Depth-order violation in structure from motion

Humans can recover the structure of a three-dimensional object from motion cues alone. Recovery of structure-from-motion (SFM) from the projected 2D motion field of a rotating object has been studied almost exclusively in the condition where the axis of rotation lies in the frontoparallel plane. Here we assess the ability of humans to recover SFM in the general case, where the axis of rotation may be tilted out of the frontoparallel plane. Using elliptical cylinders whose cross-section was constant along the axis of rotation, we find that, across a range of parameters, subjects accurately matched the simulated shape of the cylinder regardless of how much the axis of rotation is inclined away from the frontoparallel plane. We also find that subjects do not perceive the inclination of the axis of rotation veridically. These results violate a relationship between perceived angle of inclination and perceived shape that must hold if SFM is to be recovered from the instantaneous velocity field. The contradiction can be resolved if the angular speed of rotation is not consistently estimated from the instantaneous velocity field. This in turn predicts that variation in object size along the axis of rotation can cause depth-order violation in object shape perception. This prediction was verified using rotating circular cones as stimuli. Thus, the visual system reduces the complexity of computing structure from motion at the expense of introducing severe distortions in the recovered shape. The trajectories of points on a surface rotating about a frontoparallel axis are linear and parallel to one another under orthographic projection. The trajectories of points on a surface rotating about an axis tilted out of the frontoparallel plane, however, are curved and do not bear a simple geometrical relationship to each other. We investigated the ability of humans to recover SFM in this latter case. Subjects viewed a motion-defined elliptical cylinder textured with random dots. They then viewed a cylindrical cross section, which they adjusted to match the profile of the motion-defined cylinder. We define flatness (F) as the cylinder's depth-to-width ratio (i.e., F=1 for a circular cylinder). Figs. 1a-b show the ratio between perceived (F obs ) and simulated (F sim ) flatness averaged across the four subjects. F obs /F sim does not change with the simulated angle of inclination (Fig. 1a), fluctuating narrowly between the values 0.83 and 0.88. However (Fig. 1b) F obs /F sim does depend on the simulated flatness. In all cases, cylinders were perceived as flatter than simulated, but the difference was large for flattened cylinders (F sim <1). Results shown in Figs. 1 a and b are averages of four different conditions combining short and sustained dot lifetimes and occluded and unoccluded surface boundaries. The