Does the visual system exploit projective geometry to help solve the motion correspondence problem?

Abstract

Projective geometry determines how the retinal image of an object deforms as it moves through three-dimensional space. Does the visual system use constraints derived from this information, such as rigidity, to aid the tracking of moving objects? A novel psychophysical technique is introduced for assessing which of two competing motion transformations is 'preferred' by the visual system, in a two-frame sequence. In the first experiment, relative preference strengths for translations parallel and perpendicular to the major axis of a wire-frame object were measured by pitting the two against each other. It was found that parallel translations were preferred to perpendicular ones. On the basis of these data a proximity measure for normalising different transformations, independent of any effects of figural similarity, was developed. In the second experiment, two wire-frame planar structures were used to pit one of five transformations (rotation, expansion, vertical expansion, shear and random jitter) against a translation. Preference strength was measured as the translation distance at which the transformation and the translation were perceived with equal frequency. The PSEs were found to collapse on to a single line when plotted against the proximity magnitude, with the exception of a residual preference for pure translation over all other transformations. In general, these results suggest that preference strength for moving wire-frame figures is determined primarily by the proximity of local features on the displacing contour, with little regard for the projective shape transformation.