Abstract

This study examined how correlated, or filtered, noise affected efficiency for recognizing two types of signal patterns, Gabor patches and three-dimensional objects. In general, compared with the ideal observer, human observers were most efficient at performing tasks in low-pass noise, followed by white noise; they were least efficient in high-pass noise. Simulations demonstrated that contrast-dependent internal noise was likely to have limited human performance in the high-pass conditions for both signal types. Classification images showed that observers were likely adopting different strategies in the presence of low-pass versus white noise. However, efficiencies were underpredicted by the linear classification images and asymmetries were present in the classification subimages, indicating the influence of nonlinear processes. Response consistency analyses indicated that lower contrast-dependent internal noise contributed somewhat to higher efficiencies in low-pass noise for Gabor patches but not objects. Taken together, the results of these experiments suggest a complex interaction among signals, external noise spectra, and internal noise in determining efficiency in correlated and uncorrelated noise.

© 2009 Optical Society of America

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2007

2006

B. Conrey and J. M. Gold, “An ideal observer analysis of variability in visual-only speech,” Vision Res. 46, 3243-3258 (2006).
[CrossRef] [PubMed]

B. S. Tjan and A. S. Nandy, “Classification images with uncertainty,” J. Vision 6, 387-413 (2006).
[CrossRef]

2005

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

D. M. Levi, S. A. Klein, and I. N. Chen, “What is the signal in noise?” Vision Res. 45, 1835-1846 (2005).
[CrossRef] [PubMed]

2004

J. M. Gold, A. B. Sekuler, and P. J. Bennett, “Characterizing perceptual learning with external noise,” Cogn. Sci. 28, 167-207 (2004).
[CrossRef]

C. Olman and D. Kersten, “Classification objects, ideal observers & generative models,” Cogn. Sci. 28, 227-239 (2004).
[CrossRef]

2002

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]

P. Neri and D. J. Heeger, “Spatiotemporal mechanisms for detecting and identifying image features in human vision,” Nat. Neurosci. 5, 812-816 (2002).
[PubMed]

A. J. Ahumada, Jr., “Classification image weights and internal noise level estimation,” J. Vision 2, 121-131 (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]

M. P. Eckstein, S. S. Shimozaki, and C. K. Abbey, “The footprints of visual attention in the Posner cueing paradigm revealed by classification images,” J. Vision 2, 25-45 (2002).
[CrossRef]

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

2001

2000

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

C. K. Abbey and M. P. Eckstein, “Estimates of human-observer templates for simple detection tasks in correlated noise,” Proc. SPIE 3981, 70-77 (2000).
[CrossRef]

1999

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

Z. L. Lu and B. A. Dosher, “Characterizing human perceptual inefficiencies with equivalent internal noise,” J. Opt. Soc. Am. A 16, 764-778 (1999).
[CrossRef]

D. G. Pelli and B. Farell, “Why use noise?” J. Opt. Soc. Am. A 16, 647-653 (1999).
[CrossRef]

J. Gold, P. J. Bennett, and A. B. Sekuler, “Identification of band-pass filtered letters and faces by human and ideal observers,” Vision Res. 39, 3537-3560 (1999).
[CrossRef]

A. J. Ahumada and B. L. Beard, “Classification images for detection,” Invest. Ophthalmol. Visual Sci. 40, 3015 (1999).

E. Barth, B. L. Beard, and A. J. Ahumada, Jr., “Nonlinear features in vernier acuity,” Proc. SPIE 3644, 88-96 (1999).
[CrossRef]

J. M. Gold, P. J. Bennett, and A. B. Sekuler, “Signal but not noise changes with perceptual learning,” Nature 402, 176-178 (1999).
[CrossRef]

1998

B. A. Dosher and Z. Lu, “Perceptual learning reflects external noise filtering and internal noise reduction through channel reweighting,” Proc. Natl. Acad. Sci. U.S.A. 95, 13988-13993 (1998).
[CrossRef] [PubMed]

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

A. B. Watson, “Multi-category classification: template models and classification images,” Invest. Ophthalmol. Visual Sci. 39, S912 (1998).

