{"id":"https://openalex.org/W2172431334","doi":"https://doi.org/10.1109/tpami.2004.1262192","title":"A formal classification of 3d medial axis points and their local geometry","display_name":"A formal classification of 3d medial axis points and their local geometry","publication_year":2004,"publication_date":"2004-02-01","ids":{"openalex":"https://openalex.org/W2172431334","doi":"https://doi.org/10.1109/tpami.2004.1262192","mag":"2172431334","pmid":"https://pubmed.ncbi.nlm.nih.gov/15376898"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2004.1262192","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2004.1262192","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5110011211","display_name":"P. J. Giblin","orcid":null},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"P. Giblin","raw_affiliation_strings":["Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 3BX, UK. pjgiblin@liv.ac.uk","Department of Mathematical Sciences, University of Liverpool, Liverpool, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 3BX, UK. pjgiblin@liv.ac.uk","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"Department of Mathematical Sciences, University of Liverpool, Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083461641","display_name":"Benjamin B. Kimia","orcid":null},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B.B. Kimia","raw_affiliation_strings":["Division of Engineering, Brown University, Providence, RI, USA"],"affiliations":[{"raw_affiliation_string":"Division of Engineering, Brown University, Providence, RI, USA","institution_ids":["https://openalex.org/I27804330"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110011211"],"corresponding_institution_ids":["https://openalex.org/I146655781"],"apc_list":null,"apc_paid":null,"fwci":10.1121,"has_fulltext":false,"cited_by_count":154,"citation_normalized_percentile":{"value":0.98559302,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"26","issue":"2","first_page":"238","last_page":"251"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9986000061035156,"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":0.9986000061035156,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9979000091552734,"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":0.9976000189781189,"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":0.8492396473884583},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.6044235229492188},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.5933632850646973},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5346006751060486},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4866374433040619},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.4367287755012512},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3832690715789795},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3330618143081665}],"concepts":[{"id":"https://openalex.org/C185877587","wikidata":"https://www.wikidata.org/wiki/Q1757407","display_name":"Medial axis","level":2,"score":0.8492396473884583},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.6044235229492188},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.5933632850646973},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5346006751060486},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4866374433040619},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.4367287755012512},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3832690715789795},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3330618143081665}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003196","descriptor_name":"Computer Graphics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003196","descriptor_name":"Computer Graphics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003196","descriptor_name":"Computer Graphics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D009716","descriptor_name":"Numerical Analysis, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009716","descriptor_name":"Numerical Analysis, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009716","descriptor_name":"Numerical Analysis, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D013382","descriptor_name":"Subtraction Technique","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013382","descriptor_name":"Subtraction Technique","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013382","descriptor_name":"Subtraction Technique","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D014584","descriptor_name":"User-Computer Interface","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D014584","descriptor_name":"User-Computer Interface","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D014584","descriptor_name":"User-Computer Interface","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016247","descriptor_name":"Information Storage and Retrieval","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D016247","descriptor_name":"Information Storage and Retrieval","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D016247","descriptor_name":"Information Storage and Retrieval","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D021621","descriptor_name":"Imaging, Three-Dimensional","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D021621","descriptor_name":"Imaging, Three-Dimensional","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D021621","descriptor_name":"Imaging, Three-Dimensional","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2004.1262192","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2004.1262192","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:15376898","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/15376898","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309070","display_name":"Brown