{"paper":{"title":"Provably Approximated ICP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.CV","authors_text":"Alaa Maalouf, Dan Feldman, Ibrahim Jubran, Ron Kimmel","submitted_at":"2021-01-10T18:09:29Z","abstract_excerpt":"The goal of the \\emph{alignment problem} is to align a (given) point cloud $P = \\{p_1,\\cdots,p_n\\}$ to another (observed) point cloud $Q = \\{q_1,\\cdots,q_n\\}$. That is, to compute a rotation matrix $R \\in \\mathbb{R}^{3 \\times 3}$ and a translation vector $t \\in \\mathbb{R}^{3}$ that minimize the sum of paired distances $\\sum_{i=1}^n D(Rp_i-t,q_i)$ for some distance function $D$. A harder version is the \\emph{registration problem}, where the correspondence is unknown, and the minimum is also over all possible correspondence functions from $P$ to $Q$. Heuristics such as the Iterative Closest Poin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.03588","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2101.03588/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}