The perception of surface curvature from optical motion

Observers viewed the optical flow field of a rotating quadric surface patch and were required to match its perceived structure by adjusting the shape of a stereoscopically presented surface. In Experiment 1, the flow fields included rigid object rotations and constant flow fields with patterns of image acceleration that had no possible rigid interpretation. In performing their matches, observers had independent control of two parameters that determined the surface shape. One of these, called the shape characteristic, is defined as the ratio of the two principle curvatures and is independent of object size. The other, called curvedness, is defined as the sum of the squared principle curvatures and depends on the size of the object. Adjustments of shape characteristic were almost perfectly accurate for both motion conditions. Adjustments of curvedness, on the other hand, were systematically over-estimated and were not highly correlated with the simulated curvedness of the depicted surface patch. In Experiment 2, the same flow fields were masked with a global pattern of curl, divergence, or shear, which disrupted the first-order spatial derivatives of the image velocity field, while leaving the second-order spatial derivatives invariant. The addition of these masks had only negligible effects on observers' performance. These findings suggest that observers' judgments of three-dimensional surface shape from motion are primarily determined by the second-order spatial derivatives of the instantaneous field of image displacements.