{"id":"https://openalex.org/W2096013213","doi":"https://doi.org/10.1142/s0218127409024426","title":"VARIATIONAL PRINCIPLES IN IMAGE PROCESSING AND THE REGULARIZATION OF ORIENTATION FIELDS","display_name":"VARIATIONAL PRINCIPLES IN IMAGE PROCESSING AND THE REGULARIZATION OF ORIENTATION FIELDS","publication_year":2009,"publication_date":"2009-08-01","ids":{"openalex":"https://openalex.org/W2096013213","doi":"https://doi.org/10.1142/s0218127409024426","mag":"2096013213"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127409024426","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409024426","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3269415","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029825229","display_name":"Jaime Cisternas","orcid":"https://orcid.org/0000-0002-2955-1821"},"institutions":[{"id":"https://openalex.org/I189977406","display_name":"Universidad de Los Andes, Chile","ror":"https://ror.org/03v0qd864","country_code":"CL","type":"education","lineage":["https://openalex.org/I189977406"]}],"countries":["CL"],"is_corresponding":true,"raw_author_name":"JAIME CISTERNAS","raw_affiliation_strings":["Complex Systems Group, Engineering School, Universidad de los Andes, Av. San Carlos de Apoquindo 2200, Santiago, Chile"],"affiliations":[{"raw_affiliation_string":"Complex Systems Group, Engineering School, Universidad de los Andes, Av. San Carlos de Apoquindo 2200, Santiago, Chile","institution_ids":["https://openalex.org/I189977406"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036023331","display_name":"Marcelo G\u00e1lvez","orcid":"https://orcid.org/0000-0002-8638-5268"},"institutions":[{"id":"https://openalex.org/I69737025","display_name":"University of Chile","ror":"https://ror.org/047gc3g35","country_code":"CL","type":"education","lineage":["https://openalex.org/I69737025"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"MARCELO G\u00c1LVEZ","raw_affiliation_strings":["Neurosurgery Institute Dr. Asenjo, Universidad de Chile, Av. J. M. Infante 553, Santiago, Chile"],"affiliations":[{"raw_affiliation_string":"Neurosurgery Institute Dr. Asenjo, Universidad de Chile, Av. J. M. Infante 553, Santiago, Chile","institution_ids":["https://openalex.org/I69737025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013671245","display_name":"Bram Stieltjes","orcid":"https://orcid.org/0000-0002-5961-802X"},"institutions":[{"id":"https://openalex.org/I17937529","display_name":"German Cancer Research Center","ror":"https://ror.org/04cdgtt98","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I17937529"]},{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"BRAM STIELTJES","raw_affiliation_strings":["German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, 69120 Heidelberg, Germany"],"affiliations":[{"raw_affiliation_string":"German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, 69120 Heidelberg, Germany","institution_ids":["https://openalex.org/I17937529","https://openalex.org/I223822909"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008645118","display_name":"Frederik B. Laun","orcid":"https://orcid.org/0000-0002-9269-5609"},"institutions":[{"id":"https://openalex.org/I17937529","display_name":"German Cancer Research Center","ror":"https://ror.org/04cdgtt98","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I17937529"]},{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"FREDERIK B. LAUN","raw_affiliation_strings":["German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, 69120 Heidelberg, Germany"],"affiliations":[{"raw_affiliation_string":"German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, 69120 Heidelberg, Germany","institution_ids":["https://openalex.org/I17937529","https://openalex.org/I223822909"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5029825229"],"corresponding_institution_ids":["https://openalex.org/I189977406"],"apc_list":null,"apc_paid":null,"fwci":0.2542,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.65387108,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"08","first_page":"2705","last_page":"2716"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9970999956130981,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9936000108718872,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.6004416346549988},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5947583913803101},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5900319814682007},{"id":"https://openalex.org/keywords/scale-space","display_name":"Scale space","score":0.5845988988876343},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5632228851318359},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.5615141987800598},{"id":"https://openalex.org/keywords/variational-principle","display_name":"Variational principle","score":0.5066707730293274},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48768627643585205},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.4791645109653473},{"id":"https://openalex.org/keywords/image-denoising","display_name":"Image denoising","score":0.46361738443374634},{"id":"https://openalex.org/keywords/free-energy-principle","display_name":"Free energy