It is known that an orthographic image of a 3D symmetrical shape determines a one-parameter family of 3D symmetrical interpretations. Our previous study indicates that in most cases subjects' percept corresponds to the 3D shape from this family, whose compactness is maximal (Maximum Compactness Model, M2C, Li & Pizlo, 2007). In some cases, however, the perceived shape is not maximally compact: its range in depth is smaller than that of the maximally compact shape. To account for this result, we formulated a Bayesian version of M2C (BM2C). Two psychophysical experiments were performed to test these models. In Experiment 1, orthographic images of random 3D symmetrical shapes with random 3D orientations were generated. For those shapes the reconstructions of the two models are usually similar and they closely match the original shapes. Subjects were asked to adjust the unique parameter that characterizes the family of the 3D interpretations, until the reconstructed 3D shape was the same as their percepts. The perceived shapes closely matched the original shapes. In Experiment 2, the 3D shapes and their orientations were not random. Instead, they were selected to produce varying degree of differences in the reconstructions of the two models. Subjects' task was the same as that in Experiment 1. The perceived shapes were much closer to the 3D shapes reconstructed by BM2C than to those reconstructed by M2C. |