{"id":"https://openalex.org/W2142495952","doi":"https://doi.org/10.1007/b106657_6","title":"Stability and Computation of Medial Axes - a State-of-the-Art Report","display_name":"Stability and Computation of Medial Axes - a State-of-the-Art Report","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2142495952","doi":"https://doi.org/10.1007/b106657_6","mag":"2142495952"},"language":"en","primary_location":{"id":"doi:10.1007/b106657_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/b106657_6","pdf_url":null,"source":{"id":"https://openalex.org/S4210191043","display_name":"Mathematics and visualization","issn_l":"1612-3786","issn":["1612-3786","2197-666X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics and Visualization","raw_type":"book-chapter"},"type":"book-chapter","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/A5021546111","display_name":"Dominique Attali","orcid":null},"institutions":[{"id":"https://openalex.org/I4210146665","display_name":"Laboratoire Rh\u00e9ologie et Proc\u00e9d\u00e9s","ror":"https://ror.org/044ggyg50","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210095849","https://openalex.org/I4210146665","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Dominique Attali","raw_affiliation_strings":["Gipsa-lab, ENSE 3, Domaine Universitaire, BP 46, 38402, Saint Martin d\u2019H\u00e8res, France","Gipsa-lab, ENSE 3, Domaine Universitaire, BP 46, 38402, Saint Martin d'H\u00e8res, France"],"affiliations":[{"raw_affiliation_string":"Gipsa-lab, ENSE 3, Domaine Universitaire, BP 46, 38402, Saint Martin d\u2019H\u00e8res, France","institution_ids":["https://openalex.org/I4210146665"]},{"raw_affiliation_string":"Gipsa-lab, ENSE 3, Domaine Universitaire, BP 46, 38402, Saint Martin d'H\u00e8res, France","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105370783","display_name":"Jean\u2010Daniel Boissonnat","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Daniel Boissonnat","raw_affiliation_strings":["INRIA, 2004 Route des Lucioles, BP 93, 06904, Sophia-Antipolis, France"],"affiliations":[{"raw_affiliation_string":"INRIA, 2004 Route des Lucioles, BP 93, 06904, Sophia-Antipolis, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069999967","display_name":"Herbert Edelsbrunner","orcid":"https://orcid.org/0000-0002-9823-6833"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]},{"id":"https://openalex.org/I1309191912","display_name":"Research Triangle Park Foundation","ror":"https://ror.org/03eqttr49","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1309191912"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Herbert Edelsbrunner","raw_affiliation_strings":["Department of Computer Science, Duke University, Durham, and Raindrop Geomagic, Research Triangle Park, NC, USA","Department of Computer Science, Duke University, Raindrop Geomagic, Research Triangle Park, NC, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Duke University, Durham, and Raindrop Geomagic, Research Triangle Park, NC, USA","institution_ids":["https://openalex.org/I1309191912","https://openalex.org/I170897317"]},{"raw_affiliation_string":"Department of Computer Science, Duke University, Raindrop Geomagic, Research Triangle Park, NC, USA","institution_ids":["https://openalex.org/I1309191912"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021546111"],"corresponding_institution_ids":["https://openalex.org/I4210146665"],"apc_list":null,"apc_paid":null,"fwci":25.5047,"has_fulltext":false,"cited_by_count":182,"citation_normalized_percentile":{"value":0.99674267,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"109","last_page":"125"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9970999956130981,"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":0.9970999956130981,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9968000054359436,"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/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/medial-axis","display_name":"Medial axis","score":0.8288091421127319},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.7592009902000427},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7283252477645874},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.6930531859397888},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5112578868865967},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4690934419631958},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3565565049648285},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3138391971588135},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28875160217285156},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23417037725448608},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20760241150856018},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.11187976598739624},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.08875605463981628},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.06628769636154175}],"concepts":[{"id":"https://openalex.org/C185877587","wikidata":"https://www.wikidata.org/wiki/Q1757407","display_name":"Medial axis","level":2,"score":0.8288091421127319},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.7592009902000427},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7283252477645874},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.6930531859397888},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5112578868865967},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4690934419631958},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3565565049648285},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3138391971588135},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28875160217285156},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23417037725448608},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20760241150856018},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.11187976598739624},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.08875605463981628},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.06628769636154175}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/b106657_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/b106657_6","pdf_url":null,"source":{"id":"https://openalex.org/S4210191043","display_name":"Mathematics and visualization","issn_l":"1612-3786","issn":["1612-3786","2197-666X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics and Visualization","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W101508493","https://openalex.org/W200020044","https://openalex.org/W247104752","https://openalex.org/W399952771","https://openalex.org/W624249883","https://openalex.org/W1485732691","https://openalex.org/W1522983840","https://openalex.org/W1544041760","https://openalex.org/W1564419782","https://openalex.org/W1809711019","https://openalex.org/W1826313674","https://openalex.org/W1966159541","https://openalex.org/W1977289164","https://openalex.org/W2000874030","https://openalex.org/W2002053510","https://openalex.org/W2006063729","https://openalex.org/W2012689387","https://openalex.org/W2018168260","https://openalex.org/W2029041800","https://openalex.org/W2031953823","https://openalex.org/W2037162618","https://openalex.org/W2038124553","https://openalex.org/W2038517424","https://openalex.org/W2039081484","https://openalex.org/W2048712324","https://openalex.org/W2050232155","https://openalex.org/W2051200663","https://openalex.org/W2052292812","https://openalex.org/W2055884227","https://openalex.org/W2060487396","https://openalex.org/W2060942197","https://openalex.org/W2061036838","https://openalex.org/W2070308679","https://openalex.org/W2073751737","https://openalex.org/W2074080630","https://openalex.org/W2075694597","https://openalex.org/W2077976550","https://openalex.org/W2078290150","https://openalex.org/W2080053909","https://openalex.org/W2083198723","https://openalex.org/W2088352159","https://openalex.org/W2089906676","https://openalex.org/W2098077066","https://openalex.org/W2104907335","https://openalex.org/W2116044718","https://openalex.org/W2119339582","https://openalex.org/W2123577201","https://openalex.org/W2131081159","https://openalex.org/W2131141154","https://openalex.org/W2148542317","https://openalex.org/W2155067269","https://openalex.org/W2158008371","https://openalex.org/W2172431334","https://openalex.org/W2322951925","https://openalex.org/W2561675875","https://openalex.org/W2628270073","https://openalex.org/W2911001378","https://openalex.org/W3013843370","https://openalex.org/W3159914786","https://openalex.org/W4205944311","https://openalex.org/W4231619797","https://openalex.org/W4232052003","https://openalex.org/W4242811155","https://openalex.org/W4251327614","https://openalex.org/W4285719527","https://openalex.org/W6632549225","https://openalex.org/W6679470077","https://openalex.org/W6794937971","https://openalex.org/W6817088481","https://openalex.org/W7019154014"],"related_works":["https://openalex.org/W2051997380","https://openalex.org/W2541311741","https://openalex.org/W2269935213","https://openalex.org/W2057456086","https://openalex.org/W2568929922","https://openalex.org/W2065654035","https://openalex.org/W2013888270","https://openalex.org/W2011341522","https://openalex.org/W2014895678","https://openalex.org/W2046977193"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":14},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":13}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}