Abstract

Foveal and parafoveal contrast detection thresholds for Gabor and checkerboard targets were measured in white noise by means of a two-interval forced-choice paradigm. Two white-noise conditions were used: fixed and twin. In the fixed noise condition a single noise sample was presented in both intervals of all the trials. In the twin noise condition the same noise sample was used in the two intervals of a trial, but a new sample was generated for each trial. Fixed noise conditions usually resulted in lower thresholds than twin noise. Template learning models are presented that attribute this advantage of fixed over twin noise either to fixed memory templates’ reducing uncertainty by incorporation of the noise or to the introduction, by the learning process itself, of more variability in the twin noise condition. Quantitative predictions of the template learning process show that it contributes to the accelerating nonlinear increase in performance with signal amplitude at low signal-to-noise ratios.

© 1999 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]

1997 (4)

1996 (1)

D. M. Levi, S. A. Klein, “Limitations on position coding imposed by undersampling and univariance,” Vision Res. 36, 2111–2120 (1996).
[CrossRef] [PubMed]

1995 (2)

M. Fahle, S. Edelman, T. Poggio, “Fast perceptual learning in hyperacuity,” Vision Res. 35, 3003–3013 (1995).
[CrossRef] [PubMed]

B. L. Beard, D. M. Levi, L. N. Reich, “Perceptual learning in parafoveal vision,” Vision Res. 35, 1679–1690 (1995).
[CrossRef] [PubMed]

1994 (2)

M. Fahle, “Human pattern recognition: parallel processing and perceptual learning,” Perception 23, 411–427 (1994).
[CrossRef] [PubMed]

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

1992 (1)

H. Barrett, “Evaluation of image quality through linear discriminate models,” Proc. Soc. Inf. Disp. 23, 871–873 (1992).

1987 (3)

1985 (1)

1983 (1)

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

1980 (1)

G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. A 70, 1458–1471 (1980).
[CrossRef]

1979 (1)

J. Rovamo, V. Virsu, “An estimation and application of the human cortical magnification factor,” Exp. Brain Res. 37, 495–510 (1979).
[CrossRef] [PubMed]

1973 (1)

L. D. Harmon, B. Julesz, “Masking in visual recognition: effects of two-dimensional filtered noise,” Science 180, 1194–1197 (1973).
[CrossRef] [PubMed]

1961 (1)

W. P. Tanner, “Physiological implications of psychophysical data,” Ann. (N.Y.) Acad. Sci. 89, 752–765 (1961).
[CrossRef]

1949 (1)

C. E. Osgood, “The similarity paradox in human learning: a resolution,” Psychol. Rev. 56, 132–143 (1949).
[CrossRef] [PubMed]

Ahumada, A. J.

A. M. Rohaly, A. J. Ahumada, A. B. Watson, “Object detection in natural backgrounds predicted by discrimination performance and models,” Vision Res. 37, 3225–3235 (1997).
[CrossRef]

M. Eckstein, A. B. Watson, A. J. Ahumada, “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, B. L. Beard, “Image discrimination models predict detection in fixed but not random noise,” J. Opt. Soc. Am. A 14, 2471–2476 (1997).
[CrossRef]

B. L. Beard, A. J. Ahumada, “Tuning function changes after practice on a parafoveal vernier acuity task,” invited presentation at the Special Symposium on Hyperacuity at the European Conference on Visual Perception, Teubingen, Germany, September 9–13, 1996.

Barlow, H. B.

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

Barrett, H.

H. Barrett, “Evaluation of image quality through linear discriminate models,” Proc. Soc. Inf. Disp. 23, 871–873 (1992).

Beard, B. L.