1997

D. J. Field and N. Brady, “Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes,” Vision Res. 37, 3367-3383 (1997).
[CrossRef]

D. H. Brainard, “The psychophysics toolbox,” Spatial Vis. 10, 433-436 (1997).
[CrossRef]

D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vis. 10, 437-442 (1997).
[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]

1996

A. vanderSchaaf and J. H. vanHateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759-2770 (1996).
[CrossRef]

1995

Z. Liu, D. C. Knill, and D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549-568 (1995).
[CrossRef] [PubMed]

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

W. L. Braje, B. S. Tjan, and G. E. Legge, “Human-efficiency for recognizing and detecting low-pass filtered objects,” Vision Res. 35, 2955-2966 (1995).
[CrossRef] [PubMed]

1994

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

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

1992

D. J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Appl. Opt. 12, 229-232 (1992).

C. W. Tyler, H. Chan, L. Liu, B. McBride, and L. Kontsevich, “Bit-stealing: how to get 1786 or more grey levels from an 8-bit color monitor,” Proc. SPIE 1666, 351-354 (1992).
[CrossRef]

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

1989

W. S. Geisler, “Sequential ideal-observer analysis of visual discriminations,” Psychol. Rev. 96, 267-314 (1989).
[CrossRef] [PubMed]

1988

1987

1985

1983

A. B. Watson, H. B. Barlow, and J. G. Robson, “What does the eye see best,” Nature 302, 419-422 (1983).
[CrossRef] [PubMed]

1981

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]

1969

C. Blakemore and F. W. Campbell, “On existence of neurones in human visual system selectively sensitive to orientation and size of retinal images,” J. Physiol. (London) 203, 237-260 (1969).

1964

D. M. Green, “Consistency of auditory detection judgments,” Psychol. Rev. 71, 392-407 (1964).
[CrossRef] [PubMed]

1942

S. Hecht, S. Schlaer, and M. H. Pirenne, “Energy, quanta and vision,” J. Gen. Physiol. 25, 819-840 (1942).
[CrossRef] [PubMed]

Abbey, C. K.

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

M. P. Eckstein, S. S. Shimozaki, and C. K. Abbey, “The footprints of visual attention in the Posner cueing paradigm revealed by classification images,” J. Vision 2, 25-45 (2002).
[CrossRef]

C. K. Abbey and H. H. Barrett, “Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability,” J. Opt. Soc. Am. A 18, 473-488 (2001).
[CrossRef]

C. K. Abbey and M. P. Eckstein, “Estimates of human-observer templates for simple detection tasks in correlated noise,” Proc. SPIE 3981, 70-77 (2000).
[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]

Ahumada, A. J.

A. J. Ahumada, Jr., “Classification image weights and internal noise level estimation,” J. Vision 2, 121-131 (2002).
[CrossRef]

E. Barth, B. L. Beard, and A. J. Ahumada, Jr., “Nonlinear features in vernier acuity,” Proc. SPIE 3644, 88-96 (1999).
[CrossRef]

A. J. Ahumada and B. L. Beard, “Classification images for detection,” Invest. Ophthalmol. Visual Sci. 40, 3015 (1999).

Barlow, H. B.

A. B. Watson, H. B. Barlow, and J. G. Robson, “What does the eye see best,” Nature 302, 419-422 (1983).
[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]

Barrett, H. H.

Barth, E.

E. Barth, B. L. Beard, and A. J. Ahumada, Jr., “Nonlinear features in vernier acuity,” Proc. SPIE 3644, 88-96 (1999).
[CrossRef]

Beard, B. L.

