{"id":"https://openalex.org/W2031555400","doi":"https://doi.org/10.1109/tpami.1986.4767833","title":"An Investigation of Smoothness Constraints for the Estimation of Displacement Vector Fields from Image Sequences","display_name":"An Investigation of Smoothness Constraints for the Estimation of Displacement Vector Fields from Image Sequences","publication_year":1986,"publication_date":"1986-09-01","ids":{"openalex":"https://openalex.org/W2031555400","doi":"https://doi.org/10.1109/tpami.1986.4767833","mag":"2031555400","pmid":"https://pubmed.ncbi.nlm.nih.gov/21869357"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.1986.4767833","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1986.4767833","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,"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"},"type":"article","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/A5108363048","display_name":"Hans-Hellmut Nagel","orcid":null},"institutions":[{"id":"https://openalex.org/I4210088543","display_name":"Institut f\u00fcr Informationsverarbeitung","ror":"https://ror.org/0047j9t38","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210088543"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hans-Hellmut Nagel","raw_affiliation_strings":["Fraunhofer-Institut f\u00fcr Informationsund Datenverarbeitung, Sebastian-Kneipp-Str. 12-14, 7500 Karlsruhe 1, West Germany; Fakult\u00e4t f\u00fcr Informatik, Universit\u00e4t Karlsruhe, West Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fraunhofer-Institut f\u00fcr Informationsund Datenverarbeitung, Sebastian-Kneipp-Str. 12-14, 7500 Karlsruhe 1, West Germany; Fakult\u00e4t f\u00fcr Informatik, Universit\u00e4t Karlsruhe, West Germany","institution_ids":["https://openalex.org/I4210088543"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066894760","display_name":"W. Enkelmann","orcid":null},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Wilfried Enkelmann","raw_affiliation_strings":["Fachbereich Informatik, Universit\u00e4t Hamburg, Schl\u00fcterstr. 70, 2000 Hamburg 13, West Germany; Fraunhofer-Institut f\u00fcr Informationsund Datenverarbeitung, Sebastian-Kneipp-Str. 12-14, 7500 Karlsruhe 1, West Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Informatik, Universit\u00e4t Hamburg, Schl\u00fcterstr. 70, 2000 Hamburg 13, West Germany; Fraunhofer-Institut f\u00fcr Informationsund Datenverarbeitung, Sebastian-Kneipp-Str. 12-14, 7500 Karlsruhe 1, West Germany","institution_ids":["https://openalex.org/I159176309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":26.8565,"has_fulltext":false,"cited_by_count":769,"citation_normalized_percentile":{"value":0.99668417,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"PAMI-8","issue":"5","first_page":"565","last_page":"593"},"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9975000023841858,"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/T13114","display_name":"Image Processing Techniques and Applications","score":0.9914000034332275,"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/vector-field","display_name":"Vector field","score":0.6829050779342651},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6583134531974792},{"id":"https://openalex.org/keywords/displacement-field","display_name":"Displacement field","score":0.6052197217941284},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.5863058567047119},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.5225498080253601},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.49991726875305176},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.47096922993659973},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.46407273411750793},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46359768509864807},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4542919993400574},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4246312379837036},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3743162155151367},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17131614685058594},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1577921211719513},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08405578136444092}],"concepts":[{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.6829050779342651},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6583134531974792},{"id":"https://openalex.org/C29660869","wikidata":"https://www.wikidata.org/wiki/Q5282615","display_name":"Displacement field","level":3,"score":0.6052197217941284},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.5863058567047119},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.5225498080253601},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.49991726875305176},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.47096922993659973},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.46407273411750793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46359768509864807},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4542919993400574},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4246312379837036},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3743162155151367},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17131614685058594},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1577921211719513},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08405578136444092},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.1986.4767833","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1986.4767833","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,"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:21869357","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21869357","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 pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W112287601","https://openalex.org/W303359171","https://openalex.org/W1578285471","https://openalex.org/W1660110636","https://openalex.org/W1663910018","https://openalex.org/W1842319506","https://openalex.org/W1970393892","https://openalex.org/W1997893906","https://openalex.org/W1998930867","https://openalex.org/W2003368332","https://openalex.org/W2017946860","https://openalex.org/W2029343472","https://openalex.org/W2031555400","https://openalex.org/W2043257636","https://openalex.org/W2075747175","https://openalex.org/W2081171933","https://openalex.org/W2091912339","https://openalex.org/W2751023760","https://openalex.org/W2767737157","https://openalex.org/W2997169974","https://openalex.org/W4285719527","https://openalex.org/W6637132533","https://openalex.org/W6650990417","https://openalex.org/W6657651288","https://openalex.org/W6771707327"],"related_works":["https://openalex.org/W2360764675","https://openalex.org/W43236265","https://openalex.org/W1581382664","https://openalex.org/W1865242774","https://openalex.org/W2161229648","https://openalex.org/W1951168524","https://openalex.org/W2993674027","https://openalex.org/W2130228941","https://openalex.org/W4386762575","https://openalex.org/W2124037017"],"abstract_inverted_index":{"A":[0],"mapping":[1],"between":[2],"one":[3],"frame":[4,14],"from":[5],"an":[6,115,120],"image":[7,65],"sequence":[8],"and":[9,127],"the":[10,26,51,64,87,95],"preceding":[11],"or":[12,104],"following":[13],"can":[15],"be":[16,125],"represented":[17],"as":[18,60,68],"a":[19,41,54,61,69],"displacement":[20,42,55,96],"vector":[21,43,56,97],"field.":[22,44],"In":[23],"most":[24],"situations,":[25],"mere":[27],"gray":[28,76,108],"value":[29,77],"variations":[30,93],"do":[31],"not":[32],"provide":[33],"sufficient":[34],"information":[35],"in":[36,100],"order":[37],"to":[38,81],"estimate":[39],"such":[40,119],"Supplementary":[45],"constraints":[46],"are":[47],"necessary,":[48],"for":[49],"example":[50],"postulate":[52],"that":[53],"field":[57,98],"varies":[58],"smoothly":[59],"function":[62],"of":[63,94,107,114],"position.":[66],"Taken":[67],"general":[70],"requirement,":[71],"this":[72],"creates":[73],"difficulties":[74],"at":[75],"transitions":[78],"which":[79,91],"correspond":[80],"occluding":[82],"contours.":[83],"Nagel":[84],"therefore":[85],"introduced":[86],"``oriented":[88,121],"smoothness''":[89,122],"requirement":[90],"restricts":[92],"only":[99],"directions":[101],"with":[102],"small":[103],"no":[105],"variation":[106],"values.":[109],"This":[110],"contribution":[111],"reports":[112],"results":[113],"investigation":[116],"about":[117],"how":[118],"constraint":[123],"may":[124],"formulated":[126],"evaluated.":[128]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":18},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":21},{"year":2015,"cited_by_count":24},{"year":2014,"cited_by_count":17},{"year":2013,"cited_by_count":35},{"year":2012,"cited_by_count":29}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
