{"paper":{"title":"Exact simultaneous recovery of locations and structure from known orientations and corrupted point correspondences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CO","math.IT","math.OC"],"primary_cat":"cs.CV","authors_text":"Choongbum Lee, Paul Hand, Vladislav Voroninski","submitted_at":"2015-09-16T20:56:53Z","abstract_excerpt":"Let $t_1,\\ldots,t_{n_l} \\in \\mathbb{R}^d$ and $p_1,\\ldots,p_{n_s} \\in \\mathbb{R}^d$ and consider the bipartite location recovery problem: given a subset of pairwise direction observations $\\{(t_i - p_j) / \\|t_i - p_j\\|_2\\}_{i,j \\in [n_l] \\times [n_s]}$, where a constant fraction of these observations are arbitrarily corrupted, find $\\{t_i\\}_{i \\in [n_ll]}$ and $\\{p_j\\}_{j \\in [n_s]}$ up to a global translation and scale. We study the recently introduced ShapeFit algorithm as a method for solving this bipartite location recovery problem. In this case, ShapeFit consists of a simple convex progra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05064","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":""},"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"}