LINES AND POINTS IN 3 VIEWS AND THE TRIFOCAL TENSOR

This paper discusses the basic role of the trifocal tensor in scene re construction from three views. This 3 x 3 x 3 tensor plays a role in t he analysis of scenes from three views analogous to the role played by the fundamental matrix in the two-view case. In particular, the trifo cal tensor may be computed by a linear algorithm from a set of 13 line correspondences in three views. It is further shown in this paper, th at the trifocal tensor is essentially identical to a set of coefficien ts introduced by Shashua to effect point transfer in the three view ca se. 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 matrices of the images may be computed, and the sce ne may be reconstructed. For unrelated uncalibrated cameras, this reco nstruction will be unique up to projectivity. Thus, projective reconst ruction of a set of lines and points may be carried out linearly from three views.