# Resultant Based Incremental Recovery of Camera Pose from Pairwise Matches

arXiv: https://arxiv.org/abs/1901.09364 · HTML: https://mlsanity.com/paper/1901.09364/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2019.

## Built on by (most cited first, 5 of 5)

- [Six-Point Method for Multi-Camera Systems with Reduced Solution Space](https://mlsanity.com/paper/2402.18066/) (2024)
- [Depth from Camera Motion and Object Detection](https://mlsanity.com/paper/2103.01468/) (2021)
- [Sparse resultant based minimal solvers in computer vision and their connection with the action matrix](https://mlsanity.com/paper/2301.06443/) (2023)
- [On Relative Pose Recovery for Multi-Camera Systems](https://mlsanity.com/paper/2102.11996/) (2021)
- [Solving Minimal Problems Without Matrix Inversion Using FFT-Based Interpolation](https://mlsanity.com/paper/2605.06572/) (2026)

## Abstract (arXiv)

Incremental (online) structure from motion pipelines seek to recover the camera matrix associated with an image In given n-1 images, I1,...,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 In. Our algorithm uses just six corresponding pairs of 2D points, extracted each from In and from textitany 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.