principle","score":0.4129735231399536},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3707144856452942},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3598897457122803},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3530612885951996},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.33416983485221863},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29231923818588257},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15296822786331177}],"concepts":[{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.6004416346549988},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5947583913803101},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5900319814682007},{"id":"https://openalex.org/C99102927","wikidata":"https://www.wikidata.org/wiki/Q3058184","display_name":"Scale space","level":4,"score":0.5845988988876343},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5632228851318359},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.5615141987800598},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.5066707730293274},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48768627643585205},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.4791645109653473},{"id":"https://openalex.org/C2983327147","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Image denoising","level":3,"score":0.46361738443374634},{"id":"https://openalex.org/C33553690","wikidata":"https://www.wikidata.org/wiki/Q17014702","display_name":"Free energy principle","level":2,"score":0.4129735231399536},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3707144856452942},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3598897457122803},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3530612885951996},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.33416983485221863},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29231923818588257},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15296822786331177},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1142/s0218127409024426","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409024426","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:americanae.aecid.es:3269415","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3269415","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:americanae.aecid.es:3269416","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3269416","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/141092","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/141092","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/141093","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/141093","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:americanae.aecid.es:3269415","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3269415","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"score":0.8999999761581421,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1579559187","https://openalex.org/W2017492739","https://openalex.org/W2022530159","https://openalex.org/W2027401313","https://openalex.org/W2030765885","https://openalex.org/W2032236594","https://openalex.org/W2048192550","https://openalex.org/W2054225369","https://openalex.org/W2063001897","https://openalex.org/W2084761689","https://openalex.org/W2097924771","https://openalex.org/W2103559027","https://openalex.org/W2122661899","https://openalex.org/W2139158372","https://openalex.org/W2150134853","https://openalex.org/W2156715960","https://openalex.org/W2166862038","https://openalex.org/W2296319761","https://openalex.org/W2730405628","https://openalex.org/W3038054700","https://openalex.org/W4250589301"],"related_works":["https://openalex.org/W4247002362","https://openalex.org/W4250430376","https://openalex.org/W4235927465","https://openalex.org/W4251688460","https://openalex.org/W4230891546","https://openalex.org/W2347596845","https://openalex.org/W4230549275","https://openalex.org/W4236030466","https://openalex.org/W2003089385","https://openalex.org/W2140565436"],"abstract_inverted_index":{"Variational":[0],"principles":[1,38],"and":[2,21],"partial":[3],"differential":[4],"equations":[5,28],"have":[6,39],"proved":[7],"to":[8,41,47,83,91],"be":[9,42,59,79],"fundamental":[10],"elements":[11],"in":[12,19,44],"the":[13,27,63,68,96,105],"mathematical":[14],"modeling":[15],"of":[16,98,107],"extended":[17],"systems":[18],"physics":[20],"engineering.":[22],"Of":[23],"particular":[24],"interest":[25],"are":[26],"that":[29],"arise":[30],"from":[31],"a":[32],"free":[33],"energy":[34],"functional.":[35,69],"Recently":[36],"variational":[37],"begun":[40],"used":[43],"Image":[45],"Processing":[46],"perform":[48],"basic":[49],"tasks":[50],"such":[51,94],"as":[52,95],"denoising,":[53],"debluring,":[54],"etc.":[55],"Great":[56],"improvements":[57],"can":[58,78],"achieved":[60],"by":[61,104],"selecting":[62],"most":[64],"appropriate":[65],"form":[66],"for":[67],"In":[70],"this":[71],"article":[72],"we":[73],"show":[74],"how":[75],"these":[76],"ideas":[77],"applied":[80],"not":[81],"just":[82],"scalar":[84],"fields":[85],"(i.e.":[86],"grayscale":[87],"images)":[88],"but":[89],"also":[90],"curved":[92],"manifolds":[93],"space":[97],"orientations.":[99],"This":[100],"work":[101],"is":[102],"motivated":[103],"denoising":[106],"images":[108],"acquired":[109],"with":[110],"Magnetic":[111],"Resonance":[112],"scanners":[113],"using":[114],"diffusion-sensitized":[115],"magnetic":[116],"gradients.":[117]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}