{"id":"https://openalex.org/W2096451963","doi":"https://doi.org/10.1142/s0218195908002751","title":"MEDIAL AXIS APPROXIMATION AND UNSTABLE FLOW COMPLEX","display_name":"MEDIAL AXIS APPROXIMATION AND UNSTABLE FLOW COMPLEX","publication_year":2008,"publication_date":"2008-12-01","ids":{"openalex":"https://openalex.org/W2096451963","doi":"https://doi.org/10.1142/s0218195908002751","mag":"2096451963"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195908002751","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195908002751","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","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/A5027313464","display_name":"Joachim Giesen","orcid":"https://orcid.org/0000-0001-6598-6833"},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"JOACHIM GIESEN","raw_affiliation_strings":["Friedrich-Schiller-Universit\u00e4t Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Friedrich-Schiller-Universit\u00e4t Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany","institution_ids":["https://openalex.org/I76198965"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056075734","display_name":"Edgar A. Ramos","orcid":"https://orcid.org/0000-0001-6852-7472"},"institutions":[{"id":"https://openalex.org/I36243813","display_name":"Universidad Nacional de Colombia","ror":"https://ror.org/059yx9a68","country_code":"CO","type":"education","lineage":["https://openalex.org/I36243813"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"EDGAR A. RAMOS","raw_affiliation_strings":["Escuela de Matem\u00e1ticas, Universidad Nacional de Colombia, Medell\u00edn, Colombia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Escuela de Matem\u00e1ticas, Universidad Nacional de Colombia, Medell\u00edn, Colombia","institution_ids":["https://openalex.org/I36243813"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053664140","display_name":"Bardia Sadri","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"BARDIA SADRI","raw_affiliation_strings":["Department of Computer Science, University of Toronto, Toronto, Ontario M5S 3G4, Canada","Department of Computer Science, University of Toronto, Toronto, Ontario M5S 3G4, Canada#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Toronto, Ontario M5S 3G4, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Toronto, Ontario M5S 3G4, Canada#TAB#","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.09623697,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"06","first_page":"533","last_page":"565"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9993000030517578,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9993000030517578,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9945999979972839,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/medial-axis","display_name":"Medial axis","score":0.8943524360656738},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7588487863540649},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6705604791641235},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5781439542770386},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.5454800724983215},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.48834511637687683},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.47012317180633545},{"id":"https://openalex.org/keywords/simply-connected-space","display_name":"Simply connected space","score":0.4399717450141907},{"id":"https://openalex.org/keywords/closeness","display_name":"Closeness","score":0.41158172488212585},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.37808993458747864},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3260817527770996},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32251933217048645},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19988831877708435}],"concepts":[{"id":"https://openalex.org/C185877587","wikidata":"https://www.wikidata.org/wiki/Q1757407","display_name":"Medial axis","level":2,"score":0.8943524360656738},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7588487863540649},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6705604791641235},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5781439542770386},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.5454800724983215},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.48834511637687683},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.47012317180633545},{"id":"https://openalex.org/C167204820","wikidata":"https://www.wikidata.org/wiki/Q912058","display_name":"Simply connected space","level":2,"score":0.4399717450141907},{"id":"https://openalex.org/C2779545769","wikidata":"https://www.wikidata.org/wiki/Q5135364","display_name":"Closeness","level":2,"score":0.41158172488212585},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37808993458747864},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3260817527770996},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32251933217048645},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19988831877708435}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195908002751","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195908002751","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.44999998807907104}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W628756162","https://openalex.org/W1977276706","https://openalex.org/W2002053510","https://openalex.org/W2029041800","https://openalex.org/W2039081484","https://openalex.org/W2088352159","https://openalex.org/W2207289595","https://openalex.org/W2911001378"],"related_works":["https://openalex.org/W1995054232","https://openalex.org/W2156910174","https://openalex.org/W1556709767","https://openalex.org/W4231619797","https://openalex.org/W2039081484","https://openalex.org/W2083732234","https://openalex.org/W4290631031","https://openalex.org/W2963176892","https://openalex.org/W2792774748","https://openalex.org/W2185592532"],"abstract_inverted_index":{"The":[0,77,133],"medial":[1,40,62,94,176],"axis":[2,63,95],"of":[3,12,22,30,60,64,74,92,96,102,135,170],"a":[4,10,19,51,65,71,80,115,164],"shape":[5,66,98],"is":[6,79,86,105],"known":[7],"to":[8,88,124],"carry":[9],"lot":[11],"information":[13],"about":[14],"the":[15,34,55,58,61,90,93,97,100,120,130,136,144,152,157,168,171,174],"shape.":[16],"In":[17,42],"particular,":[18],"recent":[20],"result":[21],"Lieutier":[23],"establishes":[24],"that":[25,49,85,149],"every":[26],"bounded":[27],"open":[28],"subset":[29],"\u211d":[31],"n":[32],"has":[33],"same":[35],"homotopy":[36],"type":[37],"as":[38],"its":[39,75,103,139],"axis.":[41,177],"this":[43],"paper":[44],"we":[45,53],"provide":[46,163],"an":[47],"algorithm":[48],"computes":[50],"structure":[52],"call":[54],"core":[56,78,121,137,172],"for":[57,118],"approximation":[59],"with":[67],"smooth":[68],"boundary":[69,104],"from":[70,151],"discrete":[72],"sample":[73,101,158],"boundary.":[76],"piecewise":[81],"linear":[82],"cell":[83],"complex":[84],"guaranteed":[87],"capture":[89],"topology":[91],"provided":[99],"sufficiently":[106],"dense":[107],"but":[108],"not":[109],"necessarily":[110],"uniform.":[111],"We":[112,161],"also":[113,162],"present":[114],"natural":[116],"method":[117],"augmenting":[119],"in":[122],"order":[123],"extend":[125],"it":[126],"geometrically":[127],"while":[128],"maintaining":[129],"topological":[131],"guarantees.":[132],"definition":[134],"and":[138,173],"extension":[140],"are":[141],"based":[142],"on":[143,167],"steepest":[145],"ascent":[146],"flow":[147],"map":[148],"results":[150],"distance":[153],"function":[154],"induced":[155],"by":[156],"point":[159],"set.":[160],"geometric":[165],"guarantee":[166],"closeness":[169],"actual":[175]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}