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...

Prior experiments on shape constancy from novel views are inconclusive: Some show that shapes of objects can be recognized reliably from novel views, whereas others show just the opposite. Our analysis of prior results suggests that shape constancy from novel views is reliable when the object has properties that constrain its shape: The object has volumetric primitives, it has surfaces, it is symmetrical, it is composed of geons, its contours are planar, and its images provide useful topological information about its three-dimensional structure. To test the role of some of these constraints, we performed a set of experiments. Solid shapes (polyhedra) were shown on a computer monitor by means of kinetic depth effect. Experiment 1 showed that shape constancy can be reliably achieved when a polyhedron is represented by its contours (most of the constraints are present), but not when it is represented by vertices or by a polygonal line connecting the vertices in a random order (all the constraints are absent). Experiments 2 and 3 tested the role of individual constraints. Results ofthese experiments show that shape constancy from novel views is reliable when the object has planar contours and when the shapes of the contours together with topological information about the relations among the contours constrain the possible interpretations of the shape. Symmetry of the object and the topological stability of its image also contribute to shape constancy.Shape constancy refers to the fact that the percept ofthe 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 (see Pizlo, 1994, for a review of prior research on shape constancy). Consider an example of shape constancy. When you walk around your car, your retinal image of the car changes. Yet, your percept of the shape of the car is constant. One can argue that achieving shape constancy in the case of your car may represent a rather trivial accomplishment: After all, you have seen your car from almost all viewing directions, and, therefore, the constancy of the percept of the car's shape may simply involve matching ofthe current view with all previously seen views. To prevent the observer from matching familiar views (or images), one should use unfamiliar objects and test shape constancy from unfamiliar (novel) views. There have been a number of studies performed during the last decade that tested whether shape constancy can be reliably achieved from novel views. We will first briefly review the most representative results.Rock and DiVita (1987) used three-dimensional (3-0) wire objects as stimuli. Viewing was binocular with a This study was presented at the annual meetings of the Association for Research in Vision and Ophthalmology in 1997 and 1998. The authors thank the anonymous reviewers for their comments and suggestions, Moses Chan, Jan-Yuen Chen, Corrinne Lim, and Grant Wei who served as subjects, Filip J. Pizlo for his...

Interactive on-line experiments provide a unique and useful method for communicating material to students that is otherwise cumbersome and often confusing, The Java programming language is particularly suited for Internet-based programming applications of this sort because it bypasses many technical issues, including resource availability, security, and cross-platform compatibility, In most cases, topics appropriate to this medium of presentation should (l) not be easily demonstrated by other means, (2) represent an important finding in the field, and (3) be robust with respect to variations in both participants and equipment. The present paper outlines the integration of interactive experiments into an introductory cognitive psychology classroom, describing several experiments currently available on the World-Wide Web (WWW), Evaluation of the technical aspects of the technology as well as expansion of the format to other courses is discussed, For undergraduate science students, some of the most important classes involve getting hands-on experience with the methods and materials of their discipline. Thus, chemistry classes include laboratory sections where students explore the chemical properties of substances, introductory physics classes include laboratory sections where students experimentally validate the fundamental laws of motion, and biology classes include laboratory sections where students explore animal and human physiology. The laboratory sections of these classes are so important that it is difficult to imagine learning these disciplines without them.In contrast, psychology courses rarely involve hands-on experience. The few exceptions tend to be for psychobiology courses and courses that emphasize research methods. Of course, some topics in psychology do not easily lend themselves to a laboratory section, but many do. Cognitive psychology is the scientific study of mental processes (perception, memory, language, problem solving, decision making, etc.), and as a field it has gathered a number of key studies that demonstrate significant aspects of cognition in a laboratory setting.An accompanying laboratory experience in cognitive psychology allows students to better appreciate the relationship between, and need for careful control of, variables. Furthermore, given that the majority of experiments in this field are carried out on computers, a computer-based laboratory provides not only an efficient method of presenting laboratory exercises but also experience inter-

No abstract