The Poggendorff illusion explained by the statistics of natural scene geometry
One of the most intriguing discrepancies between the perception of a visual stimulus and its real-world source is the Poggendorff illusion. When an obliquely oriented line is occluded by a bar, the continuation of the line across the occluder appears to be shifted vertically, despite of the collinearity of the separated line segments. A great deal of literature on this subject notwithstanding, none of the explanations so far provided (the angle theory and the depth theory are the two major categories) has satisfactorily accounted for all aspects of this effect. Here we have tested a wholly empirical explanation of this illusion. To this end, we acquired a database of natural scenes (including indoor, outdoor and natural scenes) in which the distances of all the objects from the image plane were determined with a laser range scanner. We found the probability distribution of the possible positions of the line segments in the database lying on the 'far side' of an imagined occluder to be shifted vertically compared to the positions obtained by direct extension of the same line segments. This shift was apparent in indoor, outdoor and fully natural scenes, albeit with different magnitudes and variances. Moreover, the magnitude of the shift 1) increased with the width of the occluding bar; 2) increased with a decrease in the (acute) angle of the intersection of the line with the occluder; 3) diminished for the acute angle components of the stimulus, but was maintained for the obtuse angle components; and 4) diminished when the stimulus configuration was rotated. Each of these behaviors has been described in the perceptual responses to corresponding variations in the presentation of the Poggendorff stimulus. We conclude that this otherwise peculiar set of perceptual discrepancies is generated by the probabilistic relationship between the relevant features in the image plane and the probability distribution of the possible underlying sources of the stimulus in the real world.
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