Abstract

The statistical efficiency of human observers performing a simplified version of the motion detection task of Salzman and Newsome [Science 264, 231 (1994)] is high but not perfect. This reduced efficiency may be caused by noise internal to the observers or by the observers’ using strategies that are different from that used by an ideal machine. We therefore investigated which of three simple models best accounts for the observers’ performance. The models compared were a motion detector that uses the proportion of dots in the first frame that move coherently (as would an ideal machine), a model that bases its decision on the number of dots that move, and a model that differentially weights motions that occur at different locations in the visual field (for instance, differentially weights the point of fixation and the periphery). We compared these models by explicitly modeling the human observers’ performance. We recorded the exact stimulus configuration on each trial together with the observer’s response, and, for the different models, we found the parameters that best predicted the observer’s performance in a least-squares sense. We then used N-fold cross validation to compare the models and hence the associated hypotheses. Our results show that the performance of observers is based on the proportion, not the absolute number, of dots that are moving and that there was no evidence of any differential spatial weighting. Whereas this method of modeling the observers’ response is demonstrated only for one simple psychophysical paradigm, it is general and can be applied to any psychophysical framework in which the entire stimulus can be recorded.

© 1998 Optical Society of America

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References

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  1. D. Salzman and W. Newsome, “Neural mechanisms for forming a perceptual decision,” Science 264, 231–237 (1994).
    [CrossRef] [PubMed]
  2. S. Watamaniuk, “Ideal observer for discrimination of the global direction of dynamic random-dot stimuli,” J. Opt. Soc. Am. A 10, 16–28 (1993).
    [CrossRef] [PubMed]
  3. H. Barlow, S. Tripathy, and R. Baddeley, “The statistical efficiency for detecting coherent motion,” Perception 24, 1 (1995), European Conference for Visual Perception Suppl.
  4. H. Barlow and S. Tripathy, “Correspondence noise and signal pooling in the detection of coherent visual motion,” submitted to J. Neurosci.
  5. D. Williams and R. Sekuler, “Coherent motion percepts from stochastic local motions,” Vision Res. 24, 55–62 (1984).
    [CrossRef]
  6. C. Downing and J. Movshon, “Spatial and temporal summation in stochastic random dot displays,” Invest. Ophthalmol. Visual Sci. Suppl. 30, 72 (1989).
  7. R. Fredericksen, F. Verstraten, and W. Van de Grind, “Spatial summation and its interaction with the temporal integration mechanism in human motion perception,” Vision Res. 34, 3171–3188 (1994).
    [CrossRef] [PubMed]
  8. A. Smith, R. Snowden, and A. Milne, “Is global motion really based on spatial integration of local motion signal,” Vision Res. 34, 2425–2430 (1994).
    [CrossRef] [PubMed]
  9. A. van Doorn and J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. 24, 47–53 (1984).
    [CrossRef] [PubMed]
  10. W. van de Grind, J. Koenderink, A. van Doorn, M. Milders, and H. Voerman, “Inhomogeneity and anisotropies for motion detection in the monocular visual field of human observers,” Vision Res. 33, 1089–1107 (1993).
    [CrossRef] [PubMed]
  11. R. Scobey and P. van Kan, “A horizontal stripe of displacement sensitivity in the human visual field,” Vision Res. 31, 99–109 (1991).
    [CrossRef] [PubMed]
  12. C. Bishop, Neural Networks for Pattern Recognition (Clarendon, Oxford, 1995).
  13. W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C, 2nd ed. Cambridge U. Press, Cambridge, 1992).
  14. H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716–723 (1974).
    [CrossRef]
  15. D. Mackay, “Bayesian model comparison and backprop nets,” in Advances in Neural Information Processing Systems, J. Moody, S. Hanson, and R. Lippmann, eds. (Morgan Kaufmann, Los Altos, Calif., 1992), Vol. 4, pp. 839–846.
  16. P. Zhang, “Model selection via multifold cross-validation,” Ann. Statist. 21, 299–313 (1993).
  17. J. Bridle, “Training stochastic model recognition algorithms as networks can lead to maximum mutual information estimation of parameters,” in Neural Information Processing, D. Touretzky, ed. (Morgan Kaufmann, Los Altos, Calif., 1990), Vol. 2, pp. 211–217.
  18. D. Fotheringhame and R. Baddeley, “Nonlinear principal components analysis of neuronal spike train data shows no evidence of nonlinear structure,” Biol. Cybern. (to be published).

