{"id":"https://openalex.org/W2149648981","doi":"https://doi.org/10.1142/s0218195908002647","title":"COMPUTING THE HAUSDORFF DISTANCE BETWEEN CURVED OBJECTS","display_name":"COMPUTING THE HAUSDORFF DISTANCE BETWEEN CURVED OBJECTS","publication_year":2008,"publication_date":"2008-08-01","ids":{"openalex":"https://openalex.org/W2149648981","doi":"https://doi.org/10.1142/s0218195908002647","mag":"2149648981"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195908002647","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195908002647","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 &amp; 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/A5109875077","display_name":"Helmut Alt","orcid":null},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"HELMUT ALT","raw_affiliation_strings":["Freie Universit\u00e4t Berlin, Fachbereich Mathematik und Informatik, Takustr. 9, 14195 Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Freie Universit\u00e4t Berlin, Fachbereich Mathematik und Informatik, Takustr. 9, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046352518","display_name":"Ludmila Scharf","orcid":null},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"LUDMILA SCHARF","raw_affiliation_strings":["Freie Universit\u00e4t Berlin, Fachbereich Mathematik und Informatik, Takustr. 9, 14195 Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Freie Universit\u00e4t Berlin, Fachbereich Mathematik und Informatik, Takustr. 9, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109875077"],"corresponding_institution_ids":["https://openalex.org/I75951250"],"apc_list":null,"apc_paid":null,"fwci":2.4843,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.90383461,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"18","issue":"04","first_page":"307","last_page":"320"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9991000294685364,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9980999827384949,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.996999979019165,"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/voronoi-diagram","display_name":"Voronoi diagram","score":0.8255659341812134},{"id":"https://openalex.org/keywords/weighted-voronoi-diagram","display_name":"Weighted Voronoi diagram","score":0.7364159822463989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7186869382858276},{"id":"https://openalex.org/keywords/hausdorff-distance","display_name":"Hausdorff distance","score":0.7160964608192444},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6024099588394165},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.5088586807250977},{"id":"https://openalex.org/keywords/hausdorff-measure","display_name":"Hausdorff measure","score":0.49322909116744995},{"id":"https://openalex.org/keywords/power-diagram","display_name":"Power diagram","score":0.4866388738155365},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.4862152636051178},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4408547580242157},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4354189932346344},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.41433292627334595},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2891242802143097},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.2400626540184021},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2094704806804657},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1807675063610077},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16861283779144287},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11400976777076721},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.08805599808692932}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.8255659341812134},{"id":"https://openalex.org/C20468658","wikidata":"https://www.wikidata.org/wiki/Q17130624","display_name":"Weighted Voronoi diagram","level":3,"score":0.7364159822463989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7186869382858276},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.7160964608192444},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6024099588394165},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.5088586807250977},{"id":"https://openalex.org/C73225184","wikidata":"https://www.wikidata.org/wiki/Q1591095","display_name":"Hausdorff measure","level":3,"score":0.49322909116744995},{"id":"https://openalex.org/C20573064","wikidata":"https://www.wikidata.org/wiki/Q13410436","display_name":"Power diagram","level":3,"score":0.4866388738155365},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.4862152636051178},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4408547580242157},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4354189932346344},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.41433292627334595},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2891242802143097},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.2400626540184021},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2094704806804657},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1807675063610077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16861283779144287},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11400976777076721},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.08805599808692932},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218195908002647","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195908002647","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 &amp; Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.206.600","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.206.600","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.inf.fu-berlin.de/inst/ag-ti/people/rote/Software/MWT/ipelets/precompiled-pre23-Windows/uploads/tx_tipublications/as-chdco-06.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1555471913","https://openalex.org/W2002564702","https://openalex.org/W2039810899","https://openalex.org/W2067220482","https://openalex.org/W2079757056","https://openalex.org/W2092475777","https://openalex.org/W2093531761","https://openalex.org/W2102698015","https://openalex.org/W2119339582","https://openalex.org/W2124472301","https://openalex.org/W2148542317","https://openalex.org/W2768974198","https://openalex.org/W4376464565"],"related_works":["https://openalex.org/W2392199123","https://openalex.org/W2356605454","https://openalex.org/W2385181459","https://openalex.org/W1974181811","https://openalex.org/W2181022034","https://openalex.org/W4302030212","https://openalex.org/W1481203752","https://openalex.org/W2155547400","https://openalex.org/W2160009442","https://openalex.org/W2149648981"],"abstract_inverted_index":{"The":[0],"Hausdorff":[1,32],"distance":[2,33],"between":[3],"two":[4],"sets":[5],"of":[6,14,39,43,58],"curves":[7,27,49,59],"is":[8,60],"a":[9],"measure":[10],"for":[11],"the":[12,26,31,36,40,44,48,51,55,72],"similarity":[13],"these":[15],"objects":[16],"and":[17,68,95],"therefore":[18],"an":[19],"interesting":[20],"feature":[21],"in":[22,50,80],"shape":[23],"recognition.":[24],"If":[25],"are":[28,93,99],"algebraic":[29,90],"computing":[30,35,54],"involves":[34],"intersection":[37],"points":[38,66,83],"Voronoi":[41,56],"edges":[42],"one":[45],"set":[46],"with":[47],"other.":[52],"Since":[53],"diagram":[57],"quite":[61],"difficult":[62],"we":[63],"characterize":[64],"those":[65],"algebraically":[67],"compute":[69],"them":[70],"using":[71],"computer":[73],"algebra":[74],"system":[75],"SYNAPS.":[76],"This":[77],"paper":[78],"describes":[79],"detail":[81],"which":[82],"have":[84],"to":[85],"be":[86],"considered,":[87],"by":[88],"what":[89],"equations":[91],"they":[92,97],"characterized,":[94],"how":[96],"actually":[98],"computed.":[100]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
