3-D shape perception

In this paper, we analyze and test three theories of 3-D shape perception: (1) Helmholtzian theory, which assumes that perception of the shape of an object involves reconstructing Euclidean structure of the object (up to size scaling) from the object’s retinal image after taking into account the object’s orientation relative to the observer, (2) Gibsonian theory, which assumes that shape perception involves invariants (projective or affine) computed directly from the object’s retinal image, and (3) perspective invariants theory, which assumes that shape perception involves a new kind of invariants of perspective transformation. Predictions of these three theories were tested in four experiments. In the first experiment, we showed that reliable discrimination between a perspective and nonperspective image of a random polygon is possible even when information only about the contour of the image is present. In the second experiment, we showed that discrimination performance did not benefit from the presence of a textured surface, providing information about the 3-D orientation of the polygon, and that the subjects could not reliably discriminate between the 3-D orientation of the textured surface and that of a shape. In the third experiment, we compared discrimination for solid shapes that either had flat contours (cuboids) or did not have visible flat contours (cylinders). The discrimination was very reliable in the case of cuboids but not in the case of cylinders. In the fourth experiment, we tested the effectiveness of planar motion in perception of distances and showed that the discrimination threshold was large and similar to thresholds when other cues to 3-D orientation were used. All these results support perspective invariants as a model of 3-D shape perception.     

Book Review

Arnheim, Rudolf, “Picasso's Guernica, The Genesis of a Painting,” University of California Press, Berkeley, California, 1962. Pp. 139, $8.50. Reviewed by Irving R. Stone     

The logical investigations of jan kalicki

This paper describes the work of the Polish logician Jan Kalicki (1922–1953). After a biographical introduction, his work on logical matrices and equational logic is appraised. A bibliography of his papers and reviews is also included.     

A note on direct products and ultraproducts of logical matrices

In this contribution we shall characterize matrix consequence operation determined by a direct product and an ultraproduct of a family of logical matrices. As an application we shall describe finite consequence operations with the help of ultrapowers.