1994 (3)

R. Fredericksen, F. Verstraten, and W. Van de Grind, “Spatial summation and its interaction with the temporal integration mechanism in human motion perception,” Vision Res. 34, 3171–3188 (1994).
[CrossRef] [PubMed]

A. Smith, R. Snowden, and A. Milne, “Is global motion really based on spatial integration of local motion signal,” Vision Res. 34, 2425–2430 (1994).
[CrossRef] [PubMed]

D. Salzman and W. Newsome, “Neural mechanisms for forming a perceptual decision,” Science 264, 231–237 (1994).
[CrossRef] [PubMed]

1993 (2)

S. Watamaniuk, “Ideal observer for discrimination of the global direction of dynamic random-dot stimuli,” J. Opt. Soc. Am. A 10, 16–28 (1993).
[CrossRef] [PubMed]

W. van de Grind, J. Koenderink, A. van Doorn, M. Milders, and H. Voerman, “Inhomogeneity and anisotropies for motion detection in the monocular visual field of human observers,” Vision Res. 33, 1089–1107 (1993).
[CrossRef] [PubMed]

1991 (1)

R. Scobey and P. van Kan, “A horizontal stripe of displacement sensitivity in the human visual field,” Vision Res. 31, 99–109 (1991).
[CrossRef] [PubMed]

1989 (1)

C. Downing and J. Movshon, “Spatial and temporal summation in stochastic random dot displays,” Invest. Ophthalmol. Visual Sci. Suppl. 30, 72 (1989).

1984 (2)

D. Williams and R. Sekuler, “Coherent motion percepts from stochastic local motions,” Vision Res. 24, 55–62 (1984).
[CrossRef]

A. van Doorn and J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. 24, 47–53 (1984).
[CrossRef] [PubMed]

1974 (1)

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716–723 (1974).
[CrossRef]

Akaike, H.

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716–723 (1974).
[CrossRef]

Downing, C.

C. Downing and J. Movshon, “Spatial and temporal summation in stochastic random dot displays,” Invest. Ophthalmol. Visual Sci. Suppl. 30, 72 (1989).

Fredericksen, R.

R. Fredericksen, F. Verstraten, and W. Van de Grind, “Spatial summation and its interaction with the temporal integration mechanism in human motion perception,” Vision Res. 34, 3171–3188 (1994).
[CrossRef] [PubMed]

Koenderink, J.

W. van de Grind, J. Koenderink, A. van Doorn, M. Milders, and H. Voerman, “Inhomogeneity and anisotropies for motion detection in the monocular visual field of human observers,” Vision Res. 33, 1089–1107 (1993).
[CrossRef] [PubMed]

A. van Doorn and J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. 24, 47–53 (1984).
[CrossRef] [PubMed]

Milders, M.

W. van de Grind, J. Koenderink, A. van Doorn, M. Milders, and H. Voerman, “Inhomogeneity and anisotropies for motion detection in the monocular visual field of human observers,” Vision Res. 33, 1089–1107 (1993).
[CrossRef] [PubMed]

Milne, A.

A. Smith, R. Snowden, and A. Milne, “Is global motion really based on spatial integration of local motion signal,” Vision Res. 34, 2425–2430 (1994).
[CrossRef] [PubMed]

Movshon, J.

C. Downing and J. Movshon, “Spatial and temporal summation in stochastic random dot displays,” Invest. Ophthalmol. Visual Sci. Suppl. 30, 72 (1989).

Newsome, W.

