Abstract

Classification-image analysis has proven to be a valuable tool for revealing features used to perform visual tasks in noise. We use this methodology to investigate how the magnitude of noise influences detection mechanisms, and more specifically, to examine whether observers use a consistent perceptual template across noise magnitude as is often assumed in models. The experiments consist of 2AFC detection of a Gaussian target profile in white noise with RMS contrast levels ranging from 1.25% to 20%. Target contrast was manipulated to maintain a performance level of approximately 80% correct at each noise level. The estimated classification images are presented along with a spatial frequency analysis that consists of radial averages of the frequency domain. The resulting frequency weights show significant within-subject differences across noise levels, as do sampling efficiencies derived from these frequency weights. At low levels of external noise, the classification images are attenuated at low spatial frequencies, giving rise to a more bandpass appearance. At high noise levels, the spatial frequency weights have much less low-frequency attenuation, making them closer to an ideal matched filter. Our results provide direct evidence against the notion of a single consistent perceptual template mediating detection across different levels of noise.

© 2009 Optical Society of America

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2009

A. Tavassoli, I. Linde, A. C. Bovik, and L. K. Cormack, “Eye movements selective for spatial frequency and orientation during active visual search,” Vision Res. 49, 173-181 (2009).
[CrossRef]

S. Zhang, C. K. Abbey, and M. P. Eckstein, “Virtual evolution for visual search in natural images results in behavioral receptive fields with inhibitory surrounds,” Visual Neurosci. 26, 93-108 (2009).
[CrossRef]

2008

Z. L. Lu and B. A. Dosher, “Characterizing observers using external noise and observer models: assessing internal representations with external noise,” Psychol. Rev. 115, 44-82 (2008).
[CrossRef] [PubMed]

2007

C. J. Ludwig, M. P. Eckstein, and B. R. Beutter, “Limited flexibility in the filter underlying saccadic targeting,” Vision Res. 47, 280-288 (2007).
[CrossRef]

C. K. Abbey and M. P. Eckstein, “Classification images for simple detection and discrimination tasks in correlated noise,” J. Opt. Soc. Am. A 24, B110-B124 (2007).
[CrossRef]

2006

I. Oruc, M. S. Landy, and D. G. Pelli, “Noise masking reveals channels for second-order letters,” Vision Res. 46, 1493-1506 (2006).
[CrossRef]

Y. Zhang, C. K. Abbey, and M. P. Eckstein, “Adaptive detection mechanisms in globally statistically nonstationary-oriented noise,” J. Opt. Soc. Am. A 23, 1549-1558 (2006).
[CrossRef]

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

I. Kurki, A. Hyvärinen, and P. I. Laurinen, “Characterising signal and noise in contrast detection by classification images,” Perception 35 (ECVP Abstract Supplement), 89 (2006).

2005

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

2004

Y. Morgenstern, J. H. Elder, and Y. Hou, “Contrast dependence of spatial summation revealed by classification image analysis,” J. Vision 4, 439a (2004). (Vision Science Society Abstract Supplement).
[CrossRef]

2002

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

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

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

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

J. A. Solomon, “Noise reveals visual mechanisms of detection and discrimination,” J. Vision 2, 105-120 (2002).
[CrossRef]

P. G. Schyns, L. Bonnar, and F. Gosselin, “Show me the features! Understanding recognition from the use of visual information,” Psychol. Sci. 13, 402-409 (2002).
[CrossRef] [PubMed]

N. J. Majaj, D. G. Pelli, P. Kurshan, and M. Palomares, “The role of spatial frequency channels in letter identification,” Vision Res. 42, 1165-1184 (2002).
[CrossRef] [PubMed]

2001

F. Gosselin and P. G. Schyns, “Bubbles: a technique to reveal the use of information in recognition tasks,” Vision Res. 41, 2261-2271 (2001).
[CrossRef] [PubMed]

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

Z. L. Lu and B. A. Dosher, “Characterizing the spatial-frequency sensitivity of perceptual templates,” J. Opt. Soc. Am. A 18, 2041-2053 (2001).
[CrossRef]

2000

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

J. M. Gold, R. F. Murray, P. J. Bennett, and A. B. Sekuler, “Deriving behavioural receptive fields for visually completed contours,” Curr. Biol. 10, 663-666 (2000).
[CrossRef] [PubMed]

1999

1998

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

Z. L. Lu and B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183-1198 (1998).
[CrossRef] [PubMed]

1997

1996

A. J. Ahumada, “Classification images from Vernier acuity masked by noise,” Perception 25, 18 (1996). (ECVP Abstract Supplement).

