{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KGRJ5VSEYUK3FFSKREVRKRDLQQ","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":"38a3cd099d6206e20dc160e13d5f2be9252a90bf1496baa6db924fda75eefd51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-12-17T10:50:25Z","title_canon_sha256":"04c65d204f23efbb2930ae3272e9e0c251f3da148ded6d678d5b0d16a497b8e9"},"schema_version":"1.0","source":{"id":"1412.5328","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5328","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5328v1","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5328","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"KGRJ5VSEYUK3","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KGRJ5VSEYUK3FFSK","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KGRJ5VSE","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:e816920ebe2499a68df7bd6bd1e285bc5fd169073ac4dd13bba30418953e4446","target":"graph","created_at":"2026-05-18T02:31:03Z","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":"In this paper, we propose a new mathematical model for image processing. It is a logarithmical one. We consider the bounded interval (-1, 1) as the set of gray levels. Firstly, we define two operations: addition <+> and real scalar multiplication <x>. With these operations, the set of gray levels becomes a real vector space. Then, defining the scalar product (.|.) and the norm || . ||, we obtain an Euclidean space of the gray levels. Secondly, we extend these operations and functions for color images. We finally show the effect of various simple operations on an image.","authors_text":"Vasile Buzuloiu, Vasile Patrascu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-12-17T10:50:25Z","title":"A Mathematical Model for Logarithmic Image Processing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5328","kind":"arxiv","version":1},"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":"sha256:88105b0b607099bd7a4f759a4022fc8ca1e419ac0bda1992acf1926653373cbb","target":"record","created_at":"2026-05-18T02:31:03Z","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":"38a3cd099d6206e20dc160e13d5f2be9252a90bf1496baa6db924fda75eefd51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-12-17T10:50:25Z","title_canon_sha256":"04c65d204f23efbb2930ae3272e9e0c251f3da148ded6d678d5b0d16a497b8e9"},"schema_version":"1.0","source":{"id":"1412.5328","kind":"arxiv","version":1}},"canonical_sha256":"51a29ed644c515b2964a892b15446b84180fe3b9bd14cdb70dbf7c0beeb9b6f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51a29ed644c515b2964a892b15446b84180fe3b9bd14cdb70dbf7c0beeb9b6f6","first_computed_at":"2026-05-18T02:31:03.222387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:03.222387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4AoEx8tYL7pn18OSJ6PGw18fS1uLL4gNw/FeFKA/qRzZhLj7h1sLDl7o873kVjvXEaZZeD3Cc7ek4PdcceVODg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:03.222893Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5328","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88105b0b607099bd7a4f759a4022fc8ca1e419ac0bda1992acf1926653373cbb","sha256:e816920ebe2499a68df7bd6bd1e285bc5fd169073ac4dd13bba30418953e4446"],"state_sha256":"0f33d6a146c92f6373b7305dc81e2a206647403bc48278c55e5f0598317e038e"}