{"paper":{"title":"Multivariate Topology Simplification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Amit Chattopadhyay, David Duke, Hamish Carr, Osamu Saeki, Zhao Geng","submitted_at":"2015-09-15T09:42:59Z","abstract_excerpt":"Topological simplification of scalar and vector fields is well-established as an effective method for analysing and visualising complex data sets. For multi-field data, topological analysis requires simultaneous advances both mathematically and computationally. We propose a robust multivariate topology simplification method based on ``lip''-pruning from the Reeb Space. Mathematically, we show that the projection of the Jacobi Set of multivariate data into the Reeb Space produces a Jacobi Structure that separates the Reeb Space into simple components. We also show that the dual graph of these c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04465","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"}