Repeated structures: Image correspondence constraints and 3D structure recovery

Abstract

Recently, a number of classes of 3D structures have been identified which permit structure recovery and 3D invariants to be measured from a single image of the structure. A large class with this property is the case of repeated structures where a structure (such as a pointset, curve or surface), and a transformed copy of the structure are both observed in a single perspective image. In general the 3D reconstruction is only possible up to a 3D projectivity of space, but smaller ambiguities are possible, depending on the nature of the 3D transformation between the repeated structures. An additional theme of the paper is the development of feature correspondence relations based on the epipolar geometry induced in the image by the repeated structure. In some cases, correspondence is based on projective homologies rather than a true epipolar geometry.