It is known that a single orthographic image of a 3D symmetrical shape determines a one-parameter family of 3D symmetrical interpretations. We hypothesize that the subject's percept corresponds to the 3D shape from this family whose compactness is maximal. The 3D compactness is defined as the object's volume squared divided by the object's surface area cubed (V^2/S^3). Besides symmetry and compactness, our model also uses planarity of contours as a constraint. To test psychological plausibility of this model, we performed two experiments. In experiment 1 (preference), one 2D view of a 3D symmetrical shape was shown on the top. Two 3D rotating shapes (one was the original shape used to generate the view, and the other was a shape reconstructed by our algorithm) were shown in the bottom and the subject's task was to decide which of these two 3D shapes is closer to the 3D percept produced by the 2D view shown on the top. The subjects systematically preferred the reconstructed shape. In experiment 2 (reconstruction), the subject was shown one 2D view of a 3D symmetrical shape and a 3D rotating shape. The subject's task was to adjust the 3D shape so that it agreed with the 3D percept produced by the 2D view. The adjustment was done by setting the value of the free parameter determining the family of 3D symmetrical shapes consistent with the 2D view. The subjects' percept was always close to the 3D shape with the maximum compactness. In some cases, the perceived shape had less “depth” than the shape with maximum compactness. In order to account for these results, we use a Bayesian model in which the percept corresponds to the maximum of the posterior distribution.
Purdue Research Foundation