A. J. Ahumada, B. L. Beard, “Image discrimination models predict detection in fixed but not random noise,” J. Opt. Soc. Am. A 14, 2471–2476 (1997).
[CrossRef]

B. L. Beard, D. M. Levi, L. N. Reich, “Perceptual learning in parafoveal vision,” Vision Res. 35, 1679–1690 (1995).
[CrossRef] [PubMed]

B. L. Beard, A. J. Ahumada, “Tuning function changes after practice on a parafoveal vernier acuity task,” invited presentation at the Special Symposium on Hyperacuity at the European Conference on Visual Perception, Teubingen, Germany, September 9–13, 1996.

Borthwick, R.

A. B. Watson, R. Borthwick, M. Taylor, “Image quality and entropy masking,” in Human Vision, Visual Processing, and Digital Display, B. Rogowitz, ed., Proc. SPIE3016, 2–12 (1997).
[CrossRef]

Burgess, A.

Daly, S.

S. Daly, “The visible difference predictor: an algorithm for the assessment of image fidelity,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT, Cambridge, Mass., 1993).

Eckstein, M.

Edelman, S.

M. Fahle, S. Edelman, T. Poggio, “Fast perceptual learning in hyperacuity,” Vision Res. 35, 3003–3013 (1995).
[CrossRef] [PubMed]

Fahle, M.

M. Fahle, S. Edelman, T. Poggio, “Fast perceptual learning in hyperacuity,” Vision Res. 35, 3003–3013 (1995).
[CrossRef] [PubMed]

M. Fahle, “Human pattern recognition: parallel processing and perceptual learning,” Perception 23, 411–427 (1994).
[CrossRef] [PubMed]

Finney, D. J.

D. J. Finney, Probit Analysis: A Statistical Treatment of the Sigmoid Response Curve, Cambridge U. Press (Cambridge, UK, 1947).

Foley, J. M.

G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. A 70, 1458–1471 (1980).
[CrossRef]

Harmon, L. D.

L. D. Harmon, B. Julesz, “Masking in visual recognition: effects of two-dimensional filtered noise,” Science 180, 1194–1197 (1973).
[CrossRef] [PubMed]

Heeger, D. J.

P. C. Teo, D. J. Heeger, “Perceptual image distortion,” in Human Vision, Visual Processing, and Digital Display, B. Rogowitz, J. Allebach, eds., Proc. SPIE2179, 127–141 (1994).
[CrossRef]

Jakowatz, C. V.

C. V. Jakowatz, R. L. Shuey, G. M. White, “Adaptive waveform recognition,” presented at the Symposium on Information Theory, Royal Institute, London, August 29–September 2, 1961.

Julesz, B.

L. D. Harmon, B. Julesz, “Masking in visual recognition: effects of two-dimensional filtered noise,” Science 180, 1194–1197 (1973).
[CrossRef] [PubMed]

Kersten, D.

Klein, S. A.

D. M. Levi, S. A. Klein, “Limitations on position coding imposed by undersampling and univariance,” Vision Res. 36, 2111–2120 (1996).
[CrossRef] [PubMed]

Legge, G. E.

G. E. Legge, D. Kersten, “Contrast discrimination in peripheral vision,” J. Opt. Soc. Am. A 4, 1594–1597 (1987).
[CrossRef] [PubMed]

G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. A 70, 1458–1471 (1980).
[CrossRef]

Levi, D. M.

D. M. Levi, S. A. Klein, “Limitations on position coding imposed by undersampling and univariance,” Vision Res. 36, 2111–2120 (1996).
[CrossRef] [PubMed]

B. L. Beard, D. M. Levi, L. N. Reich, “Perceptual learning in parafoveal vision,” Vision Res. 35, 1679–1690 (1995).
[CrossRef] [PubMed]

Lubin, J.

J. Lubin, “The use of psychophysical data and models in the analysis of display system performance,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT, Cambridge, Mass., 1993).

Osgood, C. E.

C. E. Osgood, “The similarity paradox in human learning: a resolution,” Psychol. Rev. 56, 132–143 (1949).
[CrossRef] [PubMed]

Pelli, D. G.

Poggio, T.

