{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4I62Q747GI4CCZFUI2A77EXKEB","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":"33fb7c6d6dc0d0e774daff80d366950238ef31f9817390292a6998dea795b317","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2017-01-27T15:55:51Z","title_canon_sha256":"e7372125ad5ebfd3eb3aecb0f745ed340cc70ea3770e07a51077d650237a2e3c"},"schema_version":"1.0","source":{"id":"1701.08092","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08092","created_at":"2026-05-18T00:25:07Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08092v5","created_at":"2026-05-18T00:25:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08092","created_at":"2026-05-18T00:25:07Z"},{"alias_kind":"pith_short_12","alias_value":"4I62Q747GI4C","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4I62Q747GI4CCZFU","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4I62Q747","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:605d4d2b6432d6c16889db531856954b338d4957248ba61bd6de30cf3861606f","target":"graph","created_at":"2026-05-18T00:25:07Z","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 establish the link between Mathematical Morphology and the map of Asplund's distances between a probe and a grey scale function, using the Logarithmic Image Processing scalar multiplication. We demonstrate that the map is the logarithm of the ratio between a dilation and an erosion of the function by a structuring function: the probe. The dilations and erosions are mappings from the lattice of the images into the lattice of the positive functions. Using a flat structuring element, the expression of the map of Asplund's distances can be simplified with a dilation and an erosion of the image;","authors_text":"Guillaume Noyel (IPRI, IPRI), Michel Jourlin (LHC, SIGPH@iPRI)","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2017-01-27T15:55:51Z","title":"Double-sided probing by map of Asplund's distances using Logarithmic Image Processing in the framework of Mathematical Morphology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08092","kind":"arxiv","version":5},"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:b3f64ce7ec2510cea6fd203d77b12b3e03b1cf370b5b58e9976db170344c6386","target":"record","created_at":"2026-05-18T00:25:07Z","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":"33fb7c6d6dc0d0e774daff80d366950238ef31f9817390292a6998dea795b317","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2017-01-27T15:55:51Z","title_canon_sha256":"e7372125ad5ebfd3eb3aecb0f745ed340cc70ea3770e07a51077d650237a2e3c"},"schema_version":"1.0","source":{"id":"1701.08092","kind":"arxiv","version":5}},"canonical_sha256":"e23da87f9f32382164b44681ff92ea2053396fa2c98fd4113dc6f451a9039e1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e23da87f9f32382164b44681ff92ea2053396fa2c98fd4113dc6f451a9039e1c","first_computed_at":"2026-05-18T00:25:07.861108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:07.861108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ey+3UnoI1yyfuqaF+fPcs9z4iPyhBVOyv5d6V1wE7Lc01Jo0x6+RJJ3NgNe/bMM/9DfFzSjp5z1vlEIEOlnCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:07.861622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.08092","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3f64ce7ec2510cea6fd203d77b12b3e03b1cf370b5b58e9976db170344c6386","sha256:605d4d2b6432d6c16889db531856954b338d4957248ba61bd6de30cf3861606f"],"state_sha256":"512e941ef5ea3a7b1723c7790699c7a752e6ed19dad4595400d205375a2d0a3b"}