3-D SHAPE PERCEPTION

In this paper, we analyze and test three theories of 3-D shape percept ion: (1) Helmholtzian theory, which assumes that perception of the sha pe of an object involves reconstructing Euclidean structure of the obj ect (up to size scaling) from the object's retinal image after taking into account the object's orientation relative to the observer, (2) Gi bsonian theory, which assumes that shape perception involves invariant s (projective or affine) computed directly from the object's retinal i mage, and (3) perspective invariants theory, which assumes that shape perception involves a new kind of invariants of perspective transforma tion. Predictions of these three theories were tested in four experime nts. In the first experiment, we showed that reliable discrimination b etween a perspective and nonperspective image of a random polygon is p ossible even when information only about the contour of the image is p resent. In the second experiment, we showed that discrimination perfor mance did not benefit from the presence of a textured surface, providi ng information about the 3-D orientation of the textured surface and t hat of a shape. In the third experiment, we compared discrimination fo r solid shapes that either had flat contours (cuboids) or did not have visible flat contours (cylinders). The discrimination was very reliab le in the case of cuboids but not in the case of cylinders. In the fou rth experiment, we tested the effectiveness of planar motion in percep tion of distances and showed that the discrimination threshold was lar ge and similar to thresholds when other cues of 3-D orientation were u sed. All these results support perspective invariants as a model of 3- D shape perception.