M. Fahle, S. Edelman, T. Poggio, “Fast perceptual learning in hyperacuity,” Vision Res. 35, 3003–3013 (1995).
[CrossRef] [PubMed]

Reich, L. N.

B. L. Beard, D. M. Levi, L. N. Reich, “Perceptual learning in parafoveal vision,” Vision Res. 35, 1679–1690 (1995).
[CrossRef] [PubMed]

Robson, J. G.

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

Rohaly, A. M.

A. M. Rohaly, A. J. Ahumada, A. B. Watson, “Object detection in natural backgrounds predicted by discrimination performance and models,” Vision Res. 37, 3225–3235 (1997).
[CrossRef]

Rovamo, J.

J. Rovamo, V. Virsu, “An estimation and application of the human cortical magnification factor,” Exp. Brain Res. 37, 495–510 (1979).
[CrossRef] [PubMed]

Shuey, R. L.

C. V. Jakowatz, R. L. Shuey, G. M. White, “Adaptive waveform recognition,” presented at the Symposium on Information Theory, Royal Institute, London, August 29–September 2, 1961.

Solomon, J. A.

Tanner, W. P.

W. P. Tanner, “Physiological implications of psychophysical data,” Ann. (N.Y.) Acad. Sci. 89, 752–765 (1961).
[CrossRef]

Taylor, M.

A. B. Watson, R. Borthwick, M. Taylor, “Image quality and entropy masking,” in Human Vision, Visual Processing, and Digital Display, B. Rogowitz, ed., Proc. SPIE3016, 2–12 (1997).
[CrossRef]

Teo, P. C.

P. C. Teo, D. J. Heeger, “Perceptual image distortion,” in Human Vision, Visual Processing, and Digital Display, B. Rogowitz, J. Allebach, eds., Proc. SPIE2179, 127–141 (1994).
[CrossRef]

Virsu, V.

J. Rovamo, V. Virsu, “An estimation and application of the human cortical magnification factor,” Exp. Brain Res. 37, 495–510 (1979).
[CrossRef] [PubMed]

Watson, A. B.

M. Eckstein, A. B. Watson, A. J. Ahumada, “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. B. Watson, J. A. Solomon, “Model of visual contrast gain control and pattern masking,” J. Opt. Soc. Am. A 14, 2379–2391 (1997).
[CrossRef]

A. M. Rohaly, A. J. Ahumada, A. B. Watson, “Object detection in natural backgrounds predicted by discrimination performance and models,” Vision Res. 37, 3225–3235 (1997).
[CrossRef]

A. B. Watson, “Estimation of local spatial scale,” J. Opt. Soc. Am. A 4, 1579–1582 (1987).
[CrossRef] [PubMed]

A. B. Watson, “Efficiency of a model human image code,” J. Opt. Soc. Am. A 4, 2401–2417 (1987).
[CrossRef] [PubMed]

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

A. B. Watson, R. Borthwick, M. Taylor, “Image quality and entropy masking,” in Human Vision, Visual Processing, and Digital Display, B. Rogowitz, ed., Proc. SPIE3016, 2–12 (1997).
[CrossRef]

White, G. M.

C. V. Jakowatz, R. L. Shuey, G. M. White, “Adaptive waveform recognition,” presented at the Symposium on Information Theory, Royal Institute, London, August 29–September 2, 1961.

Wilson, H. R.

H. R. Wilson, “Quantitative models for pattern detection and discrimination,” in Vision Models for Target Detection and Recognition, E. Peli, ed. (World Scientific, Teaneck, N.J., 1995).

