Shape equivalence under perspective and projective transformations

When a planar shape is viewed obliquely, it is deformed by a perspective deformation. If the visual system were to pick up geometrical invariants from such projections, these would necessarily be invariant under the wider class of projective transformations. To what extent can the visual system tell the difference between perspective and nonperspective but still projective deformations of shapes? To investigate this, observers were asked to indicate which of two test patterns most resembled a standard pattern. The test patterns were related to the standard pattern by a perspective or projective transformation, or they were completely unrelated. Performance was slightly better in a matching task with perspective and unrelated test patterns (92.6%) than in a projective-random matching task (88.8%). In a direct comparison, participants had a small preference (58.5%) for the perspectively related patterns over the projectively related ones. Preferences were based on the values of the transformation parameters (slant and shear). Hence, perspective and projective transformations yielded perceptual differences, but they were not treated in a categorically different manner by the human visual system.

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