SHAPE EQUIVALENCE UNDER PERSPECTIVE AND PROJECTIVE TRANSFORMATIONS

When a planar shape is viewed obliquely, it is deformed by a perspecti ve deformation. If the visual system were to pick up geometrical invar iants from such projections, these would necessarily be invariant unde r the wider class of projective transformations. To what extent can th e visual system tell the difference between perspective and nonperspec tive but still projective deformations of shapes? To investigate this, observers were asked to indicate which of two test patterns most rese mbled a standard pattern. The test patterns were related to the standa rd pattern by a perspective or projective transformation, or they were completely unrelated. Performance was slightly better in a matching t ask with perspective and unrelated test patterns (92.6%) than in a pro jective-random matching task (88.8%). In a direct comparison, particip ants had a small preference (58.5%) for the perspectively related patt erns over the projectively related ones. Preferences were based on the values of the transformation parameters (slant and shear). Hence, per spective and projective transformations yielded perceptual differences , but they were not treated in a categorically different manner by the human visual system.