Relative orientation

Abstract

Before corresponding points in images taken with two cameras can be used to recover distances to objects in a scene, one has to determine the position and orientation of one camera relative to the other. This is the classic photogrammetric problem of relative orientation, central to the interpretation of binocular stereo information. Iterative methods for determining relative orientation were developed long ago; without them we would not have most of the topographic maps we do today. Relative orientation is also of importance in the recovery of motion and shape from an image sequence when successive frames are widely separated in time. Workers in motion vision are rediscovering some of the methods of photogrammetry.Described here is a simple iterative scheme for recovering relative orientation that, unlike existing methods, does not require a good initial guess for the baseline and the rotation. The data required is a pair of bundles of corresponding rays from the two projection centers to points in the scene. It is well known that at least five pairs of rays are needed. Less appears to be known about the existence of multiple solutions and their interpretation. These issues are discussed here. The unambiguous determination of all of the parameters of relative orientation is not possible when the observed points lie on a critical surface. These surfaces and their degenerate forms are analyzed as well.