations, and white noise,” J. Opt. Soc. Am. A 14, 2406–2419 (1997).
[CrossRef]

A. E. Burgess, X. Li, C. K. Abbey, “Visual signal detectability with two noise components: anomalous masking effects,” J. Opt. Soc. Am. A 14, 2420–2442 (1997).
[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]

P. F. Judy, R. G. Swensson, “Display thresholding of images and observer detection performance,” J. Opt. Soc. Am. A 4, 954–965 (1987).
[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]

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

M. P. Eckstein, J. S. Whiting, “Visual signal detection in structured backgrounds. I. Effect of number of possible spatial locations and signal contrast,” J. Opt. Soc. Am. A 13, 1777–1787 (1996).
[CrossRef]

M. P. Eckstein, C. K. Abbey, F. O. Bochud, “Visual signal detection in structured backgrounds. IV. Figures of merit for model performance in multiple-alternative forced-choice detection tasks with correlated responses,” J. Opt. Soc. Am. A 17, 206–217 (2000).
[CrossRef]

Kybernetik (1)

R. F. Quick, “A vector-magnitude model of contrast detection,” Kybernetik 16, 65–67 (1974).
[CrossRef] [PubMed]

Med. Phys. (5)

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

R. F. Wagner, D. G. Brown, M. S. Pastel, “Application of information theory to the assessment of computed tomography,” Med. Phys. 6, 83–94 (1979).
[CrossRef] [PubMed]

P. R. Moran, “A physical statistics theory for detectability of a target signal in noisy images. I. Mathematical background, empirical review, and development of theory,” Med. Phys. 9, 401–413 (1982).
[CrossRef] [PubMed]

S. E. Seltzer, P. F. Judy, R. G. Swensson, K. H. Chan, R. D. Nawfel, “Flattening of the contrast-detail curve for large lesions on liver CT images,” Med. Phys. 21, 1547–1555 (1994).
[CrossRef] [PubMed]

F. O. Bochud, J. F. Valley, F. R. Verdun, C. Hessler, P. Schnyder, “Estimation of the noisy component of anatomical backgrounds,” Med. Phys. 26, 1365–1370 (1999).
[CrossRef] [PubMed]

Nature (London) (1)

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal determination,” Nature (London) 214, 93–94 (1981).

Phys. Med. Biol. (4)

L. N. D. Loo, K. Doi, C. E. Metz, “A comparison of physical image quality indices and observer performance in the radiographic detection of nylon beads,” Phys. Med. Biol. 29, 837–856 (1984).
[CrossRef] [PubMed]

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

L. Desponds, C. Depeursinge, M. Grecescu, C. Hessler, A. Samiri, J. F. Valley, “Image quality index (IQI) for screen-film mammography,” Phys. Med. Biol. 36, 19–33 (1991).
[CrossRef] [PubMed]

M. S. Chesters, “Human visual perception and ROC methodology in medical imaging,” Phys. Med. Biol. 37, 1433–1476 (1992).
[CrossRef] [PubMed]

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

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

Radiology (1)

C. Hessler, C. Depeursinge, M. Grecescu, Y. Pochon, S. Raimondi, J. F. Valley, “Objective assessment of mammography systems; Part I: Method,” Radiology 156, 215–219 (1985).
[PubMed]

Sci. Am. (1)

B. Julesz, “Experiments in the visual perception of texture,” Sci. Am. 232, 34–43 (1975).
[CrossRef] [PubMed]

Other (23)

The two-point pdf is, by definition, the pdf of any pair of image points. Therefore the covariance contains only a part of the information contained in the two-point pdf.

J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974).

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

Because this way of generating images induces wraparound effects, the images are actually generated on a larger array at 256×256 pixels and then cropped to 128×128 pixels.

F. O. Bochud, C. K. Abbey, J. L. Bartroff, D. J. Vodopich, M. P. Eckstein, “Effect of the number of locations in MAFC experiments performed with mammograms,” presented at the Far West Image Perception Conference, Nakoda Lodge, Alberta, Canada, May 20–30, 1999.

The Hotelling model, when it is estimated from samples, is often referred to as the Fisher discriminant (see, for instance, Ref. 15).

