{"id":"https://openalex.org/W2126199001","doi":"https://doi.org/10.1109/smi.2009.5170145","title":"Canonical homotopy class representative using hyperbolic structure","display_name":"Canonical homotopy class representative using hyperbolic structure","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2126199001","doi":"https://doi.org/10.1109/smi.2009.5170145","mag":"2126199001"},"language":"en","primary_location":{"id":"doi:10.1109/smi.2009.5170145","is_oa":false,"landing_page_url":"https://doi.org/10.1109/smi.2009.5170145","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Conference on Shape Modeling and Applications","raw_type":"proceedings-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/A5100660204","display_name":"Wei Zeng","orcid":"https://orcid.org/0000-0002-3351-6973"},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wei Zeng","raw_affiliation_strings":["Department of Computer Science, Stony Brook University, Stony Brook, NY, USA","Dept. of Computer Science, Stony Brook University, NY 11794, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Stony Brook University, Stony Brook, NY, USA","institution_ids":["https://openalex.org/I59553526"]},{"raw_affiliation_string":"Dept. of Computer Science, Stony Brook University, NY 11794, USA","institution_ids":["https://openalex.org/I59553526"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100675221","display_name":"Miao Jin","orcid":"https://orcid.org/0000-0002-0054-4281"},"institutions":[{"id":"https://openalex.org/I79516672","display_name":"University of Louisiana at Lafayette","ror":"https://ror.org/01x8rc503","country_code":"US","type":"education","lineage":["https://openalex.org/I2799628689","https://openalex.org/I79516672"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Miao Jin","raw_affiliation_strings":["Center for Advanced Computer Studies, University of Louisiana, Lafayette, Lafayette, LA, USA","Center for Advanced Computer Studies, University of Louisiana at Lafayette, 70504, USA"],"affiliations":[{"raw_affiliation_string":"Center for Advanced Computer Studies, University of Louisiana, Lafayette, Lafayette, LA, USA","institution_ids":["https://openalex.org/I79516672"]},{"raw_affiliation_string":"Center for Advanced Computer Studies, University of Louisiana at Lafayette, 70504, USA","institution_ids":["https://openalex.org/I79516672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100683461","display_name":"Feng Luo","orcid":"https://orcid.org/0000-0001-5551-7128"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Feng Luo","raw_affiliation_strings":["Department of Mathematics, Rutgers University, Piscataway, NJ, USA","Dept. of Mathematics, Rutgers University, Piscataway, NJ 08854, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Rutgers University, Piscataway, NJ, USA","institution_ids":["https://openalex.org/I102322142"]},{"raw_affiliation_string":"Dept. of Mathematics, Rutgers University, Piscataway, NJ 08854, USA","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100607707","display_name":"Xianfeng Gu","orcid":"https://orcid.org/0000-0001-8226-5851"},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xianfeng David Gu","raw_affiliation_strings":["Department of Computer Science, Stony Brook University, Stony Brook, NY, USA","Dept. of Computer Science, Stony Brook University, NY 11794, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Stony Brook University, Stony Brook, NY, USA","institution_ids":["https://openalex.org/I59553526"]},{"raw_affiliation_string":"Dept. of Computer Science, Stony Brook University, NY 11794, USA","institution_ids":["https://openalex.org/I59553526"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100660204"],"corresponding_institution_ids":["https://openalex.org/I59553526"],"apc_list":null,"apc_paid":null,"fwci":4.4562,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.94958152,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"171","last_page":"178"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994000196456909,"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":0.9994000196456909,"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9728999733924866,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9585999846458435,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7982082962989807},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.7413448095321655},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.6193332076072693},{"id":"https://openalex.org/keywords/n-connected","display_name":"n-connected","score":0.6152273416519165},{"id":"https://openalex.org/keywords/regular-homotopy","display_name":"Regular homotopy","score":0.6096521615982056},{"id":"https://openalex.org/keywords/homotopy-lifting-property","display_name":"Homotopy lifting property","score":0.5085345506668091},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5057370662689209},{"id":"https://openalex.org/keywords/homotopy-sphere","display_name":"Homotopy sphere","score":0.45764535665512085},{"id":"https://openalex.org/keywords/constant-curvature","display_name":"Constant