E. Barth, B. L. Beard, and A. J. Ahumada, Jr., “Nonlinear features in vernier acuity,” Proc. SPIE 3644, 88-96 (1999).
[CrossRef]

A. J. Ahumada and B. L. Beard, “Classification images for detection,” Invest. Ophthalmol. Visual Sci. 40, 3015 (1999).

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]

J. M. Gold, A. B. Sekuler, and P. J. Bennett, “Characterizing perceptual learning with external noise,” Cogn. Sci. 28, 167-207 (2004).
[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, P. J. Bennett, and A. B. Sekuler, “Signal but not noise changes with perceptual learning,” Nature 402, 176-178 (1999).
[CrossRef]

J. Gold, P. J. Bennett, and A. B. Sekuler, “Identification of band-pass filtered letters and faces by human and ideal observers,” Vision Res. 39, 3537-3560 (1999).
[CrossRef]

Bialek, W.

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

Blakemore, C.

C. Blakemore and F. W. Campbell, “On existence of neurones in human visual system selectively sensitive to orientation and size of retinal images,” J. Physiol. (London) 203, 237-260 (1969).

Borgstrom, M. C.

Brady, N.

D. J. Field and N. Brady, “Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes,” Vision Res. 37, 3367-3383 (1997).
[CrossRef]

Brainard, D. H.

D. H. Brainard, “The psychophysics toolbox,” Spatial Vis. 10, 433-436 (1997).
[CrossRef]

Braje, W. L.

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

W. L. Braje, B. S. Tjan, and G. E. Legge, “Human-efficiency for recognizing and detecting low-pass filtered objects,” Vision Res. 35, 2955-2966 (1995).
[CrossRef] [PubMed]

Burgess, A. E.

Burton, G. J.

Campbell, F. W.

C. Blakemore and F. W. Campbell, “On existence of neurones in human visual system selectively sensitive to orientation and size of retinal images,” J. Physiol. (London) 203, 237-260 (1969).

Chan, H.

C. W. Tyler, H. Chan, L. Liu, B. McBride, and L. Kontsevich, “Bit-stealing: how to get 1786 or more grey levels from an 8-bit color monitor,” Proc. SPIE 1666, 351-354 (1992).
[CrossRef]

Chao, T.

D. J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Appl. Opt. 12, 229-232 (1992).

Chen, I. N.

D. M. Levi, S. A. Klein, and I. N. Chen, “What is the signal in noise?” Vision Res. 45, 1835-1846 (2005).
[CrossRef] [PubMed]

Colborne, B.

Conrey, B.

B. Conrey and J. M. Gold, “An ideal observer analysis of variability in visual-only speech,” Vision Res. 46, 3243-3258 (2006).
[CrossRef] [PubMed]

Dosher, B. A.

Z. L. Lu and B. A. Dosher, “Characterizing human perceptual inefficiencies with equivalent internal noise,” J. Opt. Soc. Am. A 16, 764-778 (1999).
[CrossRef]

B. A. Dosher and Z. Lu, “Perceptual learning reflects external noise filtering and internal noise reduction through channel reweighting,” Proc. Natl. Acad. Sci. U.S.A. 95, 13988-13993 (1998).
[CrossRef] [PubMed]

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

Eckstein, M. P.

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

M. P. Eckstein, S. S. Shimozaki, and C. K. Abbey, “The footprints of visual attention in the Posner cueing paradigm revealed by classification images,” J. Vision 2, 25-45 (2002).
[CrossRef]

C. K. Abbey and M. P. Eckstein, “Estimates of human-observer templates for simple detection tasks in correlated noise,” Proc. SPIE 3981, 70-77 (2000).
[CrossRef]

Efron, B.

B. Efron and R. Tibshirani, An Introduction to the Bootstrap, Vol. 57 of Monographs on Statistics and Applied Probability (Chapman & Hall, 1993).

Farell, B.

Field, D. J.

D. J. Field and N. Brady, “Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes,” Vision Res. 37, 3367-3383 (1997).
[CrossRef]

D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379-2394 (1987).
[CrossRef] [PubMed]

Geisler, W. S.

