{"id":"https://openalex.org/W1963605855","doi":"https://doi.org/10.1137/s1064827501386481","title":"Optimal Control Formulation for Determining Optical Flow","display_name":"Optimal Control Formulation for Determining Optical Flow","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1963605855","doi":"https://doi.org/10.1137/s1064827501386481","mag":"1963605855"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827501386481","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827501386481","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027648225","display_name":"Alfio Borz\u0131\u0300","orcid":"https://orcid.org/0000-0002-8050-1336"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Alfio Borz\u00ec","raw_affiliation_strings":["University of Graz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Graz","institution_ids":["https://openalex.org/I15766117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004826461","display_name":"Kazufumi Ito","orcid":"https://orcid.org/0000-0003-2417-2600"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Kazufumi Ito","raw_affiliation_strings":["University of Graz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Graz","institution_ids":["https://openalex.org/I15766117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074607617","display_name":"Karl Kunisch","orcid":"https://orcid.org/0000-0003-1113-7355"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Karl Kunisch","raw_affiliation_strings":["University of Graz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Graz","institution_ids":["https://openalex.org/I15766117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9648,"has_fulltext":false,"cited_by_count":84,"citation_normalized_percentile":{"value":0.91343048,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"24","issue":"3","first_page":"818","last_page":"847"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9965000152587891,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9819999933242798,"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/mathematics","display_name":"Mathematics","score":0.7627114057540894},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6592674255371094},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6500811576843262},{"id":"https://openalex.org/keywords/optical-flow","display_name":"Optical flow","score":0.5970454216003418},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4906558096408844},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.46124571561813354},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45336678624153137},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45305460691452026},{"id":"https://openalex.org/keywords/hyperbolic-partial-differential-equation","display_name":"Hyperbolic partial differential equation","score":0.4262705147266388},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.36823397874832153},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3358531594276428},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.33151698112487793},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23475924134254456},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21383503079414368},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10585471987724304},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08072534203529358}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7627114057540894},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6592674255371094},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6500811576843262},{"id":"https://openalex.org/C155542232","wikidata":"https://www.wikidata.org/wiki/Q736111","display_name":"Optical flow","level":3,"score":0.5970454216003418},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4906558096408844},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.46124571561813354},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45336678624153137},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45305460691452026},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.4262705147266388},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.36823397874832153},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3358531594276428},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.33151698112487793},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23475924134254456},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21383503079414368},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10585471987724304},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08072534203529358}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827501386481","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827501386481","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W12532419","https://openalex.org/W579709999","https://openalex.org/W1507795625","https://openalex.org/W1575147392","https://openalex.org/W1578285471","https://openalex.org/W1594759473","https://openalex.org/W1972596295","https://openalex.org/W1976342262","https://openalex.org/W2012118748","https://openalex.org/W2019771551","https://openalex.org/W2022977680","https://openalex.org/W2042280704","https://openalex.org/W2044980626","https://openalex.org/W2063819119","https://openalex.org/W2080744942","https://openalex.org/W2103559027","https://openalex.org/W2103680881","https://openalex.org/W2107262685","https://openalex.org/W2151317657","https://openalex.org/W2158167845","https://openalex.org/W2231997813","https://openalex.org/W2573399270","https://openalex.org/W2751023760","https://openalex.org/W3003662786","https://openalex.org/W3042562017","https://openalex.org/W4230055019","https://openalex.org/W4297789110","https://openalex.org/W4298228534"],"related_works":["https://openalex.org/W2066764747","https://openalex.org/W161810272","https://openalex.org/W144405564","https://openalex.org/W2969693569","https://openalex.org/W3118471514","https://openalex.org/W2069661783","https://openalex.org/W2609974967","https://openalex.org/W1978474130","https://openalex.org/W2057159272","https://openalex.org/W1994633937"],"abstract_inverted_index":{"An":[0],"optimal":[1,75],"control":[2,76],"formulation":[3],"for":[4],"determining":[5],"optical":[6,30],"flow":[7,31],"is":[8,66],"presented.":[9,67],"The":[10],"new":[11],"framework":[12],"differs":[13],"from":[14],"preceding":[15],"approaches":[16],"in":[17],"that":[18,53],"it":[19],"does":[20,28],"not":[21],"require":[22],"differentiation":[23],"of":[24,47,59,73],"the":[25,55,71,74],"data":[26],"and":[27,61],"combine":[29],"with":[32,43],"image":[33],"reconstruction.":[34],"It":[35],"can":[36],"be":[37],"considered":[38],"as":[39],"a":[40,44],"control-in-the-coefficients":[41],"problem":[42],"cost":[45],"functional":[46],"tracking":[48],"type.":[49],"A":[50],"numerical":[51],"algorithm":[52],"solves":[54],"optimality":[56],"system":[57],"consisting":[58],"hyperbolic":[60],"elliptic":[62],"partial":[63],"differential":[64],"equations":[65],"Numerical":[68],"experiments":[69],"demonstrate":[70],"effectiveness":[72],"approach.":[77]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
