Shape constancy refers to the fact that the percept of the shape of a given object remains constant despite changes in the shape of the retinal image. The retinal image may change because of changes in the orientation of the object, relative to the observer. Shape is usually defined by angles and by ratios of distances. According to this definition, rigid motions and size scaling do not change shape. In other words, shape is invariant under similarity transformations. A perspective transformation between the 3-D scene and the 2-D retina is quite different from a similarity transformation (Pizlo, Rosenfeld, & Weiss, 1997). First of all, it is a many-to-one mapping. As a result, the information about depth is lost, and the shape on the retina may change substantially when the orientation of the object, relative to the observer, changes. It follows that shape constancy is a difficult computational problem. In the case of familiar objects, shape constancy could, theoretically, be achieved by means of a simple template-matching mechanism, in which the current view is compared with all previously seen views of the object. In order to provide an adequate test between this and other mechanisms, one should use unfamiliar objects and test shape constancy from unfamiliar (novel) views. Rock and DiVita (1987) performed the first systematic study of shape constancy from novel views, using 3-D objects. They used unstructured 3-D wire objects, which were viewed binocularly from a close viewing distance. Rock and DiVita reported a complete failure of shape constancy in the presence of a difference of only 45º between the views of an object. The authors concluded that the shapes of 3-D objects are perceived (and recognized) by memorizing a large number of 2-D images taken from many different viewing directions-the template matching mentioned in the first paragraph. In a subsequent study, Rock, Wheeler, and Tudor (1989) provided additional evidence by showing that observers cannot imagine how a novel wire object looks from a new viewing direction. The results of these two studies strongly suggest that the perceptual representation of objects does not involve 3-D properties. Biederman and Gerhardstein (1993) reported a quite different result. They used line drawings of unfamiliar 3-D geometrical objects built from geons and demonstrated almost perfect shape constancy from novel views (geons are simple 3-D objects, such as a box, cone, cylinder, or pyramid; Biederman, 1987). This result is, actually, hardly surprising because, phenomenologically, it is easy to imagine how novel or familiar objects built from geons (and many other structured objects) look from new viewing directions. In other words, Biederman and Gerhardstein's study provided strong support for the claim We tested shape constancy from novel views in the case of binocular viewing, using a variety of stimuli, including polyhedra, polygonal lines, and points in 3-D. The results of the psychophysical experiments show that constraints such as planarity of surface contour...
