Abstract

Detection of signals in natural images and scenes is limited by both noise and structure. The purpose of this study is to investigate phenomenological issues of signal detection in two-component noise. One component had a broadband (white) spectrum designed to simulate image noise. The other component was filtered to simulate two classes of low-pass background structure spectra: Gaussian-filtered noise and power-law noise. Measurements of human and model observer performance are reported for several aperiodic signals and both classes of background spectra. Human results are compared with two classes of observer models and are fitted very well by suboptimal prewhitening matched filter models. The nonprewhitening model with an eye filter does not agree with human results when background-noise-component power spectrum bandwidths are less than signal energy bandwidths.

© 1999 Optical Society of America

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1997 (4)

1996 (2)

1994 (5)

F. Lefebvre, H. Benali, R. Gilles, R. DiPaola, “A simulation model of microcalcifications in digital mammograms,” Med. Phys. 21, 1865–1874 (1994).
[CrossRef] [PubMed]

A. E. Burgess, “Statistically defined backgrounds: performance of a modified nonprewhitening matched filter model,” J. Opt. Soc. Am. A 11, 1237–42 (1994).
[CrossRef]

J. A. Solomon, D. G. Pelli, “The visual filter mediating letter identification,” Nature 369, 395–397 (1994).
[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 lesion in CT liver images,” Med. Phys. 21, 1547–1555 (1994).
[CrossRef] [PubMed]

D. L. Ruderman, W. Bialeck, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994).
[CrossRef] [PubMed]

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 (3)

Y. Tadmor, D. J. Tolhurst, “Both the phase and the amplitude spectrum may determine the appearance of natural images,” Vision Res. 33, 141–145 (1992).
[CrossRef]

J. H. van Hateren, “Theoretical predictions of spatiotemporal receptive fields of fly LMCs and experimental validation,” J. Comp. Physiol. A 171, 157–170 (1992).

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]

1990 (1)

1988 (1)

1987 (4)

1985 (2)

1984 (1)

1983 (2)

G. Buchsbaum, A. Gottschalk, “Trichromaticity, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).
[CrossRef]

A. B. Watson, D. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

1977 (1)

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

1974 (1)

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

1954 (1)

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

Abbey, C. K.

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]

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]

Ahumada, A. J.

Barrett, H. H.

Barten, P. G. J.

P. G. J. Barten, “The SQRI method: a new method for the evaluation of visible resolution on a display,” Proc. Soc. Inf. Disp. 28, 253–262 (1987).

Beard, B. L.

Benali, H.

F. Lefebvre, H. Benali, R. Gilles, R. DiPaola, “A simulation model of microcalcifications in digital mammograms,” Med. Phys. 21, 1865–1874 (1994).
[CrossRef] [PubMed]

Bendat, J. S.

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

Beue, G. H.

E. Samei, M. J. Flynn, G. H. Beue, E. Peterson, “Comparison of observer performance for real and simulated nodues in chest radiography,” in Medical Imaging: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 60–70 (1996).
[CrossRef]

Bialeck, W.

D. L. Ruderman, W. Bialeck, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994).
[CrossRef] [PubMed]

Birdsall, T. G.

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.

Bouchud, F. O.

F. O. Bouchud, F. R. Verdun, J. F. Valley, C. Hessler, R. Moeckli, “The importance of anatomical noise in mammography,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 74–80 (1997).
[CrossRef]

F. O. Bouchud, F. R. Verdun, C. Hessler, J. F. Valley, “Detectability on radiological images: the influence of anatomical noise,” in Medical Imaging 1995: Image Perception, H. L. Kundel, ed., Proc. SPIE2436, 156–165 (1995).
[CrossRef]

Brown, D. G.

R. F. Wagner, M. F. Insana, D. G. Brown, B. S. Garra, R. J. Jennings, “Texture discrimination: radiologist, machine and man,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, London, 1990), pp. 310–318.

Buchsbaum, G.