Ann. (N.Y.) Acad. Sci. (1)

W. P. Tanner, “Physiological implications of psychophysical data,” Ann. (N.Y.) Acad. Sci. 89, 752–765 (1961).
[CrossRef]

Exp. Brain Res. (1)

J. Rovamo, V. Virsu, “An estimation and application of the human cortical magnification factor,” Exp. Brain Res. 37, 495–510 (1979).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (9)

Nature (London) (1)

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

Perception (1)

M. Fahle, “Human pattern recognition: parallel processing and perceptual learning,” Perception 23, 411–427 (1994).
[CrossRef] [PubMed]

Proc. Soc. Inf. Disp. (1)

H. Barrett, “Evaluation of image quality through linear discriminate models,” Proc. Soc. Inf. Disp. 23, 871–873 (1992).

Psychol. Rev. (1)

C. E. Osgood, “The similarity paradox in human learning: a resolution,” Psychol. Rev. 56, 132–143 (1949).
[CrossRef] [PubMed]

Science (1)

L. D. Harmon, B. Julesz, “Masking in visual recognition: effects of two-dimensional filtered noise,” Science 180, 1194–1197 (1973).
[CrossRef] [PubMed]

Vision Res. (4)

M. Fahle, S. Edelman, T. Poggio, “Fast perceptual learning in hyperacuity,” Vision Res. 35, 3003–3013 (1995).
[CrossRef] [PubMed]

B. L. Beard, D. M. Levi, L. N. Reich, “Perceptual learning in parafoveal vision,” Vision Res. 35, 1679–1690 (1995).
[CrossRef] [PubMed]

D. M. Levi, S. A. Klein, “Limitations on position coding imposed by undersampling and univariance,” Vision Res. 36, 2111–2120 (1996).
[CrossRef] [PubMed]

A. M. Rohaly, A. J. Ahumada, A. B. Watson, “Object detection in natural backgrounds predicted by discrimination performance and models,” Vision Res. 37, 3225–3235 (1997).
[CrossRef]

Other (8)

A. B. Watson, R. Borthwick, M. Taylor, “Image quality and entropy masking,” in Human Vision, Visual Processing, and Digital Display, B. Rogowitz, ed., Proc. SPIE3016, 2–12 (1997).
[CrossRef]

D. J. Finney, Probit Analysis: A Statistical Treatment of the Sigmoid Response Curve, Cambridge U. Press (Cambridge, UK, 1947).

S. Daly, “The visible difference predictor: an algorithm for the assessment of image fidelity,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT, Cambridge, Mass., 1993).

J. Lubin, “The use of psychophysical data and models in the analysis of display system performance,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT, Cambridge, Mass., 1993).

P. C. Teo, D. J. Heeger, “Perceptual image distortion,” in Human Vision, Visual Processing, and Digital Display, B. Rogowitz, J. Allebach, eds., Proc. SPIE2179, 127–141 (1994).
[CrossRef]

H. R. Wilson, “Quantitative models for pattern detection and discrimination,” in Vision Models for Target Detection and Recognition, E. Peli, ed. (World Scientific, Teaneck, N.J., 1995).

B. L. Beard, A. J. Ahumada, “Tuning function changes after practice on a parafoveal vernier acuity task,” invited presentation at the Special Symposium on Hyperacuity at the European Conference on Visual Perception, Teubingen, Germany, September 9–13, 1996.

C. V. Jakowatz, R. L. Shuey, G. M. White, “Adaptive waveform recognition,” presented at the Symposium on Information Theory, Royal Institute, London, August 29–September 2, 1961.

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Figures (8)

Fig. 1
Fig. 1

Top two panels, the checkerboard and Gabor stimuli used in the experiment. Bottom two panels, the 200 best-correlating positions for each target with the (centered) target in noise, showing greater spatial uncertainty for the Gabor target than for a checkerboard target.

Fig. 2
Fig. 2

Average contrast energy thresholds (in dBB) are plotted for five observers. Thresholds for the checkerboard target are shown in the left-hand panels; those for Gabor targets are in the right-hand panels. Data collected in the fovea are in the upper panels, data from 4-deg eccentricity (foveal viewing distance) are in the center panels, and data from 4-deg eccentricity from a closer (one third) distance are in the bottom panels. Solid curves represent the twin noise data. Particular symbols represent averaged thresholds for each fixed noise sample.

