{"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/tensor-based-synchronization-and-the-low","title":"Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor","arxiv_id":"2409.09313","date":"2024-09-14","proceeding":null,"authors":["Daniel Miao","Gilad Lerman","Joe Kileel"],"abstract":"The block tensor of trifocal tensors provides crucial geometric information on the three-view geometry of a scene. The underlying synchronization problem seeks to recover camera poses (locations and orientations up to a global transformation) from the block trifocal tensor. We establish an explicit Tucker factorization of this tensor, revealing a low multilinear rank of $(6,4,4)$ independent of the number of cameras under appropriate scaling conditions. We prove that this rank constraint provides sufficient information for camera recovery in the noiseless case. The constraint motivates a synchronization algorithm based on the higher-order singular value decomposition of the block trifocal tensor. Experimental comparisons with state-of-the-art global synchronization methods on real datasets demonstrate the potential of this algorithm for significantly improving location estimation accuracy. Overall this work suggests that higher-order interactions in synchronization problems can be exploited to improve performance, beyond the usual pairwise-based approaches.","url_abs":"https://arxiv.org/abs/2409.09313v2","url_pdf":"https://arxiv.org/pdf/2409.09313v2.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":"tensor-based-synchronization-and-the-low","repo_url":"https://github.com/dmiao153/trifocalsync","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"tucker","method_name":"TuckER"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2409.09313","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}