G. Buchsbaum, A. Gottschalk, “Trichromaticity, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).
[CrossRef]

Burgess, A. E.

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]

A. E. Burgess, “Statistically defined backgrounds: performance of a modified nonprewhitening matched filter model,” J. Opt. Soc. Am. A 11, 1237–42 (1994).
[CrossRef]

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

A. E. Burgess, K. Humphrey, R. F. Wagner, “Detection of bars and discs in quantum noise,” in Application of Optical Instrumentation in Medicine VII, J. E. Gray, ed., Proc. SPIE173, 34–40 (1979).
[CrossRef]

A. E. Burgess, “Prewhitening revisited,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 55–64 (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]

Castleman, K. R.

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

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 lesion in CT liver images,” Med. Phys. 21, 1547–1555 (1994).
[CrossRef] [PubMed]

Chang, Y-H.

B. Zheng, Y-H. Chang, D. Gur, “Adaptive computer-aided diagnosis scheme of digitized mammograms,” Acad. Radiol. 3, 806–814 (1996).
[CrossRef] [PubMed]

Colborne, B.

DiPaola, R.

F. Lefebvre, H. Benali, R. Gilles, R. DiPaola, “A simulation model of microcalcifications in digital mammograms,” Med. Phys. 21, 1865–1874 (1994).
[CrossRef] [PubMed]

Eckstein, M. P.

Field, D.

Fiete, R. D.

Flynn, M. J.

E. Samei, M. J. Flynn, G. H. Beue, E. Peterson, “Comparison of observer performance for real and simulated nodues in chest radiography,” in Medical Imaging: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 60–70 (1996).
[CrossRef]

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]

Garra, B. S.

R. F. Wagner, M. F. Insana, D. G. Brown, B. S. Garra, R. J. Jennings, “Texture discrimination: radiologist, machine and man,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, London, 1990), pp. 310–318.

Ghandeharian, H.

Gilles, R.

F. Lefebvre, H. Benali, R. Gilles, R. DiPaola, “A simulation model of microcalcifications in digital mammograms,” Med. Phys. 21, 1865–1874 (1994).
[CrossRef] [PubMed]

Gottschalk, A.

G. Buchsbaum, A. Gottschalk, “Trichromaticity, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).
[CrossRef]

Graham, N.

N. Graham, “Complex channels, early nonlinearities, and normalization in texture segregation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Mov-shon, eds. (MIT, Cambridge, Mass., 1991), pp. 273–290.

Gur, D.

B. Zheng, Y-H. Chang, D. Gur, “Adaptive computer-aided diagnosis scheme of digitized mammograms,” Acad. Radiol. 3, 806–814 (1996).
[CrossRef] [PubMed]

Hessler, C.

F. O. Bouchud, F. R. Verdun, J. F. Valley, C. Hessler, R. Moeckli, “The importance of anatomical noise in mammography,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 74–80 (1997).
[CrossRef]

F. O. Bouchud, F. R. Verdun, C. Hessler, J. F. Valley, “Detectability on radiological images: the influence of anatomical noise,” in Medical Imaging 1995: Image Perception, H. L. Kundel, ed., Proc. SPIE2436, 156–165 (1995).
[CrossRef]

Humphrey, K.

A. E. Burgess, K. Humphrey, R. F. Wagner, “Detection of bars and discs in quantum noise,” in Application of Optical Instrumentation in Medicine VII, J. E. Gray, ed., Proc. SPIE173, 34–40 (1979).
[CrossRef]

Insana, M. F.

R. F. Wagner, M. F. Insana, D. G. Brown, B. S. Garra, R. J. Jennings, “Texture discrimination: radiologist, machine and man,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, London, 1990), pp. 310–318.

Jennings, R. J.

R. F. Wagner, M. F. Insana, D. G. Brown, B. S. Garra, R. J. Jennings, “Texture discrimination: radiologist, machine and man,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, London, 1990), pp. 310–318.

