Resultant Based Incremental Recovery of Camera Pose from Pairwise Matches
This provides a more flexible and efficient solution for incremental structure from motion pipelines, benefiting computer vision applications like 3D reconstruction.
The paper tackles the problem of incremental camera pose recovery in structure from motion by introducing a six-point online algorithm that uses only six 2D point correspondences from a new image and any previous one, enabling full six-degree-of-freedom recovery without multi-image tracking. Experiments show it is efficient and accurate compared to existing methods.
Incremental (online) structure from motion pipelines seek to recover the camera matrix associated with an image $I_n$ given $n-1$ images, $I_1,...,I_{n-1}$, 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 \textit{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.