D. Salzman and W. Newsome, “Neural mechanisms for forming a perceptual decision,” Science 264, 231–237 (1994).
[CrossRef] [PubMed]

Salzman, D.

D. Salzman and W. Newsome, “Neural mechanisms for forming a perceptual decision,” Science 264, 231–237 (1994).
[CrossRef] [PubMed]

Scobey, R.

R. Scobey and P. van Kan, “A horizontal stripe of displacement sensitivity in the human visual field,” Vision Res. 31, 99–109 (1991).
[CrossRef] [PubMed]

Sekuler, R.

D. Williams and R. Sekuler, “Coherent motion percepts from stochastic local motions,” Vision Res. 24, 55–62 (1984).
[CrossRef]

Smith, A.

A. Smith, R. Snowden, and A. Milne, “Is global motion really based on spatial integration of local motion signal,” Vision Res. 34, 2425–2430 (1994).
[CrossRef] [PubMed]

Snowden, R.

A. Smith, R. Snowden, and A. Milne, “Is global motion really based on spatial integration of local motion signal,” Vision Res. 34, 2425–2430 (1994).
[CrossRef] [PubMed]

Van de Grind, W.

R. Fredericksen, F. Verstraten, and W. Van de Grind, “Spatial summation and its interaction with the temporal integration mechanism in human motion perception,” Vision Res. 34, 3171–3188 (1994).
[CrossRef] [PubMed]

W. van de Grind, J. Koenderink, A. van Doorn, M. Milders, and H. Voerman, “Inhomogeneity and anisotropies for motion detection in the monocular visual field of human observers,” Vision Res. 33, 1089–1107 (1993).
[CrossRef] [PubMed]

van Doorn, A.

W. van de Grind, J. Koenderink, A. van Doorn, M. Milders, and H. Voerman, “Inhomogeneity and anisotropies for motion detection in the monocular visual field of human observers,” Vision Res. 33, 1089–1107 (1993).
[CrossRef] [PubMed]

A. van Doorn and J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. 24, 47–53 (1984).
[CrossRef] [PubMed]

van Kan, P.

R. Scobey and P. van Kan, “A horizontal stripe of displacement sensitivity in the human visual field,” Vision Res. 31, 99–109 (1991).
[CrossRef] [PubMed]

Verstraten, F.

R. Fredericksen, F. Verstraten, and W. Van de Grind, “Spatial summation and its interaction with the temporal integration mechanism in human motion perception,” Vision Res. 34, 3171–3188 (1994).
[CrossRef] [PubMed]

Voerman, H.

W. van de Grind, J. Koenderink, A. van Doorn, M. Milders, and H. Voerman, “Inhomogeneity and anisotropies for motion detection in the monocular visual field of human observers,” Vision Res. 33, 1089–1107 (1993).
[CrossRef] [PubMed]

Watamaniuk, S.

Williams, D.

D. Williams and R. Sekuler, “Coherent motion percepts from stochastic local motions,” Vision Res. 24, 55–62 (1984).
[CrossRef]

IEEE Trans. Autom. Control (1)

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716–723 (1974).
[CrossRef]

Invest. Ophthalmol. Visual Sci. Suppl. (1)

C. Downing and J. Movshon, “Spatial and temporal summation in stochastic random dot displays,” Invest. Ophthalmol. Visual Sci. Suppl. 30, 72 (1989).

J. Opt. Soc. Am. A (1)

Science (1)

D. Salzman and W. Newsome, “Neural mechanisms for forming a perceptual decision,” Science 264, 231–237 (1994).
[CrossRef] [PubMed]

Vision Res. (6)

D. Williams and R. Sekuler, “Coherent motion percepts from stochastic local motions,” Vision Res. 24, 55–62 (1984).
[CrossRef]

R. Fredericksen, F. Verstraten, and W. Van de Grind, “Spatial summation and its interaction with the temporal integration mechanism in human motion perception,” Vision Res. 34, 3171–3188 (1994).
[CrossRef] [PubMed]

