The Oxford Handbook of Computational and Mathematical Psychology
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.