1994

1993

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

1990

1988

1987

1985

A. J. Ahumada, Jr. and A. B. Watson, “Equivalent-noise model for contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1133-1139 (1985).
[CrossRef] [PubMed]

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

1984

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

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

1983

H. R. Wilson, D. K. McFarlane, and G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873-882 (1983).
[CrossRef] [PubMed]

1981

J. M. Foley and G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041-1053 (1981).
[CrossRef] [PubMed]

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

P. F. Judy, R. G. Swensson, and M. Szulc, “Lesion detection and signal-to-noise ratio in CT images,” Med. Phys. 8, 13-23 (1981).
[CrossRef] [PubMed]

1980

H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybern. 38, 171-178 (1980).
[CrossRef] [PubMed]

1975

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

1974

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

1972

1971

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

1964

1958

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

1954

W. W. Peterson, T. G. Birdsall, and W. C. Fox, “The theory of signal detectability,” Trans. IRE-PGIT 4, 171-212 (1954).

Abbey, C. K.

S. Zhang, C. K. Abbey, and M. P. Eckstein, “Virtual evolution for visual search in natural images results in behavioral receptive fields with inhibitory surrounds,” Visual Neurosci. 26, 93-108 (2009).
[CrossRef]

C. K. Abbey and M. P. Eckstein, “Classification images for simple detection and discrimination tasks in correlated noise,” J. Opt. Soc. Am. A 24, B110-B124 (2007).
[CrossRef]

Y. Zhang, C. K. Abbey, and M. P. Eckstein, “Adaptive detection mechanisms in globally statistically nonstationary-oriented noise,” J. Opt. Soc. Am. A 23, 1549-1558 (2006).
[CrossRef]

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

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

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

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

C. K. Abbey and F. O. Bochud, “Modeling visual detection tasks in correlated noise with linear model observers,” in Handbook of Medical Imaging, J.Beutel, H.L.Kundel, and R.L.Van Metter, eds. (SPIE Press, 2000), pp. 629-654.

Ahumada, A.

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

Ahumada, A. J.

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

M. P. Eckstein, A. J. Ahumada, Jr., and 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. J. Ahumada, “Classification images from Vernier acuity masked by noise,” Perception 25, 18 (1996). (ECVP Abstract Supplement).

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

A. J. Ahumada, Jr. and A. B. Watson, “Equivalent-noise model for contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1133-1139 (1985).
[CrossRef] [PubMed]

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

Barlow, H. B.

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

Barrett, H. H.

Beard, B. L.

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

Bennett, P. J.

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

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

J. M. Gold, R. F. Murray, P. J. Bennett, and A. B. Sekuler, “Deriving behavioural receptive fields for visually completed contours,” Curr. Biol. 10, 663-666 (2000).
[CrossRef] [PubMed]

Beutter, B. R.

C. J. Ludwig, M. P. Eckstein, and B. R. Beutter, “Limited flexibility in the filter underlying saccadic targeting,” Vision Res. 47, 280-288 (2007).
[CrossRef]

Birdsall, T. G.

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

W. W. Peterson, T. G. Birdsall, and W. C. Fox, “The theory of signal detectability,” Trans. IRE-PGIT 4, 171-212 (1954).

Bochud, F. O.

C. K. Abbey and F. O. Bochud, “Modeling visual detection tasks in correlated noise with linear model observers,” in Handbook of Medical Imaging, J.Beutel, H.L.Kundel, and R.L.Van Metter, eds. (SPIE Press, 2000), pp. 629-654.

Bonnar, L.

P. G. Schyns, L. Bonnar, and F. Gosselin, “Show me the features! Understanding recognition from the use of visual information,” Psychol. Sci. 13, 402-409 (2002).
[CrossRef] [PubMed]

Bovik, A. C.

