{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UNUENJAZ7QW5FKEHKTAFTBPEXV","short_pith_number":"pith:UNUENJAZ","canonical_record":{"source":{"id":"1207.3056","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2012-07-12T18:39:10Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"8d394fa5f1c55855cda79362cf78ac69bf53f553fc4624058d200dec1fa8e089","abstract_canon_sha256":"4945433e803f98aa008fec8961eb999fbe9d08a65276402d4e493396b2bd6372"},"schema_version":"1.0"},"canonical_sha256":"a36846a419fc2dd2a88754c05985e4bd6d962008c1820cc0c5166bae940a2bc4","source":{"kind":"arxiv","id":"1207.3056","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3056","created_at":"2026-05-18T01:56:24Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3056v2","created_at":"2026-05-18T01:56:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3056","created_at":"2026-05-18T01:56:24Z"},{"alias_kind":"pith_short_12","alias_value":"UNUENJAZ7QW5","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UNUENJAZ7QW5FKEH","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UNUENJAZ","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UNUENJAZ7QW5FKEHKTAFTBPEXV","target":"record","payload":{"canonical_record":{"source":{"id":"1207.3056","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2012-07-12T18:39:10Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"8d394fa5f1c55855cda79362cf78ac69bf53f553fc4624058d200dec1fa8e089","abstract_canon_sha256":"4945433e803f98aa008fec8961eb999fbe9d08a65276402d4e493396b2bd6372"},"schema_version":"1.0"},"canonical_sha256":"a36846a419fc2dd2a88754c05985e4bd6d962008c1820cc0c5166bae940a2bc4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:56:24.276995Z","signature_b64":"IL6FyiEw1iluamg3OSoyZvzZ7Nd/4ROEDsxQLw6LGNhaCsK3xZR7Ps7nmb7c3aK4UsA3yFR8V/EEPedp4zEYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a36846a419fc2dd2a88754c05985e4bd6d962008c1820cc0c5166bae940a2bc4","last_reissued_at":"2026-05-18T01:56:24.276419Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:56:24.276419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.3056","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:56:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xk3AeKeBhd0k/UCxIevVmFNRHL2e0ML15DqNoQ0rQSevTRtwnIcFkAFO6+RTG+ByaXkNZPxae2GBSagMWgqhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T16:25:01.199909Z"},"content_sha256":"ae274eeb543460999f082941788a5612d37d256cadabfa0bbbd6e170363e1a50","schema_version":"1.0","event_id":"sha256:ae274eeb543460999f082941788a5612d37d256cadabfa0bbbd6e170363e1a50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UNUENJAZ7QW5FKEHKTAFTBPEXV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Local Euclidean Medians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CV","authors_text":"Amit Singer, Kunal N. Chaudhury","submitted_at":"2012-07-12T18:39:10Z","abstract_excerpt":"In this letter, we note that the denoising performance of Non-Local Means (NLM) at large noise levels can be improved by replacing the mean by the Euclidean median. We call this new denoising algorithm the Non-Local Euclidean Medians (NLEM). At the heart of NLEM is the observation that the median is more robust to outliers than the mean. In particular, we provide a simple geometric insight that explains why NLEM performs better than NLM in the vicinity of edges, particularly at large noise levels. NLEM can be efficiently implemented using iteratively reweighted least squares, and its computati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3056","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:56:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XnlNeW1ab93UF7HK6dSBaKOy3QYfq6J0QTdrZ3YGiZpJtUY9FlZ0WUKzmxGsZJDoal7X236U0h0aAsqGOu9fBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T16:25:01.200260Z"},"content_sha256":"39e9de8dc72efaea9a8091ee4439fae9eba96d0971364308dd4bdcdc08b0eb9d","schema_version":"1.0","event_id":"sha256:39e9de8dc72efaea9a8091ee4439fae9eba96d0971364308dd4bdcdc08b0eb9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UNUENJAZ7QW5FKEHKTAFTBPEXV/bundle.json","state_url":"https://pith