Accurate Recovery of Structure from Motion under Perspective Projection

For small objects rotating over a small angle, the 3-D structure and motion are inseparable. Increasing the angle of rotation helps to define image accelerations while increasing the angular size of the object produces greater perspective effects. Both of these cues could be used by the visual system to disambiguate the structure and motion.

In a 2 × 2 design we tested the influence of angular size (8 deg ‘S’ or 32 deg ‘L’) and projection type (perspective ‘P’ or orthographic ‘O’) on the perceived dihedral angle of vertically hinged planes (‘open books’). Stimuli depicted hinged planes with dihedral angles ranging from 35° to 169° rotating over angles ranging from 2° to 58°. The task of the subjects was to match the perceived dihedral angle to that of a probe defined by motion, texture, and binocular disparities. Spearman rank order correlations of subjects' settings with the simulated dihedral angles were high in condition LP (r=0.93) and decreased in the order LP>=SP>=SO>=LO. In the same order, correlations with the total displacement of the projected points increased, up to r=−0.94 in condition LO, indicating that structure and motion become more and more confounded.

While for small rotations and small dihedral angles, the settings are heavily influenced by the amount of rotation, for larger rotations and larger dihedral angles settings are more constant over rotation. These results show that both image acceleration and perspective effects play an important role in increasing the veridicality of perceived structure from motion.