F. O. Bochud, F. R. Verdun, C. Hessler, J. F. Valley, “Detectability on radiological images: the effect of the anatomical noise,” in Medical Imaging 1995: Image Perception, H. L. Kundel, ed., Proc. SPIE2436, 156–164 (1995).
[CrossRef]

F. O. Bochud, C. K. Abbey, M. P. Eckstein, “Further investigation of the effect of phase spectrum on visual detection in structured backgrounds,” in Medical Imaging 1999: Image Perception and Performance, E. A. Krupinski, ed., Proc. SPIE3663, 273–281 (1999).
[CrossRef]

A. E. Burgess, “Mammographic structure: data preparation and spatial statistics analysis,” in Medical Imaging 1999: Image Processing, K. M. Hanson, ed., Proc. SPIE3661, 642–653 (1999).
[CrossRef]

M. P. Eckstein, C. K. Abbey, J. S. Whiting, “Human vs model observers in anatomic backgrounds,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 15–26 (1998).

For a 2AFC experiment, the response variances do not have to be equal to keep the following result valid.

J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems: Methods from Signal Detection Theory (Academic, New York, 1982).

A. J. Ahumada, B. L. Beard, “Object detection in a noisy scene,” in Human Vision and Electronic Imaging, B. E. Rogowitz, J. P. Allebach, eds., Proc. SPIE2657, 190–199 (1996).
[CrossRef]

H. H. Barrett, C. K. Abbey, B. Gallas, M. P. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient structured noise,” in Medical Imaging 1998: Image Perception, H. L. Kundel, eds., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

M. P. Eckstein, A. J. Ahumada, A. B. Watson, “Image discrimination models predict signal detection in natural medical image backgrounds,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 44–56 (1997).
[CrossRef]

M. P. Eckstein, C. K. Abbey, F. O. Bochud, J. L. Bartroff, J. S. Whiting, “Effect of image compression in model and human observers,” in Medical Imaging 1999: Image Perception and Performance, E. A. Krupinski, ed., Proc. SPIE3663, 243–252 (1999).
[CrossRef]

, “Medical imaging—the assessment of image quality,” (ICRU, Bethesda, Md.), 1996.

In this paper we restricted ourselves to tasks where each possible signal location of the multiple-alternative forced-choice (MAFC) experiment is within a different independent sample background. This restriction guarantees the statistical independence of the model responses. Violations of statistical independence in model responses such as might occur in within-image MAFC tasks is investigated in detail in Paper IV in this series.18

J. P. Rolland, A. Goon, E. Clarkson, L. Yu, “Synthesis of biomedical tissue,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 85–90 (1998).
[CrossRef]

B. Picinbono, Random Signals and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1993).

The concept of stationarity is usually defined more stringently. For instance, a random function g(r) is said to be strictly stationary if all its statistical properties are invariant to any translation of the coordinate system. This means that the random functions g(r) and g(r+r0) have the same pdf for any r0. Because the full pdf of a random function is often difficult (or impossible) to compute, a wider definition limited to the mean and the covariance of the random function is also used. A random process g(r) is said to be second-order (or wide-sense, or weakly) stationary if it meets the three conditions of semistationarity but for the whole 2D space. Because any real image is defined within a finite area, the concepts of strict stationarity and second-order stationarity cannot be applied to medical images.

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

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]

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Figures (10)

Fig. 1
Fig. 1

Areas of the breast investigated: (a) areas close to the nipple and centered in the breast tissue and (b) ensemble of areas distributed all over the breast.

Fig. 2
Fig. 2

Contour plots of pixel (a) mean and (b) standard deviation of an ensemble of 128×128-pixel image samples close to the nipple. The value 0 corresponds to black, and 255 corresponds to white.

Fig. 3
Fig. 3

Contour plots of pixel (a) mean and (b) standard deviation of an ensemble of 128×128-pixel image samples centered in the breast.

Fig. 4
Fig. 4

Contour plots of pixel (a) mean and (b) standard deviation of an ensemble of 286 real mammographic image samples of 128×128 pixels.

Fig. 5
Fig. 5

Contour plots of pixel (a) mean and (b) standard deviation of an ensemble of 286 random-phase image samples of 128×128 pixels.

