{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QL54D2C6X2LBJ7M2BNNES6ZIYY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f9894e36a0418d28a3bd3edc4773d8bf292a1709f5d7e0f48585952c99af9abd","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-12-23T20:44:02Z","title_canon_sha256":"e963bf13e8bf1d9ca8ac1f3f75b7d44f6ce3126c5314e7f03cd870c2a375d5a7"},"schema_version":"1.0","source":{"id":"1412.7513","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7513","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7513v2","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7513","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"QL54D2C6X2LB","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QL54D2C6X2LBJ7M2","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QL54D2C6","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:acfa79355c1071d433777acadb46f1b1115ea70b45e2ad28a2216c922512feed","target":"graph","created_at":"2026-05-18T02:30:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be reduced resulting in compact representations of shape and spatial structure. This reduction is possible because the available data is incomplete in encoding the full deformation model. Using reduction by symmetry, we describe the reduced models in a common theoretical framework that draws on links between the registration problem and geometric mechanics. Sy","authors_text":"Henry O. Jacobs, Stefan Sommer","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-12-23T20:44:02Z","title":"Symmetry in Image Registration and Deformation Modeling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7513","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d4349d57ee5daf99ab839d89411d974ee08db212ce531f96fa6a8ea1fc92b90a","target":"record","created_at":"2026-05-18T02:30:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f9894e36a0418d28a3bd3edc4773d8bf292a1709f5d7e0f48585952c99af9abd","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-12-23T20:44:02Z","title_canon_sha256":"e963bf13e8bf1d9ca8ac1f3f75b7d44f6ce3126c5314e7f03cd870c2a375d5a7"},"schema_version":"1.0","source":{"id":"1412.7513","kind":"arxiv","version":2}},"canonical_sha256":"82fbc1e85ebe9614fd9a0b5a497b28c60401660c8302090b047f08b8d0226c0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82fbc1e85ebe9614fd9a0b5a497b28c60401660c8302090b047f08b8d0226c0a","first_computed_at":"2026-05-18T02:30:33.603644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:33.603644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w02w/YfOWGZ3PyNQH6SjTkBbyHjf74EJuSxutVhXtFLtipfc9CC08f6RzVxxEGKelbC+En9IEQ8o9A/DK7BADA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:33.604038Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7513","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4349d57ee5daf99ab839d89411d974ee08db212ce531f96fa6a8ea1fc92b90a","sha256:acfa79355c1071d433777acadb46f1b1115ea70b45e2ad28a2216c922512feed"],"state_sha256":"5ffd03eea1e1e0af1dd3477358b3b8a0acfae22551ace43b908e088ebb171b65"}