The Effects of Three-Dimensional Context on Shape Perception

Humans have a unique ability to perceive shape in different ways. Although we naturally estimate objective (physical) shape in our daily interactions with the world, we are also capable of estimating projective (retinal) shape, especially when attempting to accurately draw objects and scenes. In four experiments, we demonstrated robust effects of 3D context on shape perception. Using a binocular stereo paradigm, we presented rectangular surfaces of varying widths alone or embedded in a polyhedron. We investigated how context, judgment type, and angle affected width estimates. We found that the presence of even a small amount of 3D context aids objective judgments but hinders projective judgments, whereas a lack of context had the opposite effect. Context facilitated objective shape assessments by improving estimates of surface orientation. These results demonstrate that the typical presence of 3D context aids shape perception (shape constancy) while simultaneously making the projective judgments necessary for realistic drawing more difficult.

Shape Perception

This chapter provides a review of topics and concepts that are necessary to study and understand 3D shape perception. This includes group theory and their invariants; model-based invariants; Euclidean, affine, and projective geometry; symmetry; inverse problems; simplicity principle; Fechnerian psychophysics; regularization theory; Bayesian inference; shape constancy and shape veridicality; shape recovery; perspective and orthographic projections; camera models; as well as definitions of shape. All concepts are defined and illustrated, and the reader is provided with references providing mathematical and computational details. Material presented here will be a good starting point for students and researchers who plan to study shape, as well as for those who simply want to get prepared for reading the contemporary literature on the subject.