{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QR3VFHYG4FIXJLDC36EWLDPZAJ","short_pith_number":"pith:QR3VFHYG","schema_version":"1.0","canonical_sha256":"8477529f06e15174ac62df89658df9027731451214d0ebeedfc0430378a82580","source":{"kind":"arxiv","id":"1603.08081","version":1},"attestation_state":"computed","paper":{"title":"On Fast Bilateral Filtering using Fourier Kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Kunal N. Chaudhury, Sanjay Ghosh","submitted_at":"2016-03-26T07:09:58Z","abstract_excerpt":"It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the non-linear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation have, however, been restricted to Gaussian range kernels. In this work, we propose a novel approximation that can be applied to any range kernel, provided it has a pointwise-convergent Fourier series. More specifically, we propose to approximate the Gaussian range kernel of the bilateral filter using a Fourier basis, where the coefficients of the basis are "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.08081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2016-03-26T07:09:58Z","cross_cats_sorted":[],"title_canon_sha256":"4434f12e2f87dad893ee0358a635fc57207e980339ef5cf85658bb31bf25ddca","abstract_canon_sha256":"48cd6c147070b095bf450d262211edbde34823cc9b64e70989a8f6fbf0ef3ffd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:39.361146Z","signature_b64":"Co0hwWPJAOImaAHt6cxZd8gCEu17PNIypj4tNV4ZTcMGqOcVpb2POZqyf/t+FGBNSUpf2KMP5o3Pn2frIoUiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8477529f06e15174ac62df89658df9027731451214d0ebeedfc0430378a82580","last_reissued_at":"2026-05-18T01:16:39.360626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:39.360626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Fast Bilateral Filtering using Fourier Kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Kunal N. Chaudhury, Sanjay Ghosh","submitted_at":"2016-03-26T07:09:58Z","abstract_excerpt":"It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the non-linear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation have, however, been restricted to Gaussian range kernels. In this work, we propose a novel approximation that can be applied to any range kernel, provided it has a pointwise-convergent Fourier series. More specifically, we propose to approximate the Gaussian range kernel of the bilateral filter using a Fourier basis, where the coefficients of the basis are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08081","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.08081","created_at":"2026-05-18T01:16:39.360693+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.08081v1","created_at":"2026-05-18T01:16:39.360693+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08081","created_at":"2026-05-18T01:16:39.360693+00:00"},{"alias_kind":"pith_short_12","alias_value":"QR3VFHYG4FIX","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"QR3VFHYG4FIXJLDC","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"QR3VFHYG","created_at":"2026-05-18T12:30:41.710351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QR3VFHYG4FIXJLDC36EWLDPZAJ","json":"https://pith.science/pith/QR3VFHYG4FIXJLDC36EWLDPZAJ.json","graph_json":"https://pith.science/api/pith-number/QR3VFHYG4FIXJLDC36EWLDPZAJ/graph.json","events_json":"https://pith.science/api/pith-number/QR3VFHYG4FIXJLDC36EWLDPZAJ/events.json","paper":"https://pith.science/paper/QR3VFHYG"},"agent_actions":{"view_html":"https://pith.science/pith/QR3VFHYG4FIXJLDC36EWLDPZAJ","download_json":"https://pith.science/pith/QR3VFHYG4FIXJLDC36EWLDPZAJ.json","view_paper":"https://pith.science/paper/QR3VFHYG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.08081&json=true","fetch_graph":"https://pith.science/api/pith-number/QR3VFHYG4FIXJLDC36EWLDPZAJ/graph.json","fetch_events":"https://pith.science/api/pith-number/QR3VFHYG4FIXJLDC36EWLDPZAJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QR3VFHYG4FIXJLDC36EWLDPZAJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QR3VFHYG4FIXJLDC36EWLDPZAJ/action/storage_attestation","attest_author":"https://pith.science/pith/QR3VFHYG4FIXJLDC36EWLDPZAJ/action/author_attestation","sign_citation":"https://pith.science/pith/QR3VFHYG4FIXJLDC36EWLDPZAJ/action/citation_signature","submit_replication":"https://pith.science/pith/QR3VFHYG4FIXJLDC36EWLDPZAJ/action/replication_record"}},"created_at":"2026-05-18T01:16:39.360693+00:00","updated_at":"2026-05-18T01:16:39.360693+00:00"}