Perception of Parallelepipeds: Perkins's Law

Two experiments were carried out to study the perception of parallelepipeds. In the first, the subjects were shown images of parallelepipeds and were asked to judge the 3-D orientations of the faces of the parallelepipeds, as well as the shapes of the faces. These two types of judgments were found to be inconsistent. Specifically, the parallelepipeds reconstructed from judgments of 3-D orientations of the faces were systematically different from the parallelepipeds reconstructed from judgments of the shape of the faces. In the second experiment, the subjects were asked to choose which reconstruction was closer to their percept. In most trials the subjects chose the 3-D parallelepiped reconstructed from judgments of the shapes of the faces. These results suggest that the percept of the shape of a 3-D object is not based on the judgments of the 3-D orientations of the object's surfaces. Instead, the 3-D shape percept is based on simplicity constraints. A new computational model is presented, which generalizes Perkins's law (Perkins 1972). Instead of orthogonality, the new model uses mirror-symmetry and planarity constraints, in conjunction with maximum 3-D compactness and minimum surface-area constraints. The parallelepipeds recovered by the model are very close to the parallelepipeds perceived by the subjects.