Two metric solutions to three-dimensional reconstruction for an eye in pure rotations

Abstract

A problem in space perception concerns how a mobile observer acquires information about the structure of objects. Earlier research derived the optic-flow equations for an eye undergoing pure rotations. It was suggested that, by utilizing three points and two views, one can recover the distance of points and the motion parameters. The radius of the eyeball was the metric unit. Yet the common view regards this problem as indeterminate. We derived a unique solution in the discrete case, which required three points and two views. However, when we observed a single bright point, a substantial amount of visual stability existed. We therefore derived a solution in the differential approach for a single point, which is based on a distinction that we made between mathematical and visual points. Both solutions were checked with a computer simulation and were found to be accurate, supporting the space perception in navigation (SPIN) theory.