{"id":"https://openalex.org/W1980278852","doi":"https://doi.org/10.1145/1137856.1137905","title":"Medial axis approximation and unstable flow complex","display_name":"Medial axis approximation and unstable flow complex","publication_year":2006,"publication_date":"2006-06-05","ids":{"openalex":"https://openalex.org/W1980278852","doi":"https://doi.org/10.1145/1137856.1137905","mag":"1980278852"},"language":"en","primary_location":{"id":"doi:10.1145/1137856.1137905","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1137856.1137905","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-second annual symposium on Computational geometry","raw_type":"proceedings-article"},"type":"conference-paper","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/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Joachim Giesen","raw_affiliation_strings":["Theoretische Informatik ETH Z\u00fcrich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Theoretische Informatik ETH Z\u00fcrich","institution_ids":["https://openalex.org/I35440088"]}]},{"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/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I2801919071","display_name":"University of Illinois System","ror":"https://ror.org/05e94g991","country_code":"US","type":"education","lineage":["https://openalex.org/I2801919071"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edgar A. Ramos","raw_affiliation_strings":["University of Illinois, Urbana, IL","[University of Illinois, Urbana, IL]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois, Urbana, IL","institution_ids":["https://openalex.org/I2801919071"]},{"raw_affiliation_string":"[University of Illinois, Urbana, IL]","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053664140","display_name":"Bardia Sadri","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I2801919071","display_name":"University of Illinois System","ror":"https://ror.org/05e94g991","country_code":"US","type":"education","lineage":["https://openalex.org/I2801919071"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bardia Sadri","raw_affiliation_strings":["University of Illinois, Urbana, IL","[University of Illinois, Urbana, IL]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois, Urbana, IL","institution_ids":["https://openalex.org/I2801919071"]},{"raw_affiliation_string":"[University of Illinois, Urbana, IL]","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"327","last_page":"336"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9980000257492065,"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":0.9980000257492065,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9973999857902527,"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":0.9821000099182129,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/medial-axis","display_name":"Medial axis","score":0.9227407574653625},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.6175916790962219},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5743786692619324},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5731390714645386},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.5219337940216064},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.512054979801178},{"id":"https://openalex.org/keywords/closeness","display_name":"Closeness","score":0.4868473410606384},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.46359673142433167},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.43797773122787476},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4233367443084717},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3703957498073578},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.33761656284332275},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3297663927078247},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22774463891983032},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22472119331359863}],"concepts":[{"id":"https://openalex.org/C185877587","wikidata":"https://www.wikidata.org/wiki/Q1757407","display_name":"Medial axis","level":2,"score":0.9227407574653625},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.6175916790962219},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5743786692619324},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5731390714645386},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.5219337940216064},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.512054979801178},{"id":"https://openalex.org/C2779545769","wikidata":"https://www.wikidata.org/wiki/Q5135364","display_name":"Closeness","level":2,"score":0.4868473410606384},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.46359673142433167},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.43797773122787476},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4233367443084717},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3703957498073578},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.33761656284332275},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3297663927078247},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22774463891983032},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22472119331359863},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1137856.1137905","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1137856.1137905","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-second annual symposium on Computational geometry","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.614.5729","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.614.5729","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/~sadri/publications/medial.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.87.4478","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.4478","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.inf.ethz.ch/personal/giesen/pub/socg06.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.4099999964237213,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1977276706","https://openalex.org/W1992446047","https://openalex.org/W2002053510","https://openalex.org/W2016252883","https://openalex.org/W2029041800","https://openalex.org/W2039081484","https://openalex.org/W2082135154","https://openalex.org/W2088352159","https://openalex.org/W2115920764","https://openalex.org/W2207289595","https://openalex.org/W2612714875","https://openalex.org/W2907088218","https://openalex.org/W2911001378","https://openalex.org/W3040586665","https://openalex.org/W3139497334","https://openalex.org/W4247080677","https://openalex.org/W6648535386","https://openalex.org/W6780011183"],"related_works":["https://openalex.org/W2156910174","https://openalex.org/W1995054232","https://openalex.org/W2011510925","https://openalex.org/W1557920161","https://openalex.org/W1556709767","https://openalex.org/W2907088218","https://openalex.org/W1993023208","https://openalex.org/W2039081484","https://openalex.org/W2083732234","https://openalex.org/W4231619797"],"abstract_inverted_index":{"The":[0,117],"medial":[1,38,71,88,156],"axis":[2,72,89],"of":[3,12,21,29,60,76,86,90,119,150],"a":[4,10,18,49,61,67,77,96,144],"shape":[5,62],"is":[6],"known":[7],"to":[8,99,106,138],"carry":[9],"lot":[11],"information":[13],"about":[14],"it.":[15],"In":[16,40],"particular":[17],"recent":[19],"result":[20],"Lieutier":[22],"establishes":[23],"that":[24,82],"every":[25],"bounded":[26],"open":[27],"subset":[28],"Rn":[30],"has":[31],"the":[32,58,84,87,91,111,120,129,135,139,148,151,154],"same":[33],"homotopy":[34],"type":[35],"as":[36],"its":[37,70,114,123],"axis.":[39,157],"this":[41,102],"paper":[42],"we":[43],"provide":[44,95,143],"an":[45],"algorithm":[46],"that,":[47],"given":[48],"sufficiently":[50],"dense":[51],"but":[52],"not":[53],"necessarily":[54],"uniform":[55],"sample":[56],"from":[57],"surface":[59],"with":[63],"smooth":[64],"boundary,":[65],"computes":[66],"core":[68,103,121,152],"for":[69],"approximation,":[73],"in":[74,104],"form":[75],"piecewise":[78],"linear":[79],"cell":[80],"complex,":[81],"captures":[83],"topology":[85],"shape.":[92],"We":[93,141],"also":[94,142],"natural":[97],"method":[98,125],"freely":[100],"augment":[101],"order":[105],"enhance":[107],"it":[108],"geometrically":[109],"all":[110],"while":[112],"maintaining":[113],"topological":[115],"guarantees.":[116],"definition":[118],"and":[122,153],"extension":[124],"are":[126],"based":[127],"on":[128,147],"steepest":[130],"ascent":[131],"flow":[132],"induced":[133],"by":[134],"distance":[136],"function":[137],"sample.":[140],"geometric":[145],"guarantee":[146],"closeness":[149],"actual":[155]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
