Mark Beers¹; ¹University of California, Irvine

Mathematically, 3D shape reconstruction from a perspective image of a symmetrical object is unique, but 3D reconstruction from an orthographic image yields a one parameter family of possible 3D shapes. Last year, I showed that subject’s perceived 3D shape from a perspective image was often closer to veridical, and never less veridical, when perspective information was more reliable. Here, I elaborate on last year’s experiment to test how the human visual system incorporates symmetry and perspective information and propose a Bayesian model that explains how constraints (aka priors) are combined with the visual image. On each trial in the experiment, a static perspective image is shown on the computer monitor, as well as an adjustable rotating 3D shape. The subject adjusted the aspect ratio of the rotating 3D shape until the shape matched the 3D percept produced by the static 2D image. From trial to trial, object shown and simulated distance varied. As the simulated distance of an object to the observer increases, the perspective information becomes less reliable and the subject’s percept often becomes less veridical. All shapes used in the experiment were symmetrical or approximately symmetrical, real-world objects selected from the ModelNet-40 dataset. A hierarchical Bayesian model is introduced which performs 3D shape reconstruction. Several versions of the model are compared. The best models include the following shape constraints: compactness of the convex hull of the 3D shape and a second mirror symmetry. In addition, the model uses perspective information to aid in reconstruction but the contribution of perspective information is mediated by a measure of its reliability. The reliability of perspective information is affected by relative angles and lengths of visible symmetry line segments. The model biases the 3D reconstruction towards veridicality when perspective information is reliable.