{"id":"https://openalex.org/W2167940403","doi":"https://doi.org/10.1109/tvcg.2008.33","title":"Efficient Morse Decompositions of Vector Fields","display_name":"Efficient Morse Decompositions of Vector Fields","publication_year":2008,"publication_date":"2008-05-29","ids":{"openalex":"https://openalex.org/W2167940403","doi":"https://doi.org/10.1109/tvcg.2008.33","mag":"2167940403","pmid":"https://pubmed.ncbi.nlm.nih.gov/18467759"},"language":"en","primary_location":{"id":"doi:10.1109/tvcg.2008.33","doi":"https://doi.org/10.1109/tvcg.2008.33","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2008.33","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"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-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Visualization and Computer Graphics","raw_type":"journal-article"},"volume":null,"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/A5055426585","display_name":"Guoning Chen","orcid":"https://orcid.org/0000-0003-0581-6415","observed_orcids":["https://orcid.org/0000-0003-0581-6415","https://orcid.org/0009-0001-4212-199X"]},"institutions":[{"id":"https://openalex.org/I131249849","display_name":"Oregon State University","ror":"https://ror.org/00ysfqy60","country_code":"US","type":"education","lineage":["https://openalex.org/I131249849"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guoning Chen","raw_affiliation_strings":["School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR 97331, USA. chengu@eecs.oregonstate.edu","School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR 97331, USA. chengu@eecs.oregonstate.edu","institution_ids":["https://openalex.org/I131249849"]},{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR, USA","institution_ids":["https://openalex.org/I131249849"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049298090","display_name":"Konstantin Mischaikow","orcid":"https://orcid.org/0000-0003-2876-4558","observed_orcids":["https://orcid.org/0000-0003-2876-4558"]},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"K. Mischaikow","raw_affiliation_strings":["Department of Mathematics, Hill Center-Busch Campus Rutgers, State University of New Jersey, Piscataway, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hill Center-Busch Campus Rutgers, State University of New Jersey, Piscataway, NJ, USA","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031570473","display_name":"Robert S. Laramee","orcid":"https://orcid.org/0000-0002-3874-6145","observed_orcids":["https://orcid.org/0000-0002-3874-6145"]},"institutions":[{"id":"https://openalex.org/I39586589","display_name":"Swansea University","ror":"https://ror.org/053fq8t95","country_code":"GB","type":"education","lineage":["https://openalex.org/I39586589"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"R.S. Laramee","raw_affiliation_strings":["Department of Computer Science, Swansea University, Swansea, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Swansea University, Swansea, UK","institution_ids":["https://openalex.org/I39586589"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038282791","display_name":"Eugene Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I131249849","display_name":"Oregon State University","ror":"https://ror.org/00ysfqy60","country_code":"US","type":"education","lineage":["https://openalex.org/I131249849"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. Zhang","raw_affiliation_strings":["School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR, USA","institution_ids":["https://openalex.org/I131249849"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":7.8764,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.97397434,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"14","issue":"4","first_page":"848","last_page":"862"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.7523999810218811,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.7523999810218811,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.21230000257492065,"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"}},{"id":"https://openalex.org/T10799","display_name":"Data Visualization and Analytics","score":0.011099999770522118,"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/morse-decomposition","display_name":"Morse decomposition","score":0.9480000138282776},{"id":"https://openalex.org/keywords/vector-field-analysis","display_name":"vector field analysis","score":0.7200000286102295},{"id":"https://openalex.org/keywords/directed-graphs","display_name":"directed graphs","score":0.6269999742507935},{"id":"https://openalex.org/keywords/topological-structure","display_name":"topological structure","score":0.4779999852180481},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"periodic orbits","score":0.7329999804496765},{"id":"https://openalex.org/keywords/fixed-points","display_name":"fixed points","score":0.7900000214576721},{"id":"https://openalex.org/keywords/separatrices","display_name":"separatrices","score":0.9670000076293945},{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"adaptive mesh refinement","score":0.5789999961853027},{"id":"https://openalex.org/keywords/robustness-to-disturbances","display_name":"robustness to disturbances","score":0.6930000185966492}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6703052520751953},{"id":"https://openalex.org/C140031139","wikidata":"https://www.wikidata.org/wiki/Q79897","display_name":"Morse code","level":2,"score":0.5938650965690613},{"id":"https://openalex.org/C118965365","wikidata":"https://www.wikidata.org/wiki/Q44528","display_name":"Euclidean vector","level":2,"score":0.5713882446289062},{"id":"https://openalex.org/C167927819","wikidata":"https://www.wikidata.org/wiki/Q1930567","display_name":"Shuffling","level":2,"score":0.5164542198181152},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.48818856477737427},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48755520582199097},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.4834350347518921},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4824536442756653},{"id":"https://openalex.org/C156730297","wikidata":"https://www.wikidata.org/wiki/Q2296951","display_name":"Morse theory","level":2,"score":0.4699445068836212},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44135531783103943},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4334115982055664},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4139626920223236},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2675088942050934},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23966270685195923},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09751152992248535},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003196","descriptor_name":"Computer