{"id":"https://openalex.org/W2107462260","doi":"https://doi.org/10.1109/tip.2011.2159234","title":"Fast $O(1)$ Bilateral Filtering Using Trigonometric Range Kernels","display_name":"Fast $O(1)$ Bilateral Filtering Using Trigonometric Range Kernels","publication_year":2011,"publication_date":"2011-06-17","ids":{"openalex":"https://openalex.org/W2107462260","doi":"https://doi.org/10.1109/tip.2011.2159234","mag":"2107462260","pmid":"https://pubmed.ncbi.nlm.nih.gov/21659022"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2011.2159234","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2011.2159234","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/173386","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045035201","display_name":"Kunal N. Chaudhury","orcid":"https://orcid.org/0000-0002-8136-605X"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"K. N. Chaudhury","raw_affiliation_strings":["Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544-1000, USA. kchaudhu@princeton.edu","Program in Appl. & Comput. Math., Princeton Univ., Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544-1000, USA. kchaudhu@princeton.edu","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Program in Appl. & Comput. Math., Princeton Univ., Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019987836","display_name":"Daniel Sage","orcid":"https://orcid.org/0000-0002-1150-1623"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"D. Sage","raw_affiliation_strings":["Biomedical Imaging Group, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","Biomed. Imaging Group, Ecole Polytech. Fed. de Lausanne, Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Biomed. Imaging Group, Ecole Polytech. Fed. de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027830035","display_name":"Micha\u00ebl Unser","orcid":"https://orcid.org/0000-0003-1248-2513"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"M. Unser","raw_affiliation_strings":["Biomedical Imaging Group, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","Biomed. Imaging Group, Ecole Polytech. Fed. de Lausanne, Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Biomed. Imaging Group, Ecole Polytech. Fed. de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045035201"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":12.2846,"has_fulltext":false,"cited_by_count":234,"citation_normalized_percentile":{"value":0.99012615,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"20","issue":"12","first_page":"3376","last_page":"3382"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11019","display_name":"Image Enhancement Techniques","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11659","display_name":"Advanced Image Fusion Techniques","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bilateral-filter","display_name":"Bilateral filter","score":0.8178499937057495},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.711496889591217},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6275736689567566},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.6135504245758057},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5738477110862732},{"id":"https://openalex.org/keywords/pixel","display_name":"Pixel","score":0.5584855079650879},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.47760888934135437},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44690650701522827},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4305475950241089},{"id":"https://openalex.org/keywords/gaussian-filter","display_name":"Gaussian filter","score":0.4227464199066162},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34494322538375854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2856427729129791},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.27055925130844116},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.1960754096508026},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17004570364952087},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.10229882597923279}],"concepts":[{"id":"https://openalex.org/C156140930","wikidata":"https://www.wikidata.org/wiki/Q860417","display_name":"Bilateral filter","level":3,"score":0.8178499937057495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.711496889591217},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6275736689567566},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.6135504245758057},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5738477110862732},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.5584855079650879},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.47760888934135437},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44690650701522827},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4305475950241089},{"id":"https://openalex.org/C65892221","wikidata":"https://www.wikidata.org/wiki/Q1113935","display_name":"Gaussian