{"id":"https://openalex.org/W2008794074","doi":"https://doi.org/10.1137/060660709","title":"Simultaneous Higher-Order Optical Flow Estimation and Decomposition","display_name":"Simultaneous Higher-Order Optical Flow Estimation and Decomposition","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2008794074","doi":"https://doi.org/10.1137/060660709","mag":"2008794074"},"language":"en","primary_location":{"id":"doi:10.1137/060660709","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060660709","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/A5101561039","display_name":"Jing Yuan","orcid":"https://orcid.org/0000-0002-3548-5875"},"institutions":[{"id":"https://openalex.org/I177802217","display_name":"University of Mannheim","ror":"https://ror.org/031bsb921","country_code":"DE","type":"education","lineage":["https://openalex.org/I177802217"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Jing Yuan","raw_affiliation_strings":["University of Mannheim"],"affiliations":[{"raw_affiliation_string":"University of Mannheim","institution_ids":["https://openalex.org/I177802217"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016322773","display_name":"Christoph Sch\u00f6rr","orcid":null},"institutions":[{"id":"https://openalex.org/I177802217","display_name":"University of Mannheim","ror":"https://ror.org/031bsb921","country_code":"DE","type":"education","lineage":["https://openalex.org/I177802217"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christoph Sch\u00f6rr","raw_affiliation_strings":["University of Mannheim"],"affiliations":[{"raw_affiliation_string":"University of Mannheim","institution_ids":["https://openalex.org/I177802217"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008755474","display_name":"Gabriele Steidl","orcid":"https://orcid.org/0000-0003-4638-9245"},"institutions":[{"id":"https://openalex.org/I177802217","display_name":"University of Mannheim","ror":"https://ror.org/031bsb921","country_code":"DE","type":"education","lineage":["https://openalex.org/I177802217"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gabriele Steidl","raw_affiliation_strings":["University of Mannheim"],"affiliations":[{"raw_affiliation_string":"University of Mannheim","institution_ids":["https://openalex.org/I177802217"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101561039"],"corresponding_institution_ids":["https://openalex.org/I177802217"],"apc_list":null,"apc_paid":null,"fwci":2.9592,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.91264617,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"29","issue":"6","first_page":"2283","last_page":"2304"},"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":0.9994000196456909,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.7856135964393616},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7159432768821716},{"id":"https://openalex.org/keywords/optical-flow","display_name":"Optical flow","score":0.6421344876289368},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6187615394592285},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5471587777137756},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5393644571304321},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.4702391028404236},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.43442004919052124},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4206693172454834},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.418249249458313},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3997572064399719},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39905625581741333},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3803509473800659},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.2466581165790558},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17822784185409546},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16179510951042175},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11215704679489136}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7856135964393616},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7159432768821716},{"id":"https://openalex.org/C155542232","wikidata":"https://www.wikidata.org/wiki/Q736111","display_name":"Optical flow","level":3,"score":0.6421344876289368},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6187615394592285},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5471587777137756},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5393644571304321},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.4702391028404236},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.43442004919052124},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4206693172454834},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.418249249458313},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3997572064399719},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39905625581741333},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3803509473800659},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.2466581165790558},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17822784185409546},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16179510951042175},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11215704679489136},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060660709","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060660709","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.497.2250","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.497.2250","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ipa.iwr.uni-heidelberg.de/ipabib/Papers/SISC-07.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.570.1421","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.570.1421","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathematik.uni-kl.de/uploads/tx_sibibtex/paper_optflow.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W41051884","https://openalex.org/W172706166","https://openalex.org/W207373900","https://openalex.org/W1488881187","https://openalex.org/W1494951781","https://openalex.org/W1495696189","https://openalex.org/W1578285471","https://openalex.org/W1593038947","https://openalex.org/W1606963477","https://openalex.org/W1694289106","https://openalex.org/W1831640761","https://openalex.org/W1980423260","https://openalex.org/W1984648213","https://openalex.org/W1987508246","https://openalex.org/W1993000710","https://openalex.org/W2005067064","https://openalex.org/W2005089986","https://openalex.org/W2016187631","https://openalex.org/W2017044324","https://openalex.org/W2017085690","https://openalex.org/W2025734987","https://openalex.org/W2026414333","https://openalex.org/W2037981501","https://openalex.org/W2039744571","https://openalex.org/W2040378863","https://openalex.org/W2045094421","https://openalex.org/W2045559171","https://openalex.org/W2054654931","https://openalex.org/W2061979078","https://openalex.org/W2066630786","https://openalex.org/W2098549404","https://openalex.org/W2103559027","https://openalex.org/W2105235982","https://openalex.org/W2111841405","https://openalex.org/W2115706991","https://openalex.org/W2122890444","https://openalex.org/W2126055449","https://openalex.org/W2154996879","https://openalex.org/W2172222863","https://openalex.org/W2266761936","https://openalex.org/W2751023760"],"related_works":["https://openalex.org/W2024955095","https://openalex.org/W1976727549","https://openalex.org/W2056066177","https://openalex.org/W2127069673","https://openalex.org/W2184068959","https://openalex.org/W3088316828","https://openalex.org/W1483453436","https://openalex.org/W3202260829","https://openalex.org/W4286909305","https://openalex.org/W2136089225"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,76,83,87,94,97],"estimation":[3],"and":[4,23,61],"decomposition":[5,20],"of":[6,96],"optical":[7,30],"flows":[8],"from":[9,18],"highly":[10],"nonrigid":[11],"motions.":[12],"To":[13],"this":[14],"end,":[15],"recent":[16],"methods":[17],"image":[19],"into":[21],"structural":[22],"textural":[24],"parts":[25],"are":[26],"combined":[27],"with":[28],"variational":[29],"flow":[31,57],"estimation.":[32],"The":[33],"approaches":[34],"we":[35,74],"suggest":[36],"amount":[37],"to":[38,53,62],"minimizing":[39],"discrete":[40],"convex":[41],"functionals":[42],"using":[43],"second-order":[44],"cone":[45],"programming.":[46],"Higher-order":[47],"regularization":[48],"is":[49],"necessary":[50],"in":[51],"order":[52],"accurately":[54],"recover":[55],"important":[56],"structure":[58],"like":[59],"vortices,":[60],"incorporate":[63],"key":[64],"physical":[65],"properties":[66],"such":[67],"as":[68],"vanishing":[69],"divergence.":[70],"For":[71],"proper":[72],"discretization,":[73],"apply":[75],"finite":[77],"mimetic":[78],"difference":[79],"method,":[80],"which":[81],"preserves":[82],"identities":[84],"fulfilled":[85],"by":[86],"continuous":[88],"differential":[89],"operators.":[90],"Numerical":[91],"examples":[92],"demonstrate":[93],"feasibility":[95],"complex":[98],"approaches.":[99]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}