W. S. Geisler, “Sequential ideal-observer analysis of visual discriminations,” Psychol. Rev. 96, 267-314 (1989).
[CrossRef] [PubMed]

W. S. Geisler, “Ideal observer analysis,” in The Visual Neurosciences, J.S.Werner and L.M.Chalupa, eds. (MIT Press, 2004), p. 2 v. (various pagings).

Gold, J.

J. Gold, P. J. Bennett, and A. B. Sekuler, “Identification of band-pass filtered letters and faces by human and ideal observers,” Vision Res. 39, 3537-3560 (1999).
[CrossRef]

Gold, J. M.

B. Conrey and J. M. Gold, “An ideal observer analysis of variability in visual-only speech,” Vision Res. 46, 3243-3258 (2006).
[CrossRef] [PubMed]

J. M. Gold, A. B. Sekuler, and P. J. Bennett, “Characterizing perceptual learning with external noise,” Cogn. Sci. 28, 167-207 (2004).
[CrossRef]

J. M. Gold, P. J. Bennett, and A. B. Sekuler, “Signal but not noise changes with perceptual learning,” Nature 402, 176-178 (1999).
[CrossRef]

Graham, N. V. S.

N. V. S. Graham, Visual Pattern Analyzers, Oxford Psychology Series, No. 16 (Oxford Univ. Press, 1989), pp. xvi, 646.

Green, D. M.

D. M. Green, “Consistency of auditory detection judgments,” Psychol. Rev. 71, 392-407 (1964).
[CrossRef] [PubMed]

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

Hecht, S.

S. Hecht, S. Schlaer, and M. H. Pirenne, “Energy, quanta and vision,” J. Gen. Physiol. 25, 819-840 (1942).
[CrossRef] [PubMed]

Heeger, D. J.

P. Neri and D. J. Heeger, “Spatiotemporal mechanisms for detecting and identifying image features in human vision,” Nat. Neurosci. 5, 812-816 (2002).
[PubMed]

Jennings, R. J.

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]

Kersten, D.

C. Olman and D. Kersten, “Classification objects, ideal observers & generative models,” Cogn. Sci. 28, 227-239 (2004).
[CrossRef]

Z. Liu, D. C. Knill, and D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549-568 (1995).
[CrossRef] [PubMed]

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

D. Kersten, “Statistical efficiency for the detection of visual noise,” Vision Res. 27, 1029-1040 (1987).
[CrossRef] [PubMed]

G. Legge, D. Kersten, and A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. A 4, 391-406 (1987).
[CrossRef] [PubMed]

Klein, S. A.

D. M. Levi, S. A. Klein, and I. N. Chen, “What is the signal in noise?” Vision Res. 45, 1835-1846 (2005).
[CrossRef] [PubMed]

Knill, D. C.

Z. Liu, D. C. Knill, and D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549-568 (1995).
[CrossRef] [PubMed]

Kontsevich, L.

C. W. Tyler, H. Chan, L. Liu, B. McBride, and L. Kontsevich, “Bit-stealing: how to get 1786 or more grey levels from an 8-bit color monitor,” Proc. SPIE 1666, 351-354 (1992).
[CrossRef]

Legge, G.

Legge, G. E.

W. L. Braje, B. S. Tjan, and G. E. Legge, “Human-efficiency for recognizing and detecting low-pass filtered objects,” Vision Res. 35, 2955-2966 (1995).
[CrossRef] [PubMed]

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

Levi, D. M.

D. M. Levi, S. A. Klein, and I. N. Chen, “What is the signal in noise?” Vision Res. 45, 1835-1846 (2005).
[CrossRef] [PubMed]

Li, X.

Liu, L.

C. W. Tyler, H. Chan, L. Liu, B. McBride, and L. Kontsevich, “Bit-stealing: how to get 1786 or more grey levels from an 8-bit color monitor,” Proc. SPIE 1666, 351-354 (1992).
[CrossRef]

Liu, Z.

Z. Liu, D. C. Knill, and D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549-568 (1995).
[CrossRef] [PubMed]

Lu, Z.