filter","level":3,"score":0.4227464199066162},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34494322538375854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2856427729129791},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.27055925130844116},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.1960754096508026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17004570364952087},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.10229882597923279},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2011.2159234","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2011.2159234","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},{"id":"pmid:21659022","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21659022","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null},{"id":"pmh:oai:infoscience.epfl.ch:173386","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/173386","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:173386","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/173386","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1441312571","display_name":null,"funder_award_id":"00020","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4124273935","display_name":"Dokumentation \u00fcber Ausdehnung, Nutzung, Bewirtschaftung und Melioration organischer B\u00f6den in der Schweiz","funder_award_id":"10941","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4836148144","display_name":"Immunologie des Typ-1 Diabetes.","funder_award_id":"20002","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5599649393","display_name":null,"funder_award_id":"200020","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6278475803","display_name":"Spline methods for the continuous/discrete processing of images","funder_award_id":"109415","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G628552264","display_name":null,"funder_award_id":"200020","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W178406657","https://openalex.org/W1528144695","https://openalex.org/W1565147430","https://openalex.org/W1972292376","https://openalex.org/W1994275275","https://openalex.org/W2041032353","https://openalex.org/W2065533005","https://openalex.org/W2093117706","https://openalex.org/W2099244020","https://openalex.org/W2099431685","https://openalex.org/W2128298440","https://openalex.org/W2136396015","https://openalex.org/W2143425433","https://openalex.org/W2144531167","https://openalex.org/W2146578165","https://openalex.org/W2150134853","https://openalex.org/W2155919893","https://openalex.org/W2162618331","https://openalex.org/W2244684328","https://openalex.org/W3123186495","https://openalex.org/W3202142092","https://openalex.org/W4206567584","https://openalex.org/W4247010311","https://openalex.org/W4253999777","https://openalex.org/W4256114533","https://openalex.org/W6607236572","https://openalex.org/W6631760055"],"related_works":["https://openalex.org/W32221979","https://openalex.org/W3046800873","https://openalex.org/W2357379321","https://openalex.org/W2088352866","https://openalex.org/W2945483049","https://openalex.org/W2604146181","https://openalex.org/W2183380462","https://openalex.org/W2099748983","https://openalex.org/W4299311104","https://openalex.org/W2949618677"],"abstract_inverted_index":{"It":[0],"is":[1,61,108,137,177,193],"well":[2],"known":[3],"that":[4,78,197],"spatial":[5,49,106],"averaging":[6,66,97,118],"can":[7,120],"be":[8,121,158],"realized":[9],"(in":[10],"space":[11],"or":[12,25,39,75],"frequency":[13],"domain)":[14],"using":[15,132,147,190,201],"algorithms":[16,32,41,119],"whose":[17,71],"complexity":[18],"does":[19],"not":[20],"scale":[21],"with":[22,47],"the":[23,28,43,48,51,65,80,91,96,105,116,125,141,163,166,185],"size":[24],"shape":[26],"of":[27,79,82,152,165,174,183,187],"filter.":[29,170],"These":[30],"fast":[31],"are":[33,73],"generally":[34],"referred":[35],"to":[36,63,67,77,157,196],"as":[37],"constant-time":[38],"O(1)":[40,117],"in":[42,128],"image-processing":[44],"literature.":[45],"Along":[46],"filter,":[50],"edge-preserving":[52],"bilateral":[53,126,169],"filter":[54,107,127],"involves":[55],"an":[56],"additional":[57],"range":[58,85,134],"kernel.":[59],"This":[60,94,136],"used":[62],"restrict":[64],"those":[68],"neighborhood":[69],"pixels":[70],"intensity":[72],"similar":[74],"close":[76],"pixel":[81,92],"interest.":[83],"The":[84,150,171],"kernel":[86],"operates":[87],"by":[88,131,139,144,199],"acting":[89],"on":[90],"intensities.":[93],"makes":[95],"process":[98],"nonlinear":[99],"and":[100],"computationally":[101],"intensive,":[102],"particularly":[103],"when":[104],"large.":[109],"In":[110],"this":[111],"paper,":[112],"we":[113],"show":[114],"how":[115],"leveraged":[122],"for":[123,162,179],"realizing":[124],"constant":[129],"time,":[130],"trigonometric":[133,153,191],"kernels.":[135,149],"done":[138],"generalizing":[140],"idea":[142],"presented":[143],"Porikli,":[145],"i.e.,":[146],"polynomial":[148],"class":[151],"kernels":[154,192],"turns":[155],"out":[156],"sufficiently":[159],"rich,":[160],"allowing":[161],"approximation":[164,188],"standard":[167],"Gaussian":[168],"attractive":[172],"feature":[173],"our":[175],"approach":[176],"that,":[178],"a":[180],"fixed":[181],"number":[182],"terms,":[184],"quality":[186],"achieved":[189],"much":[194],"superior":[195],"obtained":[198],"Porikli":[200],"polynomials.":[202]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":25},{"year":2018,"cited_by_count":25},{"year":2017,"cited_by_count":26},{"year":2016,"cited_by_count":20},{"year":2015,"cited_by_count":27},{"year":2014,"cited_by_count":22},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}