The perception of motion and structure in structure-from-motion: comparisons of affine and Euclidean formulations

I investigated the discrimination of rigid from nonrigid structure and the perception of affine stretches along the line of sight [Norman & Todd (1993). Perception and Psychophysics, 53, pp. 279-291]. Investigations of performance at discriminating rigid from nonrigid structure showed that performance improved when number of views and amount of simulated three-dimensional nonrigidity increased. Investigations of rotations about the vertical which include affine stretches along the line of sight compared Euclidean interpretations of affine-stretching stimuli to human perception. These Euclidean interpretations were obtained from a simple algorithm which recovered structure and motion from this limited class of stimuli under the assumption that distances to the axis of rotation did not change. The algorithm predicted that stretches along the line of sight would be perceived as nearly rigid and have variable angular velocity. These predictions were supported by subjects' reports of occurrences of nonrigidity and minima of angular velocity. The Euclidean algorithm also provided measures of nonrigidity and motion coherence, and experimental results were consistent with a prediction of when perception of nonrigidity would be independent of perception of coherence. The results are discussed relative to the advantages and shortcomings of both the affine and Euclidean approaches to structure-from-motion.