The effect of polar projection on the perception of euclidean structure from motion

The aim of the present study was to examine whether euclidean structure could be recovered from apparent motion sequences under polar projection. In Experiment 1, length judgments of two sides of a simulated triangle rotating in depth did not reveal effects of type of projection, polar or parallel, on the perception of euclidean structure. However, there was a significant correlation between simulated and produced slants. The results also indicated that absolute depth judgments could not be accounted for by a random mechanism suggested by Todd and Bressan (1990). Experiments 2 and 3, in which a continuous dot surface was substituted for the triangle, showed that polar projection information from a relatively large visual angle, 17.40 degrees, as compared with a small visual angle, 4.35 degrees, facilitated discrimination of depth. Produced height:width ratios were consistently related to simulated shape, although the depth dimension was underestimated. Finally, Experiment 4 showed significant correlations between simulated and produced height:width ratios that could be accounted for only by an analysis in which X and Y velocities were treated independently. As in previous experiments, the variation in the depth dimension was underestimated. It was concluded that the visual system utilizes the additional information that is available in polar projection when recovering structure from motion, but that for different reasons the perceived structure does not become euclidean. These reasons are discussed briefly.