Resultant Based Incremental Recovery of Camera Pose from Pairwise Matches

Incremental (online) structure from motion pipelines seek to recover the camera matrix associated with an image I-n given n-1 images, I-1, ..., In-1, whose camera matrices have already been recovered. In this paper, we introduce a novel solution to the six-point online algorithm to recover the exterior parameters associated with I-n. Our algorithm uses just six corresponding pairs of 2D points, extracted each from I-n and from any of the preceding n - 1 images, allowing the recovery of the full six degrees of freedom of the n'th camera, and unlike common methods, does not require tracking feature points in three or more images. Our novel solution is based on constructing a Dixon resultant, yielding a solution method that is both efficient and accurate compared to existing solutions. We further use Bernstein's theorem to prove a tight bound on the number of complex solutions. Our experiments demonstrate the utility of our approach.