Bayesian line orientation perception: Human prior expectations match natural image statistics

A R Girshick, M S Landy and E P Simoncelli

Published in Computational and Systems Neuroscience (CoSyNe), (II-33), Feb 2010.

DOI: 10.3389/conf.fnins.2010.03.00208

This paper has been superseded by:
Cardinal rules: Visual orientation perception reflects knowledge of environmental statistics
A R Girshick, M S Landy and E P Simoncelli.
Nature Neuroscience, vol.14(7), pp. 926--932, Jul 2011.

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    • The visual world is replete with contours, and their location and orientation provide important information about visual scenes. Are visual estimates of local contour orientation determined by sensory measurements alone? Or are percepts biased, in a Bayesian fashion, by prior knowledge of the distribution of contour orientations in the environment? Line orientation provides a good domain for understanding how humans use prior information because orientation statistics of natural images are non-uniform: There is a preponderance of cardinal (vertical and horizontal) orientations, as compared to oblique orientations, in both natural and human-made scenes (Switkes et al., 1978). If observers behave in a Bayesian manner, orientation estimates of noisy stimuli should be biased toward cardinal orientations. We adapted a recently developed technique for estimating priors used by human observers (Stocker & Simoncelli, 2006) to determine human orientation priors, and then compared these to those measured from natural image databases.

    In the psychophysical experiment, observers performed an orientation discrimination task, comparing either two low-noise stimuli (LvL), two high-noise stimuli (HvH), or a low- and high-noise stimulus (LvH). The first two conditions were used to assess the widths of subjects' likelihood functions, whereas the LvH condition allowed us to infer the shape of observers' prior expectations. A Bayesian observer with a non-uniform prior should exhibit biases in the LvH condition, because the prior will affect the orientation estimate of a high-noise stimulus more than a low-noise stimulus. The stimuli consisted of an array of 38 Gabor patches with orientations either all identical (L) or drawn from a normal distribution with standard deviation approximately 20 deg (H; SD chosen per observer based on a pilot discrimination experiment). The observers' task was to select the stimulus whose mean orientation was more clockwise. On each trial, the mean orientation of the standard stimulus was randomly selected from 12 orientations equally distributed over 180 deg. In the LvH conditions, observers behaved as if the perceived orientation of the high-noise stimulus was systematically biased toward the nearest cardinal orientation.

    Under the assumption that our observers are acting as Bayesian estimators, we used methods similar to those in (Stocker & Simoncelli, 2006) to extract a prior distribution on orientation that would explain their perceptual biases. We compared these perceptual priors to the distribution of orientation measured in three databases of images which included natural and human-made scenes. We used a Gaussian pyramid (Burt & Adelson, 1983) to represent each image at six different spatial resolutions, computed gradients using pairs of localized rotation-invariant derivative filters (Farid & Simoncelli, 2004), and then locally combined these to compute an estimate of dominant orientation.  We found that while histograms of these measurements varied in detail across databases and spatial scale, in all cases the cardinals were significantly more frequent than the obliques. The perceptually derived priors of our observers also varied in detail, but all exhibited substantially higher probability at the cardinals.  Thus, human observers exhibit Bayesian behavior consistent with the probabilistic structure of the environment when estimating visual line orientation.


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