{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FZWWXB5BQOILJWPMCFKESMASS2","short_pith_number":"pith:FZWWXB5B","canonical_record":{"source":{"id":"1504.02206","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-09T07:21:02Z","cross_cats_sorted":["cs.CV"],"title_canon_sha256":"5c82980881fc517c96e9c9528c71783ea8d08543e168f2c4e9863188cb2a0e2f","abstract_canon_sha256":"d81cad7b0c1e14ce689aedfec857089ad9a20d08bf76c2519ec4e50371cca8f8"},"schema_version":"1.0"},"canonical_sha256":"2e6d6b87a18390b4d9ec1154493012969573d967587ea6059672462eea1aa51a","source":{"kind":"arxiv","id":"1504.02206","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02206","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02206v2","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02206","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"pith_short_12","alias_value":"FZWWXB5BQOIL","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FZWWXB5BQOILJWPM","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FZWWXB5B","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FZWWXB5BQOILJWPMCFKESMASS2","target":"record","payload":{"canonical_record":{"source":{"id":"1504.02206","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-09T07:21:02Z","cross_cats_sorted":["cs.CV"],"title_canon_sha256":"5c82980881fc517c96e9c9528c71783ea8d08543e168f2c4e9863188cb2a0e2f","abstract_canon_sha256":"d81cad7b0c1e14ce689aedfec857089ad9a20d08bf76c2519ec4e50371cca8f8"},"schema_version":"1.0"},"canonical_sha256":"2e6d6b87a18390b4d9ec1154493012969573d967587ea6059672462eea1aa51a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:36.959681Z","signature_b64":"XmREnZO7GUcJRgpsr7Atv8PcRCzrfFON4pBsUNQOHNmpUCVfQSsYVfyfcQahfVS1pnqoPYpplCaNLsz21OH1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e6d6b87a18390b4d9ec1154493012969573d967587ea6059672462eea1aa51a","last_reissued_at":"2026-05-18T01:03:36.958915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:36.958915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.02206","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":"2026-05-18T01:03:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UqjFzkt4r/q/UwqY5QQpXV46Nbbw/O8LDlYirGwVwxQXZqFWT9Jh9qUvYT7qXor3olAdLwQYzRQ6r9JRZ754DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:45:24.230176Z"},"content_sha256":"0bd31306f19908501907e1b35b25300c99bd22174f5331ecab491922549e1486","schema_version":"1.0","event_id":"sha256:0bd31306f19908501907e1b35b25300c99bd22174f5331ecab491922549e1486"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FZWWXB5BQOILJWPMCFKESMASS2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-norm Fidelity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV"],"primary_cat":"math.OC","authors_text":"Fang Li, Jing Qin, Ming Yan, Stanley Osher","submitted_at":"2015-04-09T07:21:02Z","abstract_excerpt":"In this paper, we propose a variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity. Then we apply the alternating direction method of multipliers to solve an equivalent problem. All the subproblems can be solved efficiently. Specifically, we propose a fast method to calculate the fuzzy median. Experimental results and comparisons show that the L1-norm based method is more robust to outliers such as impulse noise and keeps better contrast than its L2-norm counterpart. Theoretically, we prove the existence of the minimizer and analyze the converg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02206","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":"2026-05-18T01:03:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9NKS0rYuhchgXeakQ1T3RL08+IBPrJpVp9huVmpEia7QjMmceEB7S3wDafmOdZUSPCXWFHMN+F82AgbGjQccAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:45:24.230882Z"},"content_sha256":"d4da9934db129ab3a9aa5f3e4c6c626dc407e6b50c615503796372124bbc03ca","schema_version":"1.0","event_id":"sha256:d4da9934db129ab3a9aa5f3e4c6c626dc407e6b50c615503796372124bbc03ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZWWXB5BQOILJWPMCFKESMASS2/bundle.json","state_url":"https://pith.science/pith/FZWWXB5BQOILJWPMCFKESMASS2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZWWXB5BQOILJWPMCFKESMASS2/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":"2026-05-25T15:45:24Z","links":{"resolver":"https://pith.science/pith/FZWWXB5BQOILJWPMCFKESMASS2","bundle":"https://pith.science/pith/FZWWXB5BQOILJWPMCFKESMASS2/bundle.json","state":"https://pith.science/pith/FZWWXB5BQOILJWPMCFKESMASS2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZWWXB5BQOILJWPMCFKESMASS2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FZWWXB5BQOILJWPMCFKESMASS2","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":"d81cad7b0c1e14ce689aedfec857089ad9a20d08bf76c2519ec4e50371cca8f8","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-09T07:21:02Z","title_canon_sha256":"5c82980881fc517c96e9c9528c71783ea8d08543e168f2c4e9863188cb2a0e2f"},"schema_version":"1.0","source":{"id":"1504.02206","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02206","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02206v2","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02206","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"pith_short_12","alias_value":"FZWWXB5BQOIL","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FZWWXB5BQOILJWPM","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FZWWXB5B","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:d4da9934db129ab3a9aa5f3e4c6c626dc407e6b50c615503796372124bbc03ca","target":"graph","created_at":"2026-05-18T01:03:36Z","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 variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity. Then we apply the alternating direction method of multipliers to solve an equivalent problem. All the subproblems can be solved efficiently. Specifically, we propose a fast method to calculate the fuzzy median. Experimental results and comparisons show that the L1-norm based method is more robust to outliers such as impulse noise and keeps better contrast than its L2-norm counterpart. Theoretically, we prove the existence of the minimizer and analyze the converg","authors_text":"Fang Li, Jing Qin, Ming Yan, Stanley Osher","cross_cats":["cs.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-09T07:21:02Z","title":"A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-norm Fidelity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02206","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":"sha256:0bd31306f19908501907e1b35b25300c99bd22174f5331ecab491922549e1486","target":"record","created_at":"2026-05-18T01:03:36Z","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":"d81cad7b0c1e14ce689aedfec857089ad9a20d08bf76c2519ec4e50371cca8f8","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-09T07:21:02Z","title_canon_sha256":"5c82980881fc517c96e9c9528c71783ea8d08543e168f2c4e9863188cb2a0e2f"},"schema_version":"1.0","source":{"id":"1504.02206","kind":"arxiv","version":2}},"canonical_sha256":"2e6d6b87a18390b4d9ec1154493012969573d967587ea6059672462eea1aa51a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e6d6b87a18390b4d9ec1154493012969573d967587ea6059672462eea1aa51a","first_computed_at":"2026-05-18T01:03:36.958915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:36.958915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XmREnZO7GUcJRgpsr7Atv8PcRCzrfFON4pBsUNQOHNmpUCVfQSsYVfyfcQahfVS1pnqoPYpplCaNLsz21OH1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:36.959681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02206","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bd31306f19908501907e1b35b25300c99bd22174f5331ecab491922549e1486","sha256:d4da9934db129ab3a9aa5f3e4c6c626dc407e6b50c615503796372124bbc03ca"],"state_sha256":"655fbf12565f4e241a28073ecd46b44186b516b4cc2b9034b81382aa6fa484ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SAFh8PfMKdliK3eRb2pQq9EnwTq8Nl/Wz89QKGsVWV3mvNk3fRttpxZn9Y3ORArZSfPfuSpwYKXNIjHYeeUOBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T15:45:24.234842Z","bundle_sha256":"5a158e399be48c97d47c970afcd4e02f3a8117aeeece2f8b8a1f0c5f15cbf9cd"}}