{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/an-efficient-solution-to-non-minimal-case","title":"An Efficient Solution to Non-Minimal Case Essential Matrix Estimation","arxiv_id":"1903.09067","date":"2019-03-21","proceeding":null,"authors":["Ji Zhao"],"abstract":"Finding relative pose between two calibrated images is a fundamental task in computer vision. Given five point correspondences, the classical five-point methods can be used to calculate the essential matrix efficiently. For the case of $N$ ($N > 5$) inlier point correspondences, which is called $N$-point problem, existing methods are either inefficient or prone to local minima. In this paper, we propose a certifiably globally optimal and efficient solver for the $N$-point problem. First we formulate the problem as a quadratically constrained quadratic program (QCQP). Then a certifiably globally optimal solution to this problem is obtained by semidefinite relaxation. This allows us to obtain certifiably globally optimal solutions to the original non-convex QCQPs in polynomial time. The theoretical guarantees of the semidefinite relaxation are also provided, including tightness and local stability. To deal with outliers, we propose a robust $N$-point method using M-estimators. Though global optimality cannot be guaranteed for the overall robust framework, the proposed robust $N$-point method can achieve good performance when the outlier ratio is not high. Extensive experiments on synthetic and real-world datasets demonstrated that our $N$-point method is $2\\sim3$ orders of magnitude faster than state-of-the-art methods. Moreover, our robust $N$-point method outperforms state-of-the-art methods in terms of robustness and accuracy.","url_abs":"https://arxiv.org/abs/1903.09067v3","url_pdf":"https://arxiv.org/pdf/1903.09067v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"an-efficient-solution-to-non-minimal-case","repo_url":"https://github.com/javrtg/c2p","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"an-efficient-solution-to-non-minimal-case","repo_url":"https://github.com/utiasasrl/sdprlayer","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1903.09067","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}