B. A. Dosher and Z. Lu, “Perceptual learning reflects external noise filtering and internal noise reduction through channel reweighting,” Proc. Natl. Acad. Sci. U.S.A. 95, 13988-13993 (1998).
[CrossRef] [PubMed]

Lu, Z. L.

McBride, B.

C. W. Tyler, H. Chan, L. Liu, B. McBride, and L. Kontsevich, “Bit-stealing: how to get 1786 or more grey levels from an 8-bit color monitor,” Proc. SPIE 1666, 351-354 (1992).
[CrossRef]

Moorhead, I. R.

Murray, R. F.

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]

Myers, K. J.

Nandy, A. S.

B. S. Tjan and A. S. Nandy, “Classification images with uncertainty,” J. Vision 6, 387-413 (2006).
[CrossRef]

Neri, P.

P. Neri and D. J. Heeger, “Spatiotemporal mechanisms for detecting and identifying image features in human vision,” Nat. Neurosci. 5, 812-816 (2002).
[PubMed]

Olman, C.

C. Olman and D. Kersten, “Classification objects, ideal observers & generative models,” Cogn. Sci. 28, 227-239 (2004).
[CrossRef]

Patton, D. D.

Pelli, D. G.

D. G. Pelli and B. Farell, “Why use noise?” J. Opt. Soc. Am. A 16, 647-653 (1999).
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D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vis. 10, 437-442 (1997).
[CrossRef]

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

D. G. Pelli, “Uncertainty explains many aspects of visual contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1508-1532 (1985).
[CrossRef] [PubMed]

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

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

Pirenne, M. H.

S. Hecht, S. Schlaer, and M. H. Pirenne, “Energy, quanta and vision,” J. Gen. Physiol. 25, 819-840 (1942).
[CrossRef] [PubMed]

Robson, J. G.

A. B. Watson, H. B. Barlow, and J. G. Robson, “What does the eye see best,” Nature 302, 419-422 (1983).
[CrossRef] [PubMed]

Rolland, J. P.

Ruderman, D. L.

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

Schlaer, S.

S. Hecht, S. Schlaer, and M. H. Pirenne, “Energy, quanta and vision,” J. Gen. Physiol. 25, 819-840 (1942).
[CrossRef] [PubMed]

Seeley, G. W.

Sekuler, A. B.

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

J. M. Gold, A. B. Sekuler, and P. J. Bennett, “Characterizing perceptual learning with external noise,” Cogn. Sci. 28, 167-207 (2004).
[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, P. J. Bennett, and A. B. Sekuler, “Signal but not noise changes with perceptual learning,” Nature 402, 176-178 (1999).
[CrossRef]

J. Gold, P. J. Bennett, and A. B. Sekuler, “Identification of band-pass filtered letters and faces by human and ideal observers,” Vision Res. 39, 3537-3560 (1999).
[CrossRef]

Shimozaki, S. S.

M. P. Eckstein, S. S. Shimozaki, and C. K. Abbey, “The footprints of visual attention in the Posner cueing paradigm revealed by classification images,” J. Vision 2, 25-45 (2002).
[CrossRef]

Solomon, J. A.

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

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

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

Swets, J. A.

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

Tadmor, Y.

D. J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Appl. Opt. 12, 229-232 (1992).

Tibshirani, R.

B. Efron and R. Tibshirani, An Introduction to the Bootstrap, Vol. 57 of Monographs on Statistics and Applied Probability (Chapman & Hall, 1993).

Tjan, B. S.

B. S. Tjan and A. S. Nandy, “Classification images with uncertainty,” J. Vision 6, 387-413 (2006).
[CrossRef]

W. L. Braje, B. S. Tjan, and G. E. Legge, “Human-efficiency for recognizing and detecting low-pass filtered objects,” Vision Res. 35, 2955-2966 (1995).
[CrossRef] [PubMed]

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

Tolhurst, D. J.

