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Catherine Q. Howe, Dale Purves; A probabilistic explanation of perceived line length and orientation. Journal of Vision 2002;2(7):706. doi: 10.1167/2.7.706.
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Human perception of the length and the orientation of a straight line is systematically biased as a function of the 2D orientation of the line in the retinal image. Motivated by recent evidence that the relationship between the retinal image and perception is a wholly probabilistic one, we have explored the idea that perceived length and orientation of a linear stimulus are determined by the probabilistic relationship between the linear projection in the image plane and its possible physical sources. To test this hypothesis, we collected a database of natural scenes that included the range and luminance of every pixel in the images. The database thus relates projections in the image plane to the arrangement of objects in the physical world. Accordingly, we could determine the 3-D orientations of the physical sources of all straight-line projections on the retina (the image plane), as well as the ratio of the physical length of the sources to the length of their projections. We found that the probability distributions of the tilt, slant and the physical-to-image length ratio of straight lines determined in this way change systematically as a function of the orientation of the projected line. These variations in the probability distributions predict the perception of line length and line orientation as a function of line orientation. Because the probability distributions of the possible sources of oblique projections show greater variance than those of the linear projections in the cardinal axes, these statistical relationships can also rationalize the oblique effect (i.e., the poorer and more variable performance of human observers confronted with oblique lines compared to performance with lines in the cardinal axes).
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