{"paper":{"title":"Approximate Algorithms for Chamfer Distance Under Translation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.CG"],"primary_cat":"cs.DS","authors_text":"Daniel Zhang, Gil Halevi, Jason Zhang","submitted_at":"2026-05-24T22:20:33Z","abstract_excerpt":"Given two sets of points A and B, $|A| = m$, $|B| = n$, the Chamfer distance from $A$ to $B$ is defined as $\\operatorname{CD}(A,B) = \\sum_{a\\in A} \\min_{b\\in B} d(a,b)$, where $d$ is a distance metric. Chamfer distance is a popular measure of dissimilarity between two sets of points that has seen increasing usage in computer vision and information retrieval as a substitute for the more computationally demanding Earth Mover's distance. We propose a new problem, Chamfer distance under translation, defined as $\\operatorname{CDuT}(A,B) :=\\min_{t\\in \\mathbb{R}^d} \\operatorname{CD}(A+t,B)$, where $A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25280","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/2605.25280/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"}