University","ror":"https://ror.org/05gq02987"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W96629785","https://openalex.org/W123892526","https://openalex.org/W161498023","https://openalex.org/W1481521171","https://openalex.org/W1490482062","https://openalex.org/W1497235707","https://openalex.org/W1508115086","https://openalex.org/W1509527377","https://openalex.org/W1879165993","https://openalex.org/W1966159541","https://openalex.org/W1972131978","https://openalex.org/W1976748909","https://openalex.org/W1997276658","https://openalex.org/W2012689387","https://openalex.org/W2017115857","https://openalex.org/W2038517424","https://openalex.org/W2048663205","https://openalex.org/W2051842524","https://openalex.org/W2059923669","https://openalex.org/W2062264317","https://openalex.org/W2071657752","https://openalex.org/W2077246452","https://openalex.org/W2088114053","https://openalex.org/W2088352159","https://openalex.org/W2091392134","https://openalex.org/W2091804476","https://openalex.org/W2092924973","https://openalex.org/W2093793201","https://openalex.org/W2107284490","https://openalex.org/W2108611942","https://openalex.org/W2114766304","https://openalex.org/W2124442589","https://openalex.org/W2124472301","https://openalex.org/W2131081159","https://openalex.org/W2140598250","https://openalex.org/W2149659501","https://openalex.org/W2158008371","https://openalex.org/W2164586495","https://openalex.org/W2173138314","https://openalex.org/W2222219094","https://openalex.org/W2336918561","https://openalex.org/W2998589874","https://openalex.org/W3015303229","https://openalex.org/W3020864241","https://openalex.org/W4238332724","https://openalex.org/W4239339957","https://openalex.org/W4239377895","https://openalex.org/W4241992233","https://openalex.org/W4246482510","https://openalex.org/W4256625838"],"related_works":["https://openalex.org/W2740851372","https://openalex.org/W2031580038","https://openalex.org/W4251096081","https://openalex.org/W1966159541","https://openalex.org/W2165852999","https://openalex.org/W2145260926","https://openalex.org/W2154461127","https://openalex.org/W598462635","https://openalex.org/W2345773879","https://openalex.org/W4298297247"],"abstract_inverted_index":{"This":[0,237],"paper":[1],"proposes":[2],"a":[3,13,206,242,304,310],"novel":[4],"hypergraph":[5,254,316],"skeletal":[6,27],"representation":[7,244,255],"for":[8,245,334],"3D":[9,166,246,327],"shape":[10,328],"based":[11],"on":[12,181,189],"formal":[14,238],"derivation":[15],"of":[16,20,32,42,45,65,79,82,91,97,103,105,113,119,121,139,143,150,164,171,178,201,257,266,276,282,296,343],"the":[17,38,63,80,87,94,101,111,117,126,165,190,251,283,319,331],"generic":[18],"structure":[19],"its":[21,30,335],"medial":[22,39,167,252,314],"axis.":[23],"By":[24],"classifying":[25],"each":[26],"point":[28],"by":[29,175,288],"order":[31,132,159],"contact,":[33,83],"we":[34],"show":[35],"that,":[36],"generically,":[37],"axis":[40,168,253,315],"consists":[41,170],"five":[43],"types":[44,90,138],"points,":[46,140],"which":[47,61,115,185,204],"are":[48,62,116],"then":[49],"organized":[50],"into":[51],"sheets,":[52,114],"curves,":[53,92],"and":[54,100,109,136,147,156,192,260,269,272,329,341],"points:":[55],"1)":[56],"sheets":[57,99,172,197],"(manifolds":[58],"with":[59,68,152,318],"boundary)":[60],"locus":[64,102,118],"bitangent":[66],"spheres":[67,122,151],"regular":[69,154],"tangency":[70,155],"A1(2)":[71],"(Ak(n)":[72],"notation":[73],"means":[74],"n":[75],"distinct":[76],"k-fold":[77],"tangencies":[78],"sphere":[81],"as":[84,250],"explained":[85],"in":[86,216,231,298,337],"text);":[88],"two":[89,137,195],"2)":[93],"intersection":[95],"curve":[96,179,202],"three":[98],"centers":[104,120,142,149],"tritangent":[106],"spheres,":[107,145],"A1(3),":[108],"3)":[110],"boundary":[112],"whose":[123],"radius":[124,320],"equals":[125],"larger":[127],"principal":[128],"curvature,":[129],"i.e.,":[130],"higher":[131,158],"contact":[133],"A3":[134,211,270],"points;":[135],"4)":[141],"quad-tangent":[144],"A1(4),":[146],"5)":[148],"one":[153,157,176],"tangency,":[160],"A1A3.":[161],"The":[162,210,226,280],"geometry":[163,285],"thus":[169],"(A1(2))":[173],"bounded":[174],"type":[177,200],"(A3)":[180],"their":[182],"free":[183],"end,":[184],"corresponds":[186],"to":[187,194,241,249,292,300,308],"ridges":[188],"surface,":[191],"attached":[193],"other":[196],"at":[198,233,286],"another":[199],"(A1(3)),":[203],"support":[205],"generalized":[207],"cylinder":[208],"description.":[209],"curves":[212,228],"can":[213],"only":[214],"end":[215],"A1A3":[217,261],"points":[218],"where":[219],"they":[220],"must":[221],"meet":[222,229],"an":[223,234],"A1(3)":[224,227],"curve.":[225],"together":[230,317],"fours":[232],"A1(4)":[235],"point.":[236],"result":[239],"leads":[240],"compact":[243],"shape,":[247],"referred":[248],"consisting":[256],"nodes":[258,267,287],"(A1(4)":[259],"points),":[262],"links":[263,277],"between":[264,274],"pairs":[265],"(A1(3)":[268],"curves)":[271],"hyperlinks":[273],"groups":[275],"(A1(2)":[278],"sheets).":[279],"description":[281],"local":[284],"itself":[289],"is":[290],"sufficient":[291],"capture":[293],"qualitative":[294],"aspects":[295],"shapes,":[297],"analogy":[299],"2D.":[301],"We":[302],"derive":[303],"pointwise":[305],"reconstruction":[306],"formula":[307],"reconstruct":[309],"surface":[311],"from":[312],"this":[313,323],"function.":[321],"Thus,":[322],"information":[324],"completely":[325],"characterizes":[326],"lays":[330],"theoretical":[332],"foundation":[333],"use":[336],"recognition,":[338],"morphing,":[339],"design,":[340],"manipulation":[342],"shapes.":[344]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":8}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}