D. J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Appl. Opt. 12, 229-232 (1992).

Tyler, C. W.

C. W. Tyler, H. Chan, L. Liu, B. McBride, and L. Kontsevich, “Bit-stealing: how to get 1786 or more grey levels from an 8-bit color monitor,” Proc. SPIE 1666, 351-354 (1992).
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A. vanderSchaaf and J. H. vanHateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759-2770 (1996).
[CrossRef]

vanHateren, J. H.

A. vanderSchaaf and J. H. vanHateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759-2770 (1996).
[CrossRef]

Wagner, R. F.

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]

Watson, A. B.

A. B. Watson, “Multi-category classification: template models and classification images,” Invest. Ophthalmol. Visual Sci. 39, S912 (1998).

A. B. Watson, H. B. Barlow, and J. G. Robson, “What does the eye see best,” Nature 302, 419-422 (1983).
[CrossRef] [PubMed]

A. B. Watson, “The ideal observer concept as a modeling tool,” in Frontiers of Visual Science, The Committee on Vision, ed. (National Academy Press, 1978), pp. 32-37.

Appl. Opt.

G. J. Burton and I. R. Moorhead, “Color and spatial structure in natural scenes,” Appl. Opt. 26, 157-170 (1987).
[CrossRef] [PubMed]

D. J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Appl. Opt. 12, 229-232 (1992).

Cogn. Sci.

C. Olman and D. Kersten, “Classification objects, ideal observers & generative models,” Cogn. Sci. 28, 227-239 (2004).
[CrossRef]

J. M. Gold, A. B. Sekuler, and P. J. Bennett, “Characterizing perceptual learning with external noise,” Cogn. Sci. 28, 167-207 (2004).
[CrossRef]

Invest. Ophthalmol. Visual Sci.

A. B. Watson, “Multi-category classification: template models and classification images,” Invest. Ophthalmol. Visual Sci. 39, S912 (1998).

A. J. Ahumada and B. L. Beard, “Classification images for detection,” Invest. Ophthalmol. Visual Sci. 40, 3015 (1999).

J. Gen. Physiol.

S. Hecht, S. Schlaer, and M. H. Pirenne, “Energy, quanta and vision,” J. Gen. Physiol. 25, 819-840 (1942).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379-2394 (1987).
[CrossRef] [PubMed]

Z. L. Lu and B. A. Dosher, “Characterizing human perceptual inefficiencies with equivalent internal noise,” J. Opt. Soc. Am. A 16, 764-778 (1999).
[CrossRef]

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

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

A. E. Burgess, “Visual signal detection with two-component noise: low-pass spectrum effects,” J. Opt. Soc. Am. A 16, 694-704 (1999).
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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).
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J. P. Rolland and H. H. Barrett, “Effect of random background inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A 9, 649-658 (1992).
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C. K. Abbey and H. H. Barrett, “Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability,” J. Opt. Soc. Am. A 18, 473-488 (2001).
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[CrossRef] [PubMed]

D. G. Pelli, “Uncertainty explains many aspects of visual contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1508-1532 (1985).
[CrossRef] [PubMed]

D. G. Pelli and B. Farell, “Why use noise?” J. Opt. Soc. Am. A 16, 647-653 (1999).
[CrossRef]

G. Legge, D. Kersten, and A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. A 4, 391-406 (1987).
[CrossRef] [PubMed]

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

J. Physiol. (London)

C. Blakemore and F. W. Campbell, “On existence of neurones in human visual system selectively sensitive to orientation and size of retinal images,” J. Physiol. (London) 203, 237-260 (1969).

J. Vision

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

A. J. Ahumada, Jr., “Classification image weights and internal noise level estimation,” J. Vision 2, 121-131 (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]

B. S. Tjan and A. S. Nandy, “Classification images with uncertainty,” J. Vision 6, 387-413 (2006).
[CrossRef]

M. P. Eckstein, S. S. Shimozaki, and C. K. Abbey, “The footprints of visual attention in the Posner cueing paradigm revealed by classification images,” J. Vision 2, 25-45 (2002).
[CrossRef]

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

Nat. Neurosci.

