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Cardinal rules: visual orientation perception reflects knowledge of environmental statistics


Humans are good at performing visual tasks, but experimental measurements have revealed substantial biases in the perception of basic visual attributes. An appealing hypothesis is that these biases arise through a process of statistical inference, in which information from noisy measurements is fused with a probabilistic model of the environment. However, such inference is optimal only if the observer's internal model matches the environment. We found this to be the case. We measured performance in an orientation-estimation task and found that orientation judgments were more accurate at cardinal (horizontal and vertical) orientations. Judgments made under conditions of uncertainty were strongly biased toward cardinal orientations. We estimated observers' internal models for orientation and found that they matched the local orientation distribution measured in photographs. In addition, we determined how a neural population could embed probabilistic information responsible for such biases.

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Figure 1: Observer model for local two-dimensional orientation estimation.
Figure 2: Derivation of the estimator θ̂(m(θ)).
Figure 3: Stimuli and experimental results.
Figure 4: Example cross-noise comparison.
Figure 5: Recovered priors for subject S1 and mean subject.
Figure 6: Natural image statistics.
Figure 7: Comparison of human observers' priors and environmental distribution for subject S1 (left) and the mean subject (right).
Figure 8: Simulations of neural models with non-uniform encoder and population vector decoder.


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We wish to thank D. Ganguli for helpful discussions on image statistics and population coding, T. Saarela for the monitor calibration and N. Solomon for assisting with the experiments. This work was funded by US National Institutes of Health grants EY019451 (A.R.G.) and EY16165 (M.S.L.), and the Howard Hughes Medical Institute (E.P.S.).

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A.R.G., M.S.L. and E.P.S. contributed to the design of the experiments, design of the analyses and the writing of the manuscript. A.R.G. conducted the experiments and performed the analyses.

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Correspondence to Ahna R Girshick.

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The authors declare no competing financial interests.

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Girshick, A., Landy, M. & Simoncelli, E. Cardinal rules: visual orientation perception reflects knowledge of environmental statistics. Nat Neurosci 14, 926–932 (2011).

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