A. Smith, R. Snowden, and A. Milne, “Is global motion really based on spatial integration of local motion signal,” Vision Res. 34, 2425–2430 (1994).
[CrossRef] [PubMed]

A. van Doorn and J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. 24, 47–53 (1984).
[CrossRef] [PubMed]

W. van de Grind, J. Koenderink, A. van Doorn, M. Milders, and H. Voerman, “Inhomogeneity and anisotropies for motion detection in the monocular visual field of human observers,” Vision Res. 33, 1089–1107 (1993).
[CrossRef] [PubMed]

R. Scobey and P. van Kan, “A horizontal stripe of displacement sensitivity in the human visual field,” Vision Res. 31, 99–109 (1991).
[CrossRef] [PubMed]

Other (8)

C. Bishop, Neural Networks for Pattern Recognition (Clarendon, Oxford, 1995).

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C, 2nd ed. Cambridge U. Press, Cambridge, 1992).

H. Barlow, S. Tripathy, and R. Baddeley, “The statistical efficiency for detecting coherent motion,” Perception 24, 1 (1995), European Conference for Visual Perception Suppl.

H. Barlow and S. Tripathy, “Correspondence noise and signal pooling in the detection of coherent visual motion,” submitted to J. Neurosci.

D. Mackay, “Bayesian model comparison and backprop nets,” in Advances in Neural Information Processing Systems, J. Moody, S. Hanson, and R. Lippmann, eds. (Morgan Kaufmann, Los Altos, Calif., 1992), Vol. 4, pp. 839–846.

P. Zhang, “Model selection via multifold cross-validation,” Ann. Statist. 21, 299–313 (1993).

J. Bridle, “Training stochastic model recognition algorithms as networks can lead to maximum mutual information estimation of parameters,” in Neural Information Processing, D. Touretzky, ed. (Morgan Kaufmann, Los Altos, Calif., 1990), Vol. 2, pp. 211–217.

D. Fotheringhame and R. Baddeley, “Nonlinear principal components analysis of neuronal spike train data shows no evidence of nonlinear structure,” Biol. Cybern. (to be published).

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Figures (5)

Fig. 1
Fig. 1

(A) The motion task and two alternative ways of modeling it: (B) by fitting a psychometric curve to the subject’s response and calculating efficiencies and (C) by forming a number of models of the observer and comparing them by statistical model comparison methods.

Fig. 2
Fig. 2

Potential models of how the observer detects coherent motion. (A) Model 1 is based on the observer’s making his or her decision based on the proportion of the coherently moving. (B) Model 2 is similar but counts the number of moving dots, ignoring the number of dots that do not move coherently. (C) Model 3 weights movements differently at different spatial locations and can weight either the proportion of coherent movements (as in model 1) or the presence or absence of movements (as in model 2).

Fig. 3
Fig. 3

Three possible ways of spatially weighting incoming motion information. (A) The simplest method is to treat all signals similarly, independent of location. (B) A less restrictive method is to allow different weighting for motions in the central and peripheral regions. (C) The most flexible method explored here is to allow different weighting of the number of coherent motions in five overlapping regions of the visual field.

Fig. 4
Fig. 4

Observers’ and networks’ performance in predicting motion based on the number of coherently moving dots. Thinner curves, observers’ performance (the error bars equal the standard error, assuming a binomial distribution of responses). Thicker curves, networks’ performance on the same images; as can be seen, the logistic sigmoid provides a reasonable summary of the observers’ performance.

Fig. 5
Fig. 5

Observers’ and networks’ performance; this time based on the proportion of coherently moving dots.

Tables (2)

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Table 1 MSE for Two Observers Trained with Two Different Representations of the Input, Ratio Representation, and Absolute Representationa

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Table 2 MSE for Three Different Spatial Coding Schemesa

Equations (2)

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P ( M | S i ) = y ( a ) = 1 / [ 1 + exp ( - a ) ] ,
MSE = 1 N i = 1 N [ y ( S i ) - T ( S i ) ] 2 ,

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