{"id":"https://openalex.org/W2010942916","doi":"https://doi.org/10.1109/tpami.1987.4767897","title":"Optical Flow Estimation: An Error Analysis of Gradient-Based Methods with Local Optimization","display_name":"Optical Flow Estimation: An Error Analysis of Gradient-Based Methods with Local Optimization","publication_year":1987,"publication_date":"1987-03-01","ids":{"openalex":"https://openalex.org/W2010942916","doi":"https://doi.org/10.1109/tpami.1987.4767897","mag":"2010942916","pmid":"https://pubmed.ncbi.nlm.nih.gov/21869393"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.1987.4767897","doi":"https://doi.org/10.1109/tpami.1987.4767897","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1987.4767897","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["ccf-a","cwts-core","dongbi-a","doyens","jufo-3","medline","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2010942916"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref","pubmed"],"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/A5086786774","display_name":"Joseph K. Kearney","orcid":"https://orcid.org/0000-0002-0443-8152","observed_orcids":["https://orcid.org/0000-0002-0443-8152"]},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]},{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joseph K. Kearney","raw_affiliation_strings":["Department of Computer Science, Cornell University, Ithaca, NY 14853; Department of Computer Science, University of Iowa, Iowa City, IA 52242"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Cornell University, Ithaca, NY 14853; Department of Computer Science, University of Iowa, Iowa City, IA 52242","institution_ids":["https://openalex.org/I126307644","https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077284130","display_name":"William B. Thompson","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"William B. Thompson","raw_affiliation_strings":["Department of Computer Science, University of Minnesota, Minneapolis, MN, USA","Department of Computer Science, University Of Minnesota, Minneapolis, MN 55455"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Department of Computer Science, University Of Minnesota, Minneapolis, MN 55455","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082618302","display_name":"Daniel L. Boley","orcid":"https://orcid.org/0000-0002-2685-8449","observed_orcids":["https://orcid.org/0000-0002-2685-8449"]},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel L. Boley","raw_affiliation_strings":["Department of Computer Science, University of Minnesota, Minneapolis, MN, USA","Department of Computer Science, University Of Minnesota, Minneapolis, MN 55455"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Department of Computer Science, University Of Minnesota, Minneapolis, MN 55455","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":14.5094,"has_fulltext":false,"cited_by_count":366,"citation_normalized_percentile":{"value":0.99120352,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"PAMI-9","issue":"2","first_page":"229","last_page":"244"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","score":0.9994999766349792,"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":0.9994999766349792,"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/T10331","display_name":"Video Surveillance and Tracking Methods","score":0.0003000000142492354,"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/T10427","display_name":"Visual perception and processing mechanisms","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/optical-flow","display_name":"optical flow","score":0.9929999709129333},{"id":"https://openalex.org/keywords/gradient-based-optimization","display_name":"gradient-based optimization","score":0.9399999976158142},{"id":"https://openalex.org/keywords/error-analysis","display_name":"error analysis","score":0.8209999799728394},{"id":"https://openalex.org/keywords/local-optimization","display_name":"local optimization","score":0.9169999957084656},{"id":"https://openalex.org/keywords/motion-boundaries","display_name":"motion boundaries","score":0.6850000023841858},{"id":"https://openalex.org/keywords/depth-discontinuities","display_name":"depth discontinuities","score":0.9929999709129333},{"id":"https://openalex.org/keywords/measurement-error","display_name":"measurement error","score":0.4790000021457672},{"id":"https://openalex.org/keywords/multiple-views","display_name":"multiple views","score":0.32499998807907104}],"concepts":[{"id":"https://openalex.org/C155542232","wikidata":"https://www.wikidata.org/wiki/Q736111","display_name":"Optical flow","level":3,"score":0.7906007766723633},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.633277177810669},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.6281240582466125},{"id":"https://openalex.org/C125245961","wikidata":"https://www.wikidata.org/wiki/Q221656","display_name":"Brightness","level":2,"score":0.5901362299919128},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5369399189949036},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4963870644569397},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4563830494880676},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.45220375061035156},{"id":"https://openalex.org/C151857401","wikidata":"https://www.wikidata.org/wiki/Q640621","display_name":"Optical