{"id":"https://openalex.org/W2061599505","doi":"https://doi.org/10.1137/120897213","title":"Trust Region versus Line Search for Computing the Optical Flow","display_name":"Trust Region versus Line Search for Computing the Optical Flow","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2061599505","doi":"https://doi.org/10.1137/120897213","mag":"2061599505"},"language":"en","primary_location":{"id":"doi:10.1137/120897213","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120897213","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://diposit.ub.edu/dspace/bitstream/2445/52216/1/635635.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044035450","display_name":"El Mostafa Kalmoun","orcid":"https://orcid.org/0000-0002-1434-2541"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"El Mostafa Kalmoun","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107977303","display_name":"Lu\u00eds Garrido","orcid":"https://orcid.org/0000-0002-9860-6734"},"institutions":[{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Luis Garrido","raw_affiliation_strings":["Departament de Matem\u00e0tica Aplicada i An\u00e0lisi, Universitat de Barcelona, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tica Aplicada i An\u00e0lisi, Universitat de Barcelona, Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5107977303"],"corresponding_institution_ids":["https://openalex.org/I71999127"],"apc_list":null,"apc_paid":null,"fwci":0.2765,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.61297404,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"3","first_page":"890","last_page":"906"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","score":0.9998999834060669,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9998999834060669,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9940000176429749,"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/T10250","display_name":"Glaucoma and retinal disorders","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/2731","display_name":"Ophthalmology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/trust-region","display_name":"Trust region","score":0.8228248357772827},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.7475295662879944},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7241441011428833},{"id":"https://openalex.org/keywords/optical-flow","display_name":"Optical flow","score":0.6828030347824097},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6473450660705566},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.6053719520568848},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5821333527565002},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5763135552406311},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5431271195411682},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5341284275054932},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5263782143592834},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5036565661430359},{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.43147212266921997},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4145340323448181},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3542129397392273},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.169194757938385},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16917788982391357},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1587291955947876},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.08719280362129211},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08479779958724976}],"concepts":[{"id":"https://openalex.org/C89109886","wikidata":"https://www.wikidata.org/wiki/Q1535924","display_name":"Trust region","level":3,"score":0.8228248357772827},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.7475295662879944},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7241441011428833},{"id":"https://openalex.org/C155542232","wikidata":"https://www.wikidata.org/wiki/Q736111","display_name":"Optical flow","level":3,"score":0.6828030347824097},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6473450660705566},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.6053719520568848},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5821333527565002},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5763135552406311},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5431271195411682},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5341284275054932},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5263782143592834},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5036565661430359},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.43147212266921997},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4145340323448181},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3542129397392273},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.169194757938385},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16917788982391357},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1587291955947876},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.08719280362129211},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08479779958724976},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/120897213","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120897213","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:diposit.ub.edu:2445/52216","is_oa":true,"landing_page_url":"http://hdl.handle.net/2445/52216","pdf_url":"https://diposit.ub.edu/dspace/bitstream/2445/52216/1/635635.pdf","source":{"id":"https://openalex.org/S4306401653","display_name":"Dip\u00f2sit Digital de la Universitat de Barcelona (Universitat de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71999127","host_organization_name":"Universitat de Barcelona","host_organization_lineage":["https://openalex.org/I71999127"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Articles publicats en revistes (Matem\u00e0tiques i Inform\u00e0tica)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:www.recercat.cat:2072/225763","is_oa":false,"landing_page_url":"http://hdl.handle.net/2072/225763","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:diposit.ub.edu:2445/52216","is_oa":true,"landing_page_url":"http://hdl.handle.net/2445/52216","pdf_url":"https://diposit.ub.edu/dspace/bitstream/2445/52216/1/635635.pdf","source":{"id":"https://openalex.org/S4306401653","display_name":"Dip\u00f2sit Digital de la Universitat de Barcelona (Universitat de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71999127","host_organization_name":"Universitat de Barcelona","host_organization_lineage":["https://openalex.org/I71999127"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Articles publicats en revistes (Matem\u00e0tiques i Inform\u00e0tica)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7468692758","display_name":null,"funder_award_id":"MTM2009-08171","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320324433","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2061599505.pdf","grobid_xml":"https://content.openalex.org/works/W2061599505.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W147998453","https://openalex.org/W1536816303","https://openalex.org/W1538585633","https://openalex.org/W1578285471","https://openalex.org/W1586056472","https://openalex.org/W2025510965","https://openalex.org/W2040278487","https://openalex.org/W2069664630","https://openalex.org/W2078655374","https://openalex.org/W2088969313","https://openalex.org/W2111919691","https://openalex.org/W2130657708","https://openalex.org/W2133929848","https://openalex.org/W2142738245","https://openalex.org/W2165468772","https://openalex.org/W2184882446","https://openalex.org/W2751023760","https://openalex.org/W3003662786","https://openalex.org/W3029645440","https://openalex.org/W3150997492"],"related_works":["https://openalex.org/W2015103152","https://openalex.org/W2406735451","https://openalex.org/W2726063369","https://openalex.org/W1989684674","https://openalex.org/W4312712619","https://openalex.org/W2369920403","https://openalex.org/W2375625392","https://openalex.org/W1586056472","https://openalex.org/W4297783372","https://openalex.org/W2082203085"],"abstract_inverted_index":{"We":[0,74],"consider":[1],"the":[2,6,12,15,20,25,30,38,55,58,87,94],"numerical":[3],"treatment":[4],"of":[5,14,27,57,89],"optical":[7,43,48],"flow":[8,44,49],"problem":[9],"by":[10],"evaluating":[11],"performance":[13,56],"trust":[16,31,77],"region":[17,32,78],"method":[18,33],"versus":[19],"line":[21,83],"search":[22],"method.":[23],"To":[24],"best":[26],"our":[28],"knowledge,":[29],"is":[34],"studied":[35],"here":[36],"for":[37,41],"first":[39],"time":[40],"variational":[42],"computation.":[45],"Four":[46],"different":[47],"models":[50],"are":[51],"used":[52],"to":[53],"test":[54],"proposed":[59],"algorithm,":[60],"combining":[61],"linear":[62],"and":[63,69,91],"nonlinear":[64],"data":[65],"terms":[66],"with":[67],"quadratic":[68],"total":[70],"variation":[71],"(TV)":[72],"regularization.":[73],"show":[75],"that":[76],"often":[79],"performs":[80],"better":[81],"than":[82],"search,":[84],"especially":[85],"in":[86,93],"presence":[88],"nonlinearity":[90],"nonconvexity":[92],"model.":[95]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}