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 lesion in CT liver images,” Med. Phys. 21, 1547–1555 (1994).
[CrossRef] [PubMed]

P. F. Judy, “Detection of clusters of simulated calcifications in lumpy noise backgrounds,” in Medical Imaging: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 39–46 (1996).
[CrossRef]

Kersten, D.

Knill, D.

Lanyi, M.

M. Lanyi, Diagnosis and Differential Diagnosis of Breast Calcifications (Springer-Verlag, Berlin, 1986).

Lefebvre, F.

F. Lefebvre, H. Benali, R. Gilles, R. DiPaola, “A simulation model of microcalcifications in digital mammograms,” Med. Phys. 21, 1865–1874 (1994).
[CrossRef] [PubMed]

Li, X.

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]

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]

Miyahara, E.

Moeckli, R.

F. O. Bouchud, F. R. Verdun, J. F. Valley, C. Hessler, R. Moeckli, “The importance of anatomical noise in mammography,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 74–80 (1997).
[CrossRef]

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 lesion in CT liver 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]

Patton, D. D.

Pelli, D.

A. B. Watson, D. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

Pelli, D. G.

J. A. Solomon, D. G. Pelli, “The visual filter mediating letter identification,” Nature 369, 395–397 (1994).
[CrossRef] [PubMed]

Pentland, A.

A. Pentland, “Fractal-based descriptions of surfaces,” in Natural Computation, W. Richards, ed. (MIT, Cambridge, Mass., 1988), pp. 279–299.

Peterson, E.

E. Samei, M. J. Flynn, G. H. Beue, E. Peterson, “Comparison of observer performance for real and simulated nodues in chest radiography,” in Medical Imaging: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 60–70 (1996).
[CrossRef]

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).

Quick, R. F.

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

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]

Ruderman, D. L.

D. L. Ruderman, W. Bialeck, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994).
[CrossRef] [PubMed]

Samei, E.

E. Samei, M. J. Flynn, G. H. Beue, E. Peterson, “Comparison of observer performance for real and simulated nodues in chest radiography,” in Medical Imaging: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 60–70 (1996).
[CrossRef]

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 lesion in CT liver images,” Med. Phys. 21, 1547–1555 (1994).
[CrossRef] [PubMed]

Smith, W. E.

Solomon, J. A.

J. A. Solomon, D. G. Pelli, “The visual filter mediating letter identification,” Nature 369, 395–397 (1994).
[CrossRef] [PubMed]

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 lesion in CT liver images,” Med. Phys. 21, 1547–1555 (1994).
[CrossRef] [PubMed]

Tadmor, Y.

Y. Tadmor, D. J. Tolhurst, “Both the phase and the amplitude spectrum may determine the appearance of natural images,” Vision Res. 33, 141–145 (1992).
[CrossRef]

Tolhurst, D. J.

Y. Tadmor, D. J. Tolhurst, “Both the phase and the amplitude spectrum may determine the appearance of natural images,” Vision Res. 33, 141–145 (1992).
[CrossRef]

Valley, J. F.

F. O. Bouchud, F. R. Verdun, J. F. Valley, C. Hessler, R. Moeckli, “The importance of anatomical noise in mammography,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 74–80 (1997).
[CrossRef]

F. O. Bouchud, F. R. Verdun, C. Hessler, J. F. Valley, “Detectability on radiological images: the influence of anatomical noise,” in Medical Imaging 1995: Image Perception, H. L. Kundel, ed., Proc. SPIE2436, 156–165 (1995).
[CrossRef]

van Hateren, J. H.

J. H. van Hateren, “Theoretical predictions of spatiotemporal receptive fields of fly LMCs and experimental validation,” J. Comp. Physiol. A 171, 157–170 (1992).

Verdun, F. R.