Fig. 6
Fig. 6

Contour plots of pixel (a) mean and (b) standard deviation of an ensemble of 424 angiographic image samples of 128×128 pixels.

Fig. 7
Fig. 7

NPWE detectability indexes (d and d2AFC) computed for different integrating sizes on the mammographic structured background (multiplicative signal). Error bars are standard errors. The vertical dashed line corresponds to the signal diameter.

Fig. 8
Fig. 8

Detectability d computed by all the investigated methods. Empty symbols represent the direct applications of the template (△: patient-structured background, □: random phase). Full symbols correspond to a closed-form expression with different assumptions about image stationarity (▲: nonstationary, ■: semistationary, josaa-17-2-193-i001: locally stationary).

Fig. 9
Fig. 9

Examples of 2D power spectra of power-law image noises (β=3.5) in logarithmic scale with the zero frequency at the center: (a) “true” power spectrum, (b) without window, (c) with window.

Fig. 10
Fig. 10

Radially averaged power spectra with and without using a window compared with the true power spectrum.

Equations (41)

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

Kg(r1, r2)=g(r1)g(r2)-g(r1)g(r2),
Kg(r1, r2)=Cg(r1-r2).
Ng(u)=FT{Cg(r)},
Kg(r1, r2)=a(r1)a(r2)Cg0(r1-r2),
Kg(r1, r2)a2r1+r22Cg0(r1-r2).
σg2(r1)a2r1+r12Cg0(0)=a2(r1)σg02,
g(r1)=a(r1)g¯0.
λ=wTg,
d=λs-λb[12(σs2+σb2)]1/2,
Pc=-ΦM-1(x+dMAFC)ϕ(x)dx,
gs;m=(S+I)b,gs;a=s+b,
dadd=wTs(wTKbw)1/2,
dmult=b¯wTs[wT12(Ks+Kb)w]1/2,
dadd=w˜Hs˜(w˜HK˜bw˜)1/2,
dmult=b¯w˜Hs˜[12w˜H(K˜s+K˜b)w˜]1/2,
dadd=w˜*(u)s˜(u)du|w˜(u)|2Nb(u)du1/2,
w=ETEs.
dNPWE;a=sTETEs(sTETEKbETEs)1/2,
dNPWE;m=b¯sTETEs{sTETE12[(S+I)Kb(S+I)+Kb]ETEs}1/2.
dNPWE;a
=j=0n2-1|s˜[j]|2|E˜[j, j]|2j=0n2-1|s˜[j]|2|E˜[j, j]|4K˜b[j, j]1/2,
dNPWE;m
=2b¯j=0n2-1|s˜[j]|2|E˜[j, j]|2j=0n2-1(|s˜1[j]|2+|s˜[j]|2|E˜[j, j]|4)K˜b[j, j]1/2,
dNPWE;a=|s˜(u)|2|E˜(u)|2 du|s˜(u)|2|E˜(u)|4Nb(u)du1/2,
dNPWE;m=2b¯|s˜(u)|2|E˜(u)|2 du[|s˜1(u)|2+|s˜(u)|2|E˜(u)|4]Nb(u)du1/2,
αNPWE;a=σglobalσlocal,αNPWE;m=σglobalσlocalb¯localb¯global,
N(u)=limA1AA[g(r)-g(r)]exp(-2πiur)dr2,
Nwindow(u)=|h˜(u-u1)|2Ntrue(u1)du1.
N(u)=αuβ,
h1(x)
=1πsin πxrw+1-|x|rwcos πxrw,|x|rw0,|x|>rw.
gb;a=b,gs;a=s+b,
gb;m=b,gs;m=(S+I)b,
λ(gb;a)=λ(gb;m)=b¯wT1,
λ(gs;a)=b¯wT1+wTs,
λ(gs;m)=b¯wT(s+1).
σ2{λ(gb;a)}=σ2{λ(gb;m)}=wTKbw,
σ2{λ(gs;a)}=wTKbw,
σ2{λ(gs;m)}=wT(S+I)Kb(S+I)w.
dadd=wTs(wTKbw)1/2,
dmult=b¯wTs{wT12[(S+I)Kb(S+I)+Kb]w}1/2,

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