A. Tavassoli, I. Linde, A. C. Bovik, and L. K. Cormack, “Eye movements selective for spatial frequency and orientation during active visual search,” Vision Res. 49, 173-181 (2009).
[CrossRef]

Brown, D. G.

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

Burgess, A.

Burgess, A. E.

Colborne, B.

Cormack, L. K.

A. Tavassoli, I. Linde, A. C. Bovik, and L. K. Cormack, “Eye movements selective for spatial frequency and orientation during active visual search,” Vision Res. 49, 173-181 (2009).
[CrossRef]

Dosher, B. A.

Z. L. Lu and B. A. Dosher, “Characterizing observers using external noise and observer models: assessing internal representations with external noise,” Psychol. Rev. 115, 44-82 (2008).
[CrossRef] [PubMed]

Z. L. Lu and B. A. Dosher, “Characterizing the spatial-frequency sensitivity of perceptual templates,” J. Opt. Soc. Am. A 18, 2041-2053 (2001).
[CrossRef]

Z. L. Lu and B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183-1198 (1998).
[CrossRef] [PubMed]

Eckstein, M. P.

S. Zhang, C. K. Abbey, and M. P. Eckstein, “Virtual evolution for visual search in natural images results in behavioral receptive fields with inhibitory surrounds,” Visual Neurosci. 26, 93-108 (2009).
[CrossRef]

C. J. Ludwig, M. P. Eckstein, and B. R. Beutter, “Limited flexibility in the filter underlying saccadic targeting,” Vision Res. 47, 280-288 (2007).
[CrossRef]

C. K. Abbey and M. P. Eckstein, “Classification images for simple detection and discrimination tasks in correlated noise,” J. Opt. Soc. Am. A 24, B110-B124 (2007).
[CrossRef]

Y. Zhang, C. K. Abbey, and M. P. Eckstein, “Adaptive detection mechanisms in globally statistically nonstationary-oriented noise,” J. Opt. Soc. Am. A 23, 1549-1558 (2006).
[CrossRef]

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

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

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

M. P. Eckstein, A. J. Ahumada, Jr., and 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]

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Y. Morgenstern, J. H. Elder, and Y. Hou, “Contrast dependence of spatial summation revealed by classification image analysis,” J. Vision 4, 439a (2004). (Vision Science Society Abstract Supplement).
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Farell, B.

Field, D. J.

Fiete, R. D.

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J. M. Foley and G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041-1053 (1981).
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J. M. Gold, R. F. Murray, P. J. Bennett, and A. B. Sekuler, “Deriving behavioural receptive fields for visually completed contours,” Curr. Biol. 10, 663-666 (2000).
[CrossRef] [PubMed]

Gosselin, F.

P. G. Schyns, L. Bonnar, and F. Gosselin, “Show me the features! Understanding recognition from the use of visual information,” Psychol. Sci. 13, 402-409 (2002).
[CrossRef] [PubMed]

F. Gosselin and P. G. Schyns, “Bubbles: a technique to reveal the use of information in recognition tasks,” Vision Res. 41, 2261-2271 (2001).
[CrossRef] [PubMed]

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G. Revesz, H. L. Kundel, and M. A. Graber, “The influence of structured noise on the detection of radiologic abnormalities,” Invest. Radiol. 9, 479-486 (1974).
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D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (Peninsula, 1988).

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Hou, Y.

Y. Morgenstern, J. H. Elder, and Y. Hou, “Contrast dependence of spatial summation revealed by classification image analysis,” J. Vision 4, 439a (2004). (Vision Science Society Abstract Supplement).
[CrossRef]

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I. Kurki, A. Hyvärinen, and P. I. Laurinen, “Characterising signal and noise in contrast detection by classification images,” Perception 35 (ECVP Abstract Supplement), 89 (2006).

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

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Kersten, D.

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

Kundel, H. L.

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

Kurki, I.

I. Kurki, A. Hyvärinen, and P. I. Laurinen, “Characterising signal and noise in contrast detection by classification images,” Perception 35 (ECVP Abstract Supplement), 89 (2006).

Kurshan, P.