P. Neri and D. J. Heeger, “Spatiotemporal mechanisms for detecting and identifying image features in human vision,” Nat. Neurosci. 5, 812-816 (2002).
[PubMed]

Nature

J. M. Gold, P. J. Bennett, and A. B. Sekuler, “Signal but not noise changes with perceptual learning,” Nature 402, 176-178 (1999).
[CrossRef]

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

A. B. Watson, H. B. Barlow, and J. G. Robson, “What does the eye see best,” Nature 302, 419-422 (1983).
[CrossRef] [PubMed]

Phys. Rev. Lett.

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

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

B. A. Dosher and Z. Lu, “Perceptual learning reflects external noise filtering and internal noise reduction through channel reweighting,” Proc. Natl. Acad. Sci. U.S.A. 95, 13988-13993 (1998).
[CrossRef] [PubMed]

Proc. SPIE

E. Barth, B. L. Beard, and A. J. Ahumada, Jr., “Nonlinear features in vernier acuity,” Proc. SPIE 3644, 88-96 (1999).
[CrossRef]

C. W. Tyler, H. Chan, L. Liu, B. McBride, and L. Kontsevich, “Bit-stealing: how to get 1786 or more grey levels from an 8-bit color monitor,” Proc. SPIE 1666, 351-354 (1992).
[CrossRef]

C. K. Abbey and M. P. Eckstein, “Estimates of human-observer templates for simple detection tasks in correlated noise,” Proc. SPIE 3981, 70-77 (2000).
[CrossRef]

Psychol. Rev.

W. S. Geisler, “Sequential ideal-observer analysis of visual discriminations,” Psychol. Rev. 96, 267-314 (1989).
[CrossRef] [PubMed]

D. M. Green, “Consistency of auditory detection judgments,” Psychol. Rev. 71, 392-407 (1964).
[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]

Spatial Vis.

D. H. Brainard, “The psychophysics toolbox,” Spatial Vis. 10, 433-436 (1997).
[CrossRef]

D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vis. 10, 437-442 (1997).
[CrossRef]

Vision Res.

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

Z. Liu, D. C. Knill, and D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549-568 (1995).
[CrossRef] [PubMed]

J. Gold, P. J. Bennett, and A. B. Sekuler, “Identification of band-pass filtered letters and faces by human and ideal observers,” Vision Res. 39, 3537-3560 (1999).
[CrossRef]

A. vanderSchaaf and J. H. vanHateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759-2770 (1996).
[CrossRef]

D. J. Field and N. Brady, “Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes,” Vision Res. 37, 3367-3383 (1997).
[CrossRef]

D. Kersten, “Statistical efficiency for the detection of visual noise,” Vision Res. 27, 1029-1040 (1987).
[CrossRef] [PubMed]

D. M. Levi, S. A. Klein, and I. N. Chen, “What is the signal in noise?” Vision Res. 45, 1835-1846 (2005).
[CrossRef] [PubMed]

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

W. L. Braje, B. S. Tjan, and G. E. Legge, “Human-efficiency for recognizing and detecting low-pass filtered objects,” Vision Res. 35, 2955-2966 (1995).
[CrossRef] [PubMed]

B. Conrey and J. M. Gold, “An ideal observer analysis of variability in visual-only speech,” Vision Res. 46, 3243-3258 (2006).
[CrossRef] [PubMed]

Other

B. Efron and R. Tibshirani, An Introduction to the Bootstrap, Vol. 57 of Monographs on Statistics and Applied Probability (Chapman & Hall, 1993).

W. S. Geisler, “Ideal observer analysis,” in The Visual Neurosciences, J.S.Werner and L.M.Chalupa, eds. (MIT Press, 2004), p. 2 v. (various pagings).

