There is a perceptual tendency to see the 2-dimensional transformations of shadows as rigid movements in 3 dimensions. The significance of this illusion for veridical perception is investigated by a mathematical analysis of the correspondence between 3 dimensional object displacements and the optical motions they cause at the eye. The results show that optically equivalent object displacements share significant features, and that therefore the optical motions they produce are potentially informative about those features. Some of the objective features specified by optical motions are initial orientation, rotation, and the ratio between initial distance and translation distance. The analysis is based on coplanar sets of object points, and the fact that their displacements produce 2-dimensional projective transformations of the retinal image.
Abstract