Graphics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009038","descriptor_name":"Motion","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D009716","descriptor_name":"Numerical Analysis, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012212","descriptor_name":"Rheology","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D014584","descriptor_name":"User-Computer Interface","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":5,"locations":[{"id":"doi:10.1109/tvcg.2008.33","doi":"https://doi.org/10.1109/tvcg.2008.33","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2008.33","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"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-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Visualization and Computer Graphics","raw_type":"journal-article"},{"id":"pmid:18467759","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/18467759","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 visualization and computer graphics","raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.126.5609","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.126.5609","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eecs.oregonstate.edu/library/files/2007-42/vfmorsedecomp.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.332.9168","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.332.9168","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.engr.orst.edu/~zhange/images/morse.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.644.6667","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.644.6667","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cs.swansea.ac.uk/~csbob/research/morse/chen08morse.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W33450621","https://openalex.org/W57661438","https://openalex.org/W162901799","https://openalex.org/W597049470","https://openalex.org/W1514578360","https://openalex.org/W1561234899","https://openalex.org/W1584952761","https://openalex.org/W1597944220","https://openalex.org/W1910188845","https://openalex.org/W1942928910","https://openalex.org/W1977532084","https://openalex.org/W1999616998","https://openalex.org/W2000922989","https://openalex.org/W2011095097","https://openalex.org/W2028617788","https://openalex.org/W2029359030","https://openalex.org/W2031178395","https://openalex.org/W2036304985","https://openalex.org/W2092929058","https://openalex.org/W2094468738","https://openalex.org/W2107746850","https://openalex.org/W2111474755","https://openalex.org/W2124431309","https://openalex.org/W2125638038","https://openalex.org/W2131042673","https://openalex.org/W2131621291","https://openalex.org/W2136690777","https://openalex.org/W2137748495","https://openalex.org/W2139796514","https://openalex.org/W2142195325","https://openalex.org/W2142917543","https://openalex.org/W2151406969","https://openalex.org/W2206545234","https://openalex.org/W2242798320","https://openalex.org/W2325850497","https://openalex.org/W2432517183","https://openalex.org/W2532599107","https://openalex.org/W2752885492","https://openalex.org/W2981264952","https://openalex.org/W2998888370","https://openalex.org/W3143140022","https://openalex.org/W3145128584","https://openalex.org/W3148803860","https://openalex.org/W3149886328","https://openalex.org/W4235260292","https://openalex.org/W4235767492","https://openalex.org/W4285719527","https://openalex.org/W6633427090","https://openalex.org/W6679516948"],"related_works":["https://openalex.org/W7099626044","https://openalex.org/W1993400445","https://openalex.org/W7098497726","https://openalex.org/W2574230460","https://openalex.org/W2020374487","https://openalex.org/W3148722355","https://openalex.org/W2031871226","https://openalex.org/W2514928301","https://openalex.org/W2299747440","https://openalex.org/W1976948755"],"abstract_inverted_index":{"Existing":[0],"topology-based":[1],"vector":[2,39,67,88],"field":[3,40,68],"analysis":[4,41],"techniques":[5,96,185,222],"rely":[6],"on":[7,134,174,251],"the":[8,12,48,62,70,118,135,148,157,160,163,178,195,198,201,209,217,227,230,233,239,248],"ability":[9],"to":[10,26,58,60,114,216],"extract":[11],"individual":[13],"trajectories":[14],"such":[15,38],"as":[16],"fixed":[17],"points,":[18],"periodic":[19],"orbits,":[20],"and":[21,28,33,105,162,182,186,232,250],"separatrices":[22],"that":[23,110],"are":[24,54,102,111],"sensitive":[25],"noise":[27],"errors":[29],"introduced":[30],"by":[31],"simulation":[32,255],"interpolation.":[34],"This":[35],"can":[36],"make":[37],"unsuitable":[42],"for":[43,86,97,117,129,204],"rigorous":[44],"interpretations.":[45],"We":[46,166,237],"advocate":[47],"use":[49,179,210],"of":[50,65,72,137,150,159,170,180,194,197,211,229,235,241],"Morse":[51,78,131,171],"decompositions,":[52],"which":[53,139,176],"robust":[55],"with":[56,244],"respect":[57],"perturbations,":[59],"encode":[61],"topological":[63],"structures":[64],"a":[66,73,77,126,153],"in":[69,108,190,200,214,247],"form":[71],"directed":[74],"graph,":[75],"called":[76],"connection":[79],"graph":[80],"(MCG).":[81],"While":[82],"an":[83,187],"MCG":[84],"exists":[85],"every":[87],"field,":[89],"it":[90],"need":[91],"not":[92],"be":[93,115],"unique.":[94],"Previous":[95],"computing":[98],"MCG's,":[99],"while":[100],"fast,":[101],"overly":[103],"conservative":[104],"usually":[106],"results":[107],"MCG's":[109,143,161],"too":[112],"coarse":[113],"useful":[116],"applications.":[119],"To":[120],"address":[121],"this":[122],"issue,":[123],"we":[124,207],"present":[125],"new":[127],"technique":[128,243],"performing":[130],"decomposition":[132,172],"based":[133,173],"concept":[136],"tau-maps,":[138,175],"typically":[140],"provides":[141,152],"finer":[142],"than":[144],"existing":[145],"techniques.":[146],"Furthermore,":[147,206],"choice":[149],"tau":[151],"natural":[154],"tradeoff":[155],"between":[156,226],"fineness":[158],"computational":[164],"costs.":[165],"provide":[167,223],"efficient":[168],"implementations":[169],"include":[177],"forward":[181],"backward":[183],"mapping":[184],"adaptive":[188],"approach":[189],"constructing":[191],"better":[192],"approximations":[193],"images":[196],"triangles":[199],"meshes":[202],"used":[203],"simulation..":[205],"propose":[208],"spatial":[212],"tau-maps":[213],"addition":[215],"original":[218],"temporal":[219],"tau-maps.":[220],"These":[221],"additional":[224],"trade-offs":[225],"quality":[228],"MCGs":[231],"speed":[234],"computation.":[236],"demonstrate":[238],"utility":[240],"our":[242],"various":[245],"examples":[246],"plane":[249],"surfaces":[252],"including":[253],"engine":[254],"data":[256],"sets.":[257]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":7}],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2016-06-24T00:00:00"}