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Figures (7)

Fig. 1
Fig. 1

(a) Examples of radial power spectra (log scale) with Gaussian-filtered N2 noise components. Four N2 correlation distances are shown (1, 2, 4, and 8 pixels). All the N2 components had rms noise amplitude of 16 gray levels. The N1 whitenoise-component spectrum had rms amplitude of eight gray levels. The energy spectrum of the Gaussian signal (s=3 pixels) is also shown. (b) Examples of radial power spectra for power-law N2 noise components (log scale). Four N2 exponents are shown (1, 2, 3, and 4). All the N2 components had rms noise amplitude of 16 gray levels. The N1 white-noise-component spectrum had rms amplitude of eight gray levels.

Fig. 2
Fig. 2

(a) Example noise images with N2 Gaussian power spectra. Correlation distances are 1, 2, 4, and 8 pixels for the quadrants in the upper left, upper right, lower left, and lower right, respectively. (b) Examples noise with N2 power-law spectra. Exponents are 1, 2, 3, and 4 for the quadrants in the upper left, upper right, lower left, and lower right, respectively.

Fig. 3
Fig. 3

Images of the signals used in these experiments: two-dimensional Gaussian on the upper left, nodule (n=1.5) on the upper right, and MCC below. Note that the images are not to scale; the Gaussian and the nodule signals are magnified relative to the MCC signal.

Fig. 4
Fig. 4

(a) Amplitude thresholds for Gaussian signal (s=3 pixels) detection as a function of log(correlation distance) (corr dist, in pixels) of the N2 noise with Gaussian power spectra. Data are for four well-trained human observers and three models: a prewhitening matched filter model with an eye filter and internal noise (PWE model), a PW approximation with spatial-frequency channels (PWCavg), and a nonprewhitening model with an eye filter (NPWE model). The model data are β scaled ( for induced internal noise as described in the text) to fit average human data for the two shortest correlation distances (average efficiency, 0.45). The average human threshold for N1 noise only is also shown. (b) Observer detection efficiency (log scale) based on the same human and model data as in (a).

Fig. 5
Fig. 5

(a) Amplitude threshold for nodule signal (μ=1.5, R=4 pixels) detection as a function of N2 log(correlation distance). Data are for four human observers and three models. The model data are β scaled to fit average human data for the two shortest correlation distances (average efficiency, 0.58). The human threshold for N1 only is also shown. (b) Observer detection efficiency (log scale) based on the same data as in (a).

Fig. 6
Fig. 6

(a) Amplitude threshold for nodule signal (μ=1.5, R=4 pixels) detection as a function of exponent of the N2 power-law noise. Data are for four human observers and three models. The model data are β scaled to fit average human data for the two lowest exponents (average efficiency, 0.51). The average human threshold for N1 only is also shown. (b) Observer efficiency (log scale) based on the same data as in (a).

Fig. 7
Fig. 7

(a) Amplitude threshold for MCC (five elements) detection as a function of exponent of the N2 power-law noise. Data are for four human observers and three models. The model data are β scaled to fit average human data for the two lowest exponents (average efficiency, 0.13). The average human threshold for N1 only is also shown. (b) Observer efficiency (log scale) based on the same data as in (a).

Tables (1)

Tables Icon

Table 1 Parameters Used to Scale Observer Models to Fit Average Human Observer Efficiencies (Eff.) for Two Types of N2 Noise Power Spectrum and Three Signalsa

Equations (7)

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(dI)2=2π0|S(f)|2fdfN1(f)+N2(f).
(dPWE)2=2π0E(f)2|S(f)|2fdfE(f)2(1+β)[N1(f)+N2(f)]+Nint.
(dPWC)f02=i=1NVi(f0), Vi=2π0S(f)E(f)Ci(f)fdf22π0E(f)2(1+β)[N1(f)+N2(f)+Nint]C(f)i2fdf.
(dNPWE)2=2π0|S(f)|2|E(f)|2fdf22π0{|E(f)|4(1+β)[N1(f)+N2(f)]+Nint}|S(f)|2fdf.
σβ2=2π0W(f)fdf=2πK201/2cos(πf)(f0β+fβ)fdf.
Ct2=aN0+bNi.
(d0/d)2=1+βNx,

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