{"paper":{"title":"A class of fast geodesic shooting algorithms for template matching and its applications via the $N$-particle system of the Euler-Poincar\\'e equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dongyang Kuang, Long Lee, Roberto Camassa","submitted_at":"2015-10-13T18:51:26Z","abstract_excerpt":"The Euler-Poincar\\'e (EP) equations describe the geodesic motion on the diffeomorphism group. For template matching (template deformation), the Euler-Lagrangian equation, arising from minimizing an energy function, falls into the Euler-Poincar\\'e theory and can be recast into the EP equations. By casting the EP equations in the Lagrangian (or characteristics) form, we formulate the equations as a finite dimensional particle system. The evolution of this particle system describes the geodesic motion of landmark points on a Riemann manifold. In this paper we present a class of novel algorithms t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03816","kind":"arxiv","version":2},"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"}