The orthographic projection of a rotating planar surface produces a linear velocity field that can be described by only three parameters: deformation, tilt and average velocity. In this kind of velocity field, deformation and tilt of local patches remain constant across the visual field but average velocity can largely vary from region to region. A linear velocity field is perceived as a planar surface whose slant is: (1) An increasing function of deformation, (2) A decreasing function of tilt, and (3) A decreasing function of the average velocity (Domini and Caudek, 1999; Todd and Perotti, 1999).

The compelling impression of planarity of a linear velocity field seems to suggest that human SFM must involve a process of spatial integration. In fact, since different local regions do not have the same average velocities, pure local processes would derive slants of different magnitudes according to finding (3). To investigate whether SFM undergoes a process of spatial integration we ask observers to judge the local orientation of a surface when the whole velocity field is visible or only a local region of the velocity field is visible.

Abstract: Observers' perceptions of the three-dimensional structure of smoothly curved surfaces defined by patterns of image shading were investigated under varying conditions of illumination. In five experiments, observers judged the global orientation and the motion of the simulated surfaces from both static and dynamic patterns of image shading. We found that perceptual performance was more accurate with static than with dynamic displays. Dynamic displays evoked systematic biases in perceptual performance when the surface and the illumination source were simulated as rotating in opposite directions. In these conditions, the surface was incorrectly perceived as rotating in the same direction as the illumination source. Conversely, the orientation of the simulated surfaces was perceived correctly when the frames making up the apparent-motion sequences of the dynamic displays were presented as static images. In Experiment 6, moreover, the results obtained with the computer-generated displays were replicated with solid objects.

Corrado Caudek; Fulvio Domini; Massimiliano Di Luca. Short-term temporal recruitment in structure from motion. Vision Research 2002 May, Volume 42 Number 10:1213-23
 

Abstract: Temporal integration was investigated in the minimal conditions necessary to perform a structure-from-motion (SFM) task. Observers were asked to discriminate three-dimensional (3D) surface orientations in conditions in which the stimulus displays simulated velocity fields providing, in each frame transition, either sufficient (3 moving dots) or insufficient information (1 or 2 moving dots) to perform the task. When only two moving dots were shown in each frame transition of the stimulus displays (Experiment 1), we found that performance decreased as dot-lifetime increased. A facilitation effect of the overall display duration was also found. The negative effect of dot-lifetime on performance contrasts with what found in Experiment 2 with three dots in each frame transition, where performance improved with increasing dot-lifetime up to 170 ms, and then reached a plateau. Finally, for an optimal dot-lifetime of 150 ms, we found that performance was still above chance when each frame transition specified the motion of only one dot (Experiment 3). These results indicate that temporal recruitment alone can support the recovery of 3D information from sparse motion signals, thus providing a strong indication for the importance of temporal integration in the perceptual analysis of the optic flow. Our results reveal, moreover, that temporal integration in SFM has different characteristics, depending on whether, in each frame transition, the stimulus displays provide either sufficient (3 or more moving dots) or insufficient information (1 or 2 moving dots) to specify the higher-order properties of the optic flow necessary for 3D surface recovery.