December 2001
Volume 1, Issue 3
Vision Sciences Society Annual Meeting Abstract  |   December 2001
Bayesian slant estimation
Author Affiliations
  • Wendy J. Adams
    University of Glasgow, Glasgow, Scotland, UK
  • Pascal Mamassian
    University of Glasgow, Glasgow, Scotland, UK
Journal of Vision December 2001, Vol.1, 175. doi:
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      Wendy J. Adams, Pascal Mamassian; Bayesian slant estimation. Journal of Vision 2001;1(3):175. doi:

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      © ARVO (1962-2015); The Authors (2016-present)

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Purpose: An observer estimating the slant of a surface from noisy information must have a strategy to make his decision. A Bayesian observer will make the optimal decision by minimizing the expected loss. We investigated whether human observers behave in a Bayesian manner. Methods: Stereoscopic surfaces were depicted by a back-projected, random-dot texture. Half of the dots within each stimulus were randomly assigned to one slant population, and half to another. The mean slant of the first population was s, and the second was −s. Hence the average slant was always zero. The total noise in the stimulus was constant. However, the ratio of noise between the two populations varied. Observers matched the perceived slant of the stimulus by rotating a stereoscopically defined probe. A Bayesian observer calculates a posterior distribution of world slants from the information in the image and his prior knowledge. Each response has an expected loss, computed from the loss function and the posterior distribution. The expected loss, and therefore the decision, is determined by the shape of the loss function used by the observer. A narrow loss function rewards only correct responses, whereas a broad (or robust) loss function rewards responses in the vicinity of the true slant. In our experiment, a Bayesian observer would change its decision based on the ratio of the stimulus noises. Results: Observers' responses varied with the noise ratio; they did not simply respond with the mean of the slant information present in the stimulus. Their response was biased towards the less noisy slant population. Discussion: Our result is consistent with a Bayesian model, in which a broad loss function is employed.

Adams, W.J., Mamassian, P.(2001). Bayesian slant estimation [Abstract]. Journal of Vision, 1( 3): 175, 175a,, doi:10.1167/1.3.175. [CrossRef]
 Supported by the Human Frontier Science Program RG 0109/1999-B.

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