{"paper":{"title":"Camera Pose Filtering with Local Regression Geodesics on the Riemannian Manifold of Dual Quaternions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Benjamin Busam, Nassir Navab, Tolga Birdal","submitted_at":"2017-04-24T07:52:41Z","abstract_excerpt":"Time-varying, smooth trajectory estimation is of great interest to the vision community for accurate and well behaving 3D systems. In this paper, we propose a novel principal component local regression filter acting directly on the Riemannian manifold of unit dual quaternions $\\mathbb{D} \\mathbb{H}_1$. We use a numerically stable Lie algebra of the dual quaternions together with $\\exp$ and $\\log$ operators to locally linearize the 6D pose space. Unlike state of the art path smoothing methods which either operate on $SO\\left(3\\right)$ of rotation matrices or the hypersphere $\\mathbb{H}_1$ of qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07072","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}