{"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/essential-matrix-estimation-using-convex","title":"Essential Matrix Estimation using Convex Relaxations in Orthogonal Space","arxiv_id":null,"date":"2023-01-01","proceeding":"ICCV 2023 1","authors":["Arman Karimian","Roberto Tron"],"abstract":"    We introduce a novel method to estimate the essential matrix for two-view Structure from Motion (SfM). We show that every 3 by 3 essential matrix can be embedded in a 4 by 4 rotation, having its bottom right entry fixed to zero; we call the latter the quintessential matrix. This embedding leads to rich relations with the space of 4-D rotations, quaternions, and the classical twisted-pair ambiguity in two-view SfM. We use this structure to derive a succession of semidefinite relaxations that require fewer parameters than the existing non-minimal solvers and yield faster convergence with certifiable optimality. We then exploit the low-rank geometry of these relaxations to reduce them to an equivalent optimization on a Riemannian manifold and solve them via the Riemannian Staircase method. The experimental evaluation confirms that our algorithm always finds the globally optimal solution and outperforms the existing non-minimal methods. We make our implementations open source.    ","url_abs":"http://openaccess.thecvf.com//content/ICCV2023/html/Karimian_Essential_Matrix_Estimation_using_Convex_Relaxations_in_Orthogonal_Space_ICCV_2023_paper.html","url_pdf":"http://openaccess.thecvf.com//content/ICCV2023/papers/Karimian_Essential_Matrix_Estimation_using_Convex_Relaxations_in_Orthogonal_Space_ICCV_2023_paper.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":"essential-matrix-estimation-using-convex","repo_url":"https://github.com/armandok/qme","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}