N. J. Majaj, D. G. Pelli, P. Kurshan, and M. Palomares, “The role of spatial frequency channels in letter identification,” Vision Res. 42, 1165-1184 (2002).
[CrossRef] [PubMed]

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I. Oruc, M. S. Landy, and D. G. Pelli, “Noise masking reveals channels for second-order letters,” Vision Res. 46, 1493-1506 (2006).
[CrossRef]

Laurinen, P. I.

I. Kurki, A. Hyvärinen, and P. I. Laurinen, “Characterising signal and noise in contrast detection by classification images,” Perception 35 (ECVP Abstract Supplement), 89 (2006).

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G. E. Legge, D. Kersten, and A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. A 4, 391-404 (1987).
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J. M. Foley and G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041-1053 (1981).
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Linde, I.

A. Tavassoli, I. Linde, A. C. Bovik, and L. K. Cormack, “Eye movements selective for spatial frequency and orientation during active visual search,” Vision Res. 49, 173-181 (2009).
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A. J. Ahumada and J. Lovell, “Stimulus features in signal detection,” J. Acoust. Soc. Am. 49, 1751-1756 (1971).
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Z. L. Lu and B. A. Dosher, “Characterizing observers using external noise and observer models: assessing internal representations with external noise,” Psychol. Rev. 115, 44-82 (2008).
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C. J. Ludwig, M. P. Eckstein, and B. R. Beutter, “Limited flexibility in the filter underlying saccadic targeting,” Vision Res. 47, 280-288 (2007).
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N. J. Majaj, D. G. Pelli, P. Kurshan, and M. Palomares, “The role of spatial frequency channels in letter identification,” Vision Res. 42, 1165-1184 (2002).
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I. Oruc, M. S. Landy, and D. G. Pelli, “Noise masking reveals channels for second-order letters,” Vision Res. 46, 1493-1506 (2006).
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N. J. Majaj, D. G. Pelli, P. Kurshan, and M. Palomares, “The role of spatial frequency channels in letter identification,” Vision Res. 42, 1165-1184 (2002).
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I. Oruc, M. S. Landy, and D. G. Pelli, “Noise masking reveals channels for second-order letters,” Vision Res. 46, 1493-1506 (2006).
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H. R. Wilson, D. K. McFarlane, and G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873-882 (1983).
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D. Q. Nykamp and D. L. Ringach, “Full identification of a linear-nonlinear system via cross-correlation analysis,” J. Vision 2, 1-11 (2002).
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H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).
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P. G. Schyns, L. Bonnar, and F. Gosselin, “Show me the features! Understanding recognition from the use of visual information,” Psychol. Sci. 13, 402-409 (2002).
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F. Gosselin and P. G. Schyns, “Bubbles: a technique to reveal the use of information in recognition tasks,” Vision Res. 41, 2261-2271 (2001).
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R. F. Murray, P. J. Bennett, and A. B. Sekuler, “Classification images predict absolute efficiency,” J. Vision 5, 139-149 (2005).
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J. A. Solomon, “Noise reveals visual mechanisms of detection and discrimination,” J. Vision 2, 105-120 (2002).
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S. Zhang, C. K. Abbey, and M. P. Eckstein, “Virtual evolution for visual search in natural images results in behavioral receptive fields with inhibitory surrounds,” Visual Neurosci. 26, 93-108 (2009).
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Biol. Cybern.

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Curr. Biol.

J. M. Gold, R. F. Murray, P. J. Bennett, and A. B. Sekuler, “Deriving behavioural receptive fields for visually completed contours,” Curr. Biol. 10, 663-666 (2000).
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A. P. Pentland, “Fractal-based description of natural scenes,” IEEE Trans. Pattern Anal. Mach. Intell. 6, 661-673 (1984).
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G. Revesz, H. L. Kundel, and M. A. Graber, “The influence of structured noise on the detection of radiologic abnormalities,” Invest. Radiol. 9, 479-486 (1974).
[CrossRef] [PubMed]

J. Acoust. Soc. Am.

W. P. Tanner and T. G. Birdsall, “Definitions of d′ and η as psychophysical measures,” J. Acoust. Soc. Am. 30, 922-928 (1958).
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A. J. Ahumada and J. Lovell, “Stimulus features in signal detection,” J. Acoust. Soc. Am. 49, 1751-1756 (1971).
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A. Ahumada, Jr. and R. Marken, “Time and frequency analyses of auditory signal detection,” J. Acoust. Soc. Am. 57, 385-390 (1975).
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J. Opt. Soc. Am. A