.science/pith/UNUENJAZ7QW5FKEHKTAFTBPEXV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UNUENJAZ7QW5FKEHKTAFTBPEXV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-28T16:25:01Z","links":{"resolver":"https://pith.science/pith/UNUENJAZ7QW5FKEHKTAFTBPEXV","bundle":"https://pith.science/pith/UNUENJAZ7QW5FKEHKTAFTBPEXV/bundle.json","state":"https://pith.science/pith/UNUENJAZ7QW5FKEHKTAFTBPEXV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UNUENJAZ7QW5FKEHKTAFTBPEXV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UNUENJAZ7QW5FKEHKTAFTBPEXV","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":"4945433e803f98aa008fec8961eb999fbe9d08a65276402d4e493396b2bd6372","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2012-07-12T18:39:10Z","title_canon_sha256":"8d394fa5f1c55855cda79362cf78ac69bf53f553fc4624058d200dec1fa8e089"},"schema_version":"1.0","source":{"id":"1207.3056","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3056","created_at":"2026-05-18T01:56:24Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3056v2","created_at":"2026-05-18T01:56:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3056","created_at":"2026-05-18T01:56:24Z"},{"alias_kind":"pith_short_12","alias_value":"UNUENJAZ7QW5","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UNUENJAZ7QW5FKEH","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UNUENJAZ","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:39e9de8dc72efaea9a8091ee4439fae9eba96d0971364308dd4bdcdc08b0eb9d","target":"graph","created_at":"2026-05-18T01:56:24Z","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 letter, we note that the denoising performance of Non-Local Means (NLM) at large noise levels can be improved by replacing the mean by the Euclidean median. We call this new denoising algorithm the Non-Local Euclidean Medians (NLEM). At the heart of NLEM is the observation that the median is more robust to outliers than the mean. In particular, we provide a simple geometric insight that explains why NLEM performs better than NLM in the vicinity of edges, particularly at large noise levels. NLEM can be efficiently implemented using iteratively reweighted least squares, and its computati","authors_text":"Amit Singer, Kunal N. Chaudhury","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2012-07-12T18:39:10Z","title":"Non-Local Euclidean Medians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3056","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:ae274eeb543460999f082941788a5612d37d256cadabfa0bbbd6e170363e1a50","target":"record","created_at":"2026-05-18T01:56:24Z","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":"4945433e803f98aa008fec8961eb999fbe9d08a65276402d4e493396b2bd6372","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2012-07-12T18:39:10Z","title_canon_sha256":"8d394fa5f1c55855cda79362cf78ac69bf53f553fc4624058d200dec1fa8e089"},"schema_version":"1.0","source":{"id":"1207.3056","kind":"arxiv","version":2}},"canonical_sha256":"a36846a419fc2dd2a88754c05985e4bd6d962008c1820cc0c5166bae940a2bc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a36846a419fc2dd2a88754c05985e4bd6d962008c1820cc0c5166bae940a2bc4","first_computed_at":"2026-05-18T01:56:24.276419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:24.276419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IL6FyiEw1iluamg3OSoyZvzZ7Nd/4ROEDsxQLw6LGNhaCsK3xZR7Ps7nmb7c3aK4UsA3yFR8V/EEPedp4zEYAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:24.276995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3056","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae274eeb543460999f082941788a5612d37d256cadabfa0bbbd6e170363e1a50","sha256:39e9de8dc72efaea9a8091ee4439fae9eba96d0971364308dd4bdcdc08b0eb9d"],"state_sha256":"e65fc321f1b9da2caac6e089728bbc269940acf8756deb94dab00916fa8800b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k3fIOUxKtcFRvGwDdCXQ9ZJ+U7VXSbi7uKrqvkRfNibzqJn5zsWcbu9XvrZfEtjiKOEqMbzRsPEDgRUZlrZ7Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T16:25:01.202589Z","bundle_sha256":"a62e5c680f0a31d039c53ec88b802f23acf77ecf4a4e2189240c5cdf499257d2"}}