Analysis and Computation of an Affine Trifocal

This paper investigates the trifocal tensor for an affine trinocular rig and de-fines an affine trifocal tensor. The question of the degrees of freedom of the tensor entries will be addressed, and a novel algorithm to compute the tensor by a linear technique is presented. It will be shown that 4 point or 8 line correspondences along the three images are enough for a reliable computa-tion of the trifocal tensor in the affine case (uncalibrated, weak perspective camera model), in contrast to the projective case, where at least 7 point or 13 line correspondences are needed for a linear computation (and usually with poor results). An analysis of the error in the approximation of a generic trifocal tensor by the affine trifocal tensor is carried out and preliminary ex-periments with synthetic and real data show the reliability and robustness of the approximation under a wide range of conditions.