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D. G. Pelli and B. Farell, “Why use noise?” J. Opt. Soc. Am. A 16, 647-653 (1999).
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Z. L. Lu and B. A. Dosher, “Characterizing the spatial-frequency sensitivity of perceptual templates,” J. Opt. Soc. Am. A 18, 2041-2053 (2001).
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C. K. Abbey and M. P. Eckstein, “Classification images for detection, contrast discrimination, and identification tasks with a common ideal observer,” J. Vision 6, 335-355 (2006).
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Y. Morgenstern, J. H. Elder, and Y. Hou, “Contrast dependence of spatial summation revealed by classification image analysis,” J. Vision 4, 439a (2004). (Vision Science Society Abstract Supplement).
[CrossRef]

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

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

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

J. A. Solomon, “Noise reveals visual mechanisms of detection and discrimination,” J. Vision 2, 105-120 (2002).
[CrossRef]

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

Med. Phys.

P. F. Judy, R. G. Swensson, and M. Szulc, “Lesion detection and signal-to-noise ratio in CT images,” Med. Phys. 8, 13-23 (1981).
[CrossRef] [PubMed]

Nature

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

Percept. Psychophys.

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

Perception

I. Kurki, A. Hyvärinen, and P. I. Laurinen, “Characterising signal and noise in contrast detection by classification images,” Perception 35 (ECVP Abstract Supplement), 89 (2006).

A. J. Ahumada, “Classification images from Vernier acuity masked by noise,” Perception 25, 18 (1996). (ECVP Abstract Supplement).

Phys. Med. Biol.

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

Proc. Natl. Acad. Sci. U.S.A.

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

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[CrossRef]

Psychol. Rev.

Z. L. Lu and B. A. Dosher, “Characterizing observers using external noise and observer models: assessing internal representations with external noise,” Psychol. Rev. 115, 44-82 (2008).
[CrossRef] [PubMed]

Psychol. Sci.

P. G. Schyns, L. Bonnar, and F. Gosselin, “Show me the features! Understanding recognition from the use of visual information,” Psychol. Sci. 13, 402-409 (2002).
[CrossRef] [PubMed]

Science

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

Trans. IRE-PGIT

W. W. Peterson, T. G. Birdsall, and W. C. Fox, “The theory of signal detectability,” Trans. IRE-PGIT 4, 171-212 (1954).

Vision Res.

N. J. Majaj, D. G. Pelli, P. Kurshan, and M. Palomares, “The role of spatial frequency channels in letter identification,” Vision Res. 42, 1165-1184 (2002).
[CrossRef] [PubMed]

I. Oruc, M. S. Landy, and D. G. Pelli, “Noise masking reveals channels for second-order letters,” Vision Res. 46, 1493-1506 (2006).
[CrossRef]

F. Gosselin and P. G. Schyns, “Bubbles: a technique to reveal the use of information in recognition tasks,” Vision Res. 41, 2261-2271 (2001).
[CrossRef] [PubMed]

Z. L. Lu and B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183-1198 (1998).
[CrossRef] [PubMed]

J. M. Foley and G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041-1053 (1981).
[CrossRef] [PubMed]

H. R. Wilson, D. K. McFarlane, and G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873-882 (1983).
[CrossRef] [PubMed]

A. Tavassoli, I. Linde, A. C. Bovik, and L. K. Cormack, “Eye movements selective for spatial frequency and orientation during active visual search,” Vision Res. 49, 173-181 (2009).
[CrossRef]

C. J. Ludwig, M. P. Eckstein, and B. R. Beutter, “Limited flexibility in the filter underlying saccadic targeting,” Vision Res. 47, 280-288 (2007).
[CrossRef]

Visual Neurosci.

S. Zhang, C. K. Abbey, and M. P. Eckstein, “Virtual evolution for visual search in natural images results in behavioral receptive fields with inhibitory surrounds,” Visual Neurosci. 26, 93-108 (2009).
[CrossRef]

Other

D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (Peninsula, 1988).

