A linear method for reconstruction from lines and points

Abstract

Discusses the basic role of the trifocal tensor in scene reconstruction. This 3/spl times/3/spl times/3 tensor plays a role in the analysis of scenes from three views analogous to the role played by the fundamental matrix in the two-view case. In particular, the trifocal tensor maybe computed by a linear algorithm from a set of 13 line correspondences in three views. It is further shown in this paper to be essentially identical to a set of coefficients introduced by Shashua (1994) to effect point transfer in the three-view case. This observation means that the 13-line algorithm may be extended to allow for the computation of the trifocal tensor given any mixture of sufficiently many line and point correspondences. From the trifocal tensor, the camera image matrices may be computed, and the scene may be reconstructed. For unrelated uncalibrated cameras, this reconstruction is unique up to projectivity. Thus, projective reconstruction of a set of lines and points may be reconstructed linearly from three views.