{"id":"https://openalex.org/W1567812959","doi":"https://doi.org/10.1109/visual.2005.1532842","title":"Extracting Higher Order Critical Points and Topological Simplification of 3D Vector Fields","display_name":"Extracting Higher Order Critical Points and Topological Simplification of 3D Vector Fields","publication_year":2006,"publication_date":"2006-10-11","ids":{"openalex":"https://openalex.org/W1567812959","doi":"https://doi.org/10.1109/visual.2005.1532842","mag":"1567812959"},"language":"en","primary_location":{"id":"doi:10.1109/visual.2005.1532842","is_oa":false,"landing_page_url":"https://doi.org/10.1109/visual.2005.1532842","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VIS 05. IEEE Visualization, 2005.","raw_type":"proceedings-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/A5082234726","display_name":"Tino Weinkauf","orcid":"https://orcid.org/0000-0002-1498-9062"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"T. Weinkauf","raw_affiliation_strings":["ZIB Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ZIB Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039626800","display_name":"Holger Theisel","orcid":"https://orcid.org/0000-0002-8009-7070"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"H. Theisel","raw_affiliation_strings":["MPI Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MPI Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083651238","display_name":"Kuangyu Shi","orcid":"https://orcid.org/0000-0002-8714-3084"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Kuangyu Shi","raw_affiliation_strings":["MPI Saarbr\u00fccken, Germany","Computer Graphics, MPI for Informatics, Max Planck Society"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MPI Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"Computer Graphics, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I4210109712","https://openalex.org/I149899117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091630951","display_name":"Hans\u2010Christian Hege","orcid":"https://orcid.org/0000-0002-6574-0988"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"H.-C. Hege","raw_affiliation_strings":["ZIB Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ZIB Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111879543","display_name":"H.-P. Seidel","orcid":null},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"H.-P. Seidel","raw_affiliation_strings":["MPI Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MPI Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.9371,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.92986968,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"559","last_page":"566"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9994999766349792,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9943000078201294,"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/T10799","display_name":"Data Visualization and Analytics","score":0.9876000285148621,"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/topological-skeleton","display_name":"Topological skeleton","score":0.6012346148490906},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.5711004734039307},{"id":"https://openalex.org/keywords/euclidean-vector","display_name":"Euclidean vector","score":0.5708596706390381},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.563878059387207},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5498417615890503},{"id":"https://openalex.org/keywords/critical-point","display_name":"Critical point (mathematics)","score":0.537650465965271},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5235333442687988},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.49585065245628357},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4653072953224182},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.46519696712493896},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4493827223777771},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4154323637485504},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32842132449150085},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2449156939983368},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2252732813358307},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1679498255252838},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13071590662002563}],"concepts":[{"id":"https://openalex.org/C112785775","wikidata":"https://www.wikidata.org/wiki/Q786441","display_name":"Topological skeleton","level":4,"score":0.6012346148490906},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.5711004734039307},{"id":"https://openalex.org/C118965365","wikidata":"https://www.wikidata.org/wiki/Q44528","display_name":"Euclidean vector","level":2,"score":0.5708596706390381},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.563878059387207},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5498417615890503},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.537650465965271},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5235333442687988},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.49585065245628357},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4653072953224182},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.46519696712493896},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4493827223777771},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4154323637485504},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32842132449150085},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2449156939983368},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2252732813358307},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1679498255252838},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13071590662002563},{"id":"https://openalex.org/C129641003","wikidata":"https://www.wikidata.org/wiki/Q267189","display_name":"Active shape model","level":3,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/visual.2005.1532842","is_oa":false,"landing_page_url":"https://doi.org/10.1109/visual.2005.1532842","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VIS 05. IEEE Visualization, 2005.","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.143.1929","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.143.1929","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://isgwww.cs.uni-magdeburg.de/visual/publications/Extract3DCPoints.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.250.9443","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.250.9443","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.zib.de/visual/publications/sources/src-2005/weinkauf05a.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:278965","is_oa":false,"landing_page_url":"http://edoc.mpg.de/278965","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Visualization 2005 (VIS 2005), IEEE, 559-566 (2005)","raw_type":"Conference-Paper"},{"id":"pmh:oai:pure.mpg.de:item_1328914","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-000F-267D-4","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Visualization 2005","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1505871258","https://openalex.org/W1552632109","https://openalex.org/W1597773817","https://openalex.org/W1993327963","https://openalex.org/W1999616998","https://openalex.org/W2131332803","https://openalex.org/W2137748495","https://openalex.org/W2142195325","https://openalex.org/W2142579447","https://openalex.org/W2142917543","https://openalex.org/W2146680024","https://openalex.org/W2161414603","https://openalex.org/W2161541208","https://openalex.org/W3143140022","https://openalex.org/W3144229920","https://openalex.org/W3144233241","https://openalex.org/W3147220190","https://openalex.org/W4235361483","https://openalex.org/W4240558544","https://openalex.org/W4248931898","https://openalex.org/W6635590004","https://openalex.org/W6679435979","https://openalex.org/W6684040624","https://openalex.org/W6813741318"],"related_works":["https://openalex.org/W2041424614","https://openalex.org/W2162397090","https://openalex.org/W1982006972","https://openalex.org/W1530031806","https://openalex.org/W3036909545","https://openalex.org/W4212888252","https://openalex.org/W1967471690","https://openalex.org/W2164419793","https://openalex.org/W1535397896","https://openalex.org/W4383901015"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"an":[3,58,72,83],"approach":[4],"to":[5,52,100,112],"extracting":[6,53],"and":[7],"classifying":[8],"higher":[9],"order":[10],"critical":[11,42,67,109],"points":[12],"of":[13,30,40,46,57,75,78,106,108,115],"3D":[14,38,118],"vector":[15,61,119],"fields.":[16,120],"To":[17],"do":[18],"so,":[19],"we":[20,33,81],"place":[21],"a":[22,41,102],"closed":[23],"convex":[24],"surface":[25],"s":[26,92],"around":[27],"the":[28,36,54,87,94],"area":[29],"interest.":[31],"Then":[32],"show":[34],"that":[35],"complete":[37,88],"classification":[39],"point":[43,68],"into":[44],"areas":[45],"different":[47],"flow":[48],"behavior":[49],"is":[50,69],"equivalent":[51],"topological":[55,89],"skeleton":[56],"appropriate":[59],"2D":[60],"field":[62],"on":[63],"s,":[64],"if":[65],"each":[66],"equipped":[70],"with":[71],"additional":[73],"bit":[74],"information.":[76],"Out":[77],"this":[79],"skeleton,":[80],"create":[82],"icon":[84],"which":[85],"replaces":[86],"structure":[90],"inside":[91],"for":[93],"visualization.":[95],"We":[96],"apply":[97],"our":[98],"method":[99],"find":[101],"simplified":[103],"visual":[104],"representation":[105],"clusters":[107],"points,":[110],"leading":[111],"expressive":[113],"visualizations":[114],"topologically":[116],"complex":[117]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