Fig. 3
Fig. 3

Foveal contrast energy threshold (in dBB) is plotted as a function of the training day. Each data point is based on 60 two-alternative forced-choice trials. Solid curves represent the twin noise data. The remaining symbols represent fixed noise data. Fixed noise samples have the symbols assigned in Fig. 3. Checkerboard target thresholds are shown in the left-hand panels; Gabor target thresholds in the right-hand panels. The foveal data for three of the five observers are shown.

Fig. 4
Fig. 4

Schematic of an image detection model with template learning and positional uncertainty. An input image plus added noise enters the visual system, where an internal sensory representation is formed of the stimulus. This noisy sensory representation is correlated with memory templates of the targets over a range of positions, and a decision is made as to which target was present. Based on the trialwise feedback, the template is updated. The visual system module and the decision noise module are in dashed boxes because they are not included in our current models.

Fig. 5
Fig. 5

Template learning model generates a response indicating which input image contains the target. For each image the model forms an internal sensory representation (I) composed of the image plus internal sensory noise. This representation is cross correlated with memory templates for the target (MS) and no target (MN). The careted dot symbol indicates the maximum of correlations over a range of positions. The difference of the two maximum correlations represents the signal-presence likelihood for each interval, and a comparison of these likelihoods determines the response.

Fig. 6
Fig. 6

Learning rule. Correct feedback assigns the internal images to the appropriate memory template, which is assumed to be translated to the best-correlating position. Each template is then replaced by a weighted average of the old template, and the associated internal sensory representation. If λ, the learning rate parameter (a number between 0 and 1), is large, the average contains mostly the current internal image; if it is small, the template is only slightly changed.

Fig. 7
Fig. 7

Model simulations of the fixed/twin effect. Proportion correct scores from six 400-trial repetitions at four signal levels were converted by regression in the d domain to 79% correct threshold estimates for each of 36 conditions [two noise types (fixed, twin); two target types (Gabor, checkerboard); three internal-to-external noise ratios (0.5, 1, 2); and three learning rates (0, 0.1, 1)]. The graphs show the amount that the twin threshold exceeded the fixed threshold (in dB) as a function of the other variables. The horizontal lines show the average foveal difference for our observers and the 95% confidence interval based on variability over observers. Parameters: λ = 0.0, 0.1, and internal-to-external noise ratio equals one best fit to the target results.

Fig. 8
Fig. 8

Mathematical formula predictions and simulation results for the template learning model with no positional uncertainty. Performance in twin and fixed noise conditions is plotted as a function of the signal-to-noise level. The ideal observer with internal noise would perform along the main diagonal. The simulation proportions of correct responses were transformed to d by means of the cumulative Gaussian distribution, which seems to fit well. Note that the model predicts an accelerating nonlinearity in the absence of uncertainty or a transducer function.

Equations (19)

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

dBB=10 log10 (CE/CE0),
CE=ATcij2,
cij=(aij-B)/B,
I=S+Next+Nint.
(MSN-MN)·I1>(MSN-MN)·I2,
(MSN-MN)·(I1-I2)>0.
M(1-λ)M+λI.
MN(1-λ)MN+λI2ifI2isatarget-absentinterval,
MSN(1-λ)MSN+λI2ifI2isatarget-presentinterval.
Mn=(1-λ)nM0+λ(1-λ)(n-1)I1++Inλ.
F+Rn-iλ(1-λ)i,
M=Rλ2/[1-(1-λ)2]=Rλ/(2-λ)=R/nλ.
DM·DS>0.
d=[E-(-E)]/SD[DM·DS]=2E/SD[DM·DS],
SD[DM·DS]2=E(σM2+σS2)+nσM2σS2,
σS2=2σint2.
σM2=2(σint2)/nλ,
σM2=2(σint2+σext2)/nλ.
dIdeal=Sqrt[2E/σint2].

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