{"paper":{"title":"OffsetAxis: UDF Mesh Reconstruction via Offset-Volume Medial Axis Extraction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Mesh extraction from unsigned distance fields reduces to medial axis extraction of the alpha-offset volume","cross_cats":[],"primary_cat":"cs.GR","authors_text":"Dominique Bechmann, Pierre Kraemer, Qijia Huang","submitted_at":"2026-05-14T19:49:15Z","abstract_excerpt":"Unsigned distance fields (UDFs) offer broader modeling capabilities than signed distance fields (SDFs), enabling the representation of shapes with open boundaries, non-manifold structures or mixed curve and surface parts. However, extracting coherent meshes from UDFs is fundamentally harder, as classical grid-based iso-surfacing techniques are not applicable since they require a way to distinguish the inside from the outside of the shape. We introduce OffsetAxis, a new UDF reconstruction pipeline that supports open, non-manifold, and curve-like geometries. Our key insight is that the 0-level s"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The 0-level set extraction problem can be restated as the extraction of the medial axis of the α-offset volume of the UDF. This formulation unlocks mature medial-axis machinery that naturally supports boundaries, non-manifold junctions and curves.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That sampling the α-offset surface via ray casting and optimizing medial balls with a variant of Variational Medial Axis Sampling will produce clusters whose dual connectivity yields structurally coherent meshes across open, non-manifold, and curve-like topologies, including for imperfect neural or point-cloud-derived UDFs.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"OffsetAxis reconstructs meshes from unsigned distance fields by extracting the medial axis of the alpha-offset volume using ray casting and variational medial ball optimization.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Mesh extraction from unsigned distance fields reduces to medial axis extraction of the alpha-offset volume","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"777dba7cc1ea2b96e04e4998387824b44f70390ef50b0111c7214decff304c3e"},"source":{"id":"2605.15369","kind":"arxiv","version":1},"verdict":{"id":"863ddc0f-1857-4e8d-b2ea-4da2ebac74d3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T15:11:25.143147Z","strongest_claim":"The 0-level set extraction problem can be restated as the extraction of the medial axis of the α-offset volume of the UDF. This formulation unlocks mature medial-axis machinery that naturally supports boundaries, non-manifold junctions and curves.","one_line_summary":"OffsetAxis reconstructs meshes from unsigned distance fields by extracting the medial axis of the alpha-offset volume using ray casting and variational medial ball optimization.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That sampling the α-offset surface via ray casting and optimizing medial balls with a variant of Variational Medial Axis Sampling will produce clusters whose dual connectivity yields structurally coherent meshes across open, non-manifold, and curve-like topologies, including for imperfect neural or point-cloud-derived UDFs.","pith_extraction_headline":"Mesh extraction from unsigned distance fields reduces to medial axis extraction of the alpha-offset volume"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15369/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T15:31:17.882898Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:22:38.758039Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T14:21:54.188217Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T13:33:22.737154Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"183fefeba09e9e39848c76ce4920be0e246a03d4ac5cee3c3ab7049716f34a19"},"references":{"count":18,"sample":[{"doi":"","year":2015,"title":"ShapeNet: An Information-Rich 3D Model Repository","work_id":"b2ac5b60-daa9-435b-9369-12271e126edd","ref_index":1,"cited_arxiv_id":"1512.03012","is_internal_anchor":true},{"doi":"10.1145/1064092.1064132","year":2025,"title":"Stability of persistence diagrams","work_id":"f9caf915-366a-4014-8b16-f46de5de5017","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Xu Cheng, Hou Fei, Wang Wencheng, Qin Hong, Zhang Zhebin, and Ying He","work_id":"1d65f697-5e42-4cc8-be18-203fd0e00446","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1111/cgf.14484","year":2022,"title":"Computer Graphics Forum41, 2 (2022), 419–432","work_id":"e2561b5f-974a-4d1f-b9bf-c93b2f497d46","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1145/3618314","year":2023,"title":"2023 , publisher =","work_id":"ba1bf710-a199-4902-93f0-47bf76ea27b2","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":18,"snapshot_sha256":"b8b9550e3d65a30266623d560c4dc57a493da84f5015746d311f51e4fd3761f8","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"bc49c5bac12dc1ef93e032f85dafef7c090ffdbc1c037f45780a9bc94b27c23b"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}