Plane-based projective reconstruction

Abstract

A linear method for computing a projective reconstruction from a large number of images is presented and then evaluated. The method uses planar homographies between views to linearize the resecting of the cameras. Constraints based on the fundamental matrix, trifocus tensor or quadrifocal tensor are used to derive relationship between the position vectors of all the cameras at once. The resulting set of equations are solved using a SVD. The algorithm is computationally efficient as it is linear in the number of matched points used. A key feature of the algorithm is that all of the images are processed simultaneously, as in the Sturm-Triggs factorization method, but it differs in not requiring that all points be visible in all views. An additional advantage is that it works with any mixture of line and point correspondence through the constraints these impose on the multilinear tensors. Experiments on both synthetic and real data confirm the method's utility.