C. K. Abbey and F. O. Bochud, “Modeling visual detection tasks in correlated noise with linear model observers,” in Handbook of Medical Imaging, J.Beutel, H.L.Kundel, and R.L.Van Metter, eds. (SPIE Press, 2000), pp. 629-654.

D. G. Pelli, “Vision: coding and efficiency,” in The Quantum Efficiency of Vision, C.Blakemore, ed. (Cambridge Univ. Press, 1990), pp. 3-24.

D. G. Pelli, “Effects of visual noise,” Ph.D. thesis (Cambridge Univ., 1981).

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Figures (9)

Fig. 1
Fig. 1

Operational model of noise spectral density effects. A, Sources of inefficiency in visual detection are manifested as increases in threshold energy. The ideal observer (IO) exhibits a linear increase in threshold as noise spectral density (NSD) increases. A suboptimal sampling efficiency steepens the slope of the threshold line, and this is steepened further with incorporation of a proportional noise component. An additive noise component gives the line a nonzero intercept. B, A typical plot of threshold energy as a function of NSD graphs log threshold (or uses a logarithmic scale) against log NSD. Shown are ideal observer thresholds, some example subject thresholds from experiments described below, and a line with fitted slope and intercept. Because of the logarithmic compression and nonzero intercept of the model, the line appears as a curve in this plot. C, Detection efficiency rises and saturates as the additive noise component is swamped by the proportional effects at higher NSD.

Fig. 2
Fig. 2

Sample images and target spectrum. A, The target profile and sample images show the RMS noise contrast used in the experiments. Target contrast has been adjusted to give roughly equal visibility at each noise contrast level. Crosshair cues indicate target location. B, The spectrum of the Gaussian target is plotted as a function of frequency for the viewing conditions of the psychophysical experiment.

Fig. 3
Fig. 3

Subject thresholds. Target contrast energy thresholds as a function of NSD along with the ideal observer. Curves represent lines fitted to each subject (on linear axes).

Fig. 4
Fig. 4

Performance in the classification-image experiments. A, Subjects were generally reasonably close to the target accuracy of 80% correct across experimental conditions (1, lowest NSD; 5 highest NSD). B, Interval bias was generally small, and bias correction had little effect on overall performance.

Fig. 5
Fig. 5

Detection efficiency across noise spectral density. Subject efficiency ranges over approximately one order of magnitude and demonstrates typical increase and saturation across NSD. The linear threshold model appears to characterize group trends over this range.

Fig. 6
Fig. 6

Subject classification images derived from Eq. (14). These are the raw data for the spatial frequency analysis that follows.

Fig. 7
Fig. 7

Spatial frequency weights of classification images. Plots of average frequency weights are shown across RMS noise contrast for each subject. As the noise contrast increases, the frequency weights grow at lower spatial frequencies.

Fig. 8
Fig. 8

Sampling efficiency derived from classification images. Sampling efficiency is generally high and increases with noise spectral density.

Fig. 9
Fig. 9

Frequency weighting of classification images. A, After normalizing to equal energy, averages of classification images across subjects can be compared with the ideal observer filter. B, Frequency weighting of the classification images relative to the ideal observer shows that as noise magnitude decreases, the relative weighting shifts to higher spatial frequencies. Estimates of relative weighting are unstable above 6 cpd and hence are not shown.

Equations (15)

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N = σ n 2 Δ A Δ τ ,
E = Δ A Δ τ m = 1 M s m 2 = Δ A Δ τ ( s T s ) ,
λ = w T g + ϵ ,
d = w T s σ n 2 + σ ϵ 2 .
P C = Φ ( d 2 ) .
d = s T s σ n = E N ,
E t = d t 2 N .
η = E t IO E t Obs .
J w = ( w T s ) 2 s 2 ,
d t 2 = J w s 2 σ n 2 + σ ϵ 2 .
d t 2 = J w E t N + N ϵ ,
E t = d t 2 J w ( N + N ϵ ) .
λ = U N ( w T g ) + ϵ .
Δ q = ( o P C ) Δ z .
Δ q = e ( d 2 ) 2 π ( 1 + σ ϵ 2 σ n 2 ) w ,

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