N. V. S. Graham, Visual Pattern Analyzers, Oxford Psychology Series, No. 16 (Oxford Univ. Press, 1989), pp. xvi, 646.

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

A. B. Watson, “The ideal observer concept as a modeling tool,” in Frontiers of Visual Science, The Committee on Vision, ed. (National Academy Press, 1978), pp. 32-37.

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

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

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Figures (11)

Fig. 1
Fig. 1

Leftmost column, the two oriented Gabor patch signals; remaining columns, the six three-dimensional object signals used in the experiment.

Fig. 2
Fig. 2

Example noise fields and the associated filters for each of the external noise conditions. Amplitude is not to scale but was normalized to have unit power on average for each spatial frequency and orientation.

Fig. 3
Fig. 3

Top row, human, ideal observer, and noise-limited ideal observer thresholds for the Gabor (left) and object (right) recognition tasks. Bottom row, corresponding efficiencies for the Gabor and object recognition tasks. Error bars correspond to ± 1 standard deviation, estimated by bootstrap simulations [42].

Fig. 4
Fig. 4

Efficiencies for the Gabor (left panel) and the 1-of-2 object (right panel) recognition tasks, computed from the response classification data.

Fig. 5
Fig. 5

Classification images calculated from the ideal observer templates (top row) and from the combined human observer data (middle and bottom rows) for the Gabor patch task in all three noise conditions. Human images in the middle row were calculated from the raw data. For the images in the bottom row, the raw data were smoothed with a 9 × 9 convolution kernel (the matrix product of the vector [1 2 3 4 5 4 3 2 1] with itself transposed) so as to make it easier to visualize the structure in the images.

Fig. 6
Fig. 6

Classification images calculated from the ideal observer templates (top row) and from the combined human observer data (middle and bottom rows) for the object task in all three noise conditions. Human images in the middle row were calculated from the raw data. For the images in the bottom row, the raw data were smoothed as described for Fig. 5.

Fig. 7
Fig. 7

Actual/predicted efficiency ratios measured from the response classification data in the Gabor and object tasks.

Fig. 8
Fig. 8

Classification subimages for human and simulated ideal observers in the Gabor patch task in the white (top panels), 1 f (middle panels), and flipped f (bottom panels) noise conditions.

Fig. 9
Fig. 9

Classification subimages for human and simulated ideal observers in the object task in the white (top panels), 1 f (middle panels), and flipped f (bottom panels) noise conditions.

Fig. 10
Fig. 10

Response consistency plots for observers JL (upper panels) and BC (lower panels) in the Gabor task in the white (left), 1 f (middle), and flipped f (right) conditions.

Fig. 11
Fig. 11

Response consistency plots for observers SK (upper panels) and BC (lower panels) in the object task in the white (left), 1 f (middle), and flipped f (right) conditions.

Equations (13)

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

c x y = l x y L L ,
C RMS = 1 n m x = 1 n y = 1 m c x y 2 ,
E = ( C RMS ) 2 n m a pixel ,
E = k ( N e + N i ) ,
C = ( S 1 R 1 ¯ + S 2 R 1 ¯ ) ( S 1 R 2 ¯ + S 2 R 2 ¯ ) ,
p c = m log 10 ( p a 100 ) + 100 ,
σ i σ e = α + γ 1 e β 1 m + γ 2 e β 2 m ,
N C = F 1 [ filt A ( N W ) e i ϕ ( N W ) ] ,
I = S + N C = F 1 [ A ( S ) e i ϕ ( S ) + filt A ( N W ) e i ϕ ( N W ) ] ,
I C 1 = F 1 [ A ( S ) filt e i ϕ ( S ) + filt A ( N W ) filt e i ϕ ( N W ) ] = F 1 [ A ( S ) filt e i ϕ ( S ) + A ( N W ) e i ϕ ( N W ) ] .
SNR I C 1 = A ( S ) filt A ( N W ) = A ( S ) filt A ( N W ) = SNR I .
r = ( S C 1 + N W ) T C 1 ,
r = ( S + N W ) T .

Metrics