Projective invariance and picture perception

Four experiments test the assumption that, in the visual perception of pictures, observers have reliable and direct access to the equivalence of shapes in projective geometry. The assumption is that perception of projective equivalence is the basis of shape constancy ('the projective thesis'). Observers matched or reproduced abstract planar shapes under conditions of rotation in the picture plane, and pictured rotation in depth. Departure from projective equivalence was assessed in each study by measuring the planar analogue of cross ratio. Projective equivalence was not found to be perceived uniformly where Euclidean equivalence was not judged uniformly, either in recognition tasks or in production tasks. When the projective thesis is put to a suitably general test, confidence in the thesis is undermined.