engineering","level":2,"score":0.4515031576156616},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.4449623227119446},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.41340985894203186},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.4106614291667938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29300209879875183},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.1930377185344696},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10427045822143555},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0894453227519989},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tpami.1987.4767897","doi":"https://doi.org/10.1109/tpami.1987.4767897","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1987.4767897","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["ccf-a","cwts-core","dongbi-a","doyens","jufo-3","medline","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:21869393","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21869393","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,"listed_in":[],"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 pattern analysis and machine intelligence","raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.220.2793","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.220.2793","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.utah.edu/~thompson/publications/Kearney:1987:OFE.pdf","raw_type":"text"},{"id":"mag:2188799641","doi":null,"is_oa":false,"landing_page_url":"http://www.cs.utah.edu/~thompson/publications/Kearney:1987:OFE.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W112287601","https://openalex.org/W166240046","https://openalex.org/W1578285471","https://openalex.org/W1970393892","https://openalex.org/W1989701469","https://openalex.org/W1993223529","https://openalex.org/W1994552597","https://openalex.org/W2000020986","https://openalex.org/W2015157402","https://openalex.org/W2025786274","https://openalex.org/W2067265395","https://openalex.org/W2081171933","https://openalex.org/W2083353204","https://openalex.org/W2083883139","https://openalex.org/W2085261163","https://openalex.org/W2118877769","https://openalex.org/W2135622428","https://openalex.org/W2150912583","https://openalex.org/W2598939527","https://openalex.org/W2751023760","https://openalex.org/W4285719527","https://openalex.org/W6735087678"],"related_works":["https://openalex.org/W1895932455","https://openalex.org/W7095858521","https://openalex.org/W2214745880","https://openalex.org/W2146205914","https://openalex.org/W2007580307","https://openalex.org/W2560298370","https://openalex.org/W318136591","https://openalex.org/W1487573600","https://openalex.org/W1526907883","https://openalex.org/W1633722303"],"abstract_inverted_index":{"Multiple":[0],"views":[1],"of":[2,15,19,29,36,45,58,77,96,131,156,165,171,174,194,199,202,208,216,219],"a":[3,151],"scene":[4],"can":[5,104,118],"provide":[6],"important":[7,43],"information":[8,25],"about":[9],"the":[10,20,27,34,53,56,78,122,129,169,172,175,191,195,200,206,209,213],"structure":[11],"and":[12,75,101,168,211],"dynamic":[13],"behavior":[14],"three-dimensional":[16],"objects.":[17],"Many":[18],"methods":[21,63,81,143],"that":[22,136,145],"recover":[23],"this":[24,125,159],"require":[26],"determination":[28],"optical":[30,49,140,146],"flow-the":[31],"velocity,":[32],"on":[33,39,52],"image,":[35],"visible":[37],"points":[38],"object":[40],"surfaces.":[41],"An":[42],"class":[44],"techniques":[46,135],"for":[47,108,133,139],"estimating":[48],"flow":[50,147],"depend":[51],"relationship":[54],"between":[55],"gradients":[57],"image":[59],"brightness.":[60],"While":[61],"gradient-based":[62,109,134],"have":[64],"been":[65,71],"widely":[66],"studied,":[67],"little":[68],"attention":[69],"has":[70],"paid":[72],"to":[73,84,189],"accuracy":[74,201],"reliability":[76],"approach.":[79],"Gradient-based":[80],"are":[82,115,178,187],"sensitive":[83],"conditions":[85],"commonly":[86],"encountered":[87],"in":[88,121,150,158],"real":[89],"imagery.":[90],"Highly":[91],"textured":[92],"surfaces,":[93],"large":[94],"areas":[95,114],"constant":[97,149],"brightness,":[98],"motion":[99],"boundaries,":[100],"depth":[102],"discontinuities":[103],"all":[105],"be":[106,119],"troublesome":[107],"methods.":[110],"Fortunately,":[111],"these":[112],"problematic":[113],"usually":[116],"localized":[117],"identified":[120],"image.":[123],"In":[124],"paper":[126],"we":[127,186],"examine":[128],"sources":[130],"errors":[132,167,184],"locally":[137],"solve":[138],"flow.":[141],"These":[142],"assume":[144],"is":[148,161],"small":[152],"neighborhood.":[153],"The":[154,163],"consequence":[155],"violating":[157],"assumption":[160],"examined.":[162],"causes":[164],"measurement":[166],"determinants":[170],"conditioning":[173],"solution":[176],"system":[177],"also":[179],"considered.":[180],"By":[181],"understanding":[182],"how":[183],"arise,":[185],"able":[188],"define":[190],"inherent":[192],"limitations":[193],"technique,":[196,210],"obtain":[197],"estimates":[198],"computed":[203],"values,":[204],"enhance":[205],"performance":[207],"demonstrate":[212],"informative":[214],"value":[215],"some":[217],"types":[218],"error.":[220]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":7}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2016-06-24T00:00:00"}
