Perception of 3D surface orientation from skew symmetry

In this paper, we investigate how symmetry can be used to perceive 3D surface orientation. When a symmetric planar object is viewed from an angle, the projected contour has skew symmetry, which provides partial information about the 3D orientation of the object. For a given skew symmetry, this information can be characterized by a constraint curve of possible slant/tilt combinations that are consistent with a mirror-symmetric interpretation. These constraint curves move around when an object is rotated within a plane, and depend on what we will term the spin of the object: the angle between its axis of symmetry and the direction of tilt. To test the influence of symmetry constraint curves, we presented subjects with stereo images of symmetric objects that varied in spin, and had them perform an orientation-matching task. We found that the judgments showed biases that depended on the spin of the objects. Since other sources of information depend only on slant and tilt, not on spin, the biases imply that skew symmetry contributed to subjects' judgments. In a second experiment, we introduced conflicts between stereo and symmetry cues, and found that the spin-dependent biases can be modulated by selectively changing stereo slant. We propose an explanation of these results involving the optimal integration of stereo and skew symmetry, and present a Bayesian model that can account for the pattern of biases.