curvature","score":0.4414879381656647},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.390722393989563},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.376992404460907},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3591182827949524},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1658252775669098},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08700010180473328}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7982082962989807},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.7413448095321655},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6193332076072693},{"id":"https://openalex.org/C191752858","wikidata":"https://www.wikidata.org/wiki/Q6358325","display_name":"n-connected","level":3,"score":0.6152273416519165},{"id":"https://openalex.org/C168334404","wikidata":"https://www.wikidata.org/wiki/Q7309601","display_name":"Regular homotopy","level":4,"score":0.6096521615982056},{"id":"https://openalex.org/C35234519","wikidata":"https://www.wikidata.org/wiki/Q3983973","display_name":"Homotopy lifting property","level":4,"score":0.5085345506668091},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5057370662689209},{"id":"https://openalex.org/C18003601","wikidata":"https://www.wikidata.org/wiki/Q5891833","display_name":"Homotopy sphere","level":4,"score":0.45764535665512085},{"id":"https://openalex.org/C2779668893","wikidata":"https://www.wikidata.org/wiki/Q2250422","display_name":"Constant curvature","level":3,"score":0.4414879381656647},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.390722393989563},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.376992404460907},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3591182827949524},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1658252775669098},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08700010180473328}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/smi.2009.5170145","is_oa":false,"landing_page_url":"https://doi.org/10.1109/smi.2009.5170145","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Conference on Shape Modeling and Applications","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W181601562","https://openalex.org/W561652724","https://openalex.org/W1496383623","https://openalex.org/W1530161281","https://openalex.org/W1535869571","https://openalex.org/W1968751837","https://openalex.org/W1990120195","https://openalex.org/W1996445144","https://openalex.org/W2000504285","https://openalex.org/W2005356779","https://openalex.org/W2006248644","https://openalex.org/W2007578533","https://openalex.org/W2065838536","https://openalex.org/W2093766264","https://openalex.org/W2094163096","https://openalex.org/W2099151424","https://openalex.org/W2100607348","https://openalex.org/W2104095591","https://openalex.org/W2108082108","https://openalex.org/W2118125272","https://openalex.org/W2125351893","https://openalex.org/W2136126748","https://openalex.org/W2143075606","https://openalex.org/W2151552710","https://openalex.org/W2486762503","https://openalex.org/W4252778798","https://openalex.org/W4253512733","https://openalex.org/W6673964125","https://openalex.org/W6674187824","https://openalex.org/W6675213996","https://openalex.org/W6678514030"],"related_works":["https://openalex.org/W121514703","https://openalex.org/W1966906304","https://openalex.org/W4288482056","https://openalex.org/W4394656522","https://openalex.org/W2952105607","https://openalex.org/W2919432047","https://openalex.org/W1511021991","https://openalex.org/W1522115346","https://openalex.org/W1986843420","https://openalex.org/W2033792851"],"abstract_inverted_index":{"Homotopy":[0],"group":[1,140],"plays":[2],"a":[3,9,23,27,59,66,87,102,150],"role":[4],"in":[5,35,203],"computational":[6,33,36],"topology":[7],"with":[8,105],"fundamental":[10],"importance.":[11],"Each":[12],"homotopy":[13,28,41,71,84,172,183,220,227],"equivalence":[14],"class":[15,29,85,173,184,221],"contains":[16],"an":[17],"infinite":[18],"number":[19],"of":[20,142,174,188,215],"loops.":[21],"Finding":[22],"canonical":[24,47,195],"representative":[25,48,68,222],"within":[26],"will":[30],"simplify":[31],"many":[32],"tasks":[34],"topology,":[37],"such":[38,81],"as":[39,52],"loop":[40,152],"detection,":[42],"pants":[43],"decomposition.":[44],"Furthermore,":[45],"the":[46,53,93,98,117,132,138,143,146,154,160,166,171,175,182,186,189,194,211,216],"can":[49,223],"be":[50,224],"used":[51],"shape":[54,230],"descriptor.":[55],"This":[56],"work":[57],"introduces":[58],"rigorous":[60],"and":[61,128,198,213,229],"practical":[62],"method":[63],"to":[64,77,115,131,159,164,170,209],"compute":[65,116,137],"unique":[67,88,118,178,219],"for":[69,101,226],"each":[70,83],"class.":[72],"The":[73,95,177,218],"main":[74],"strategy":[75],"is":[76,92,97,129,185,193],"use":[78],"hyperbolic":[79,111,147],"structure,":[80],"that":[82],"has":[86,122],"closed":[89,179],"geodesic,":[90],"which":[91,121,192],"representative.":[94,196],"following":[96],"algorithm":[99],"pipeline:":[100],"given":[103,151],"surface":[104,144],"negative":[106,124],"Euler":[107],"number,":[108],"we":[109,136,156],"apply":[110],"Yamabe":[112],"curvature":[113,126],"flow":[114],"Riemannian":[119],"metric,":[120],"constant":[123],"one":[125],"everywhere":[127],"conformal":[130],"original":[133],"metric.":[134],"Then":[135],"Fuchsian":[139,167,190],"generators":[141],"on":[145,153],"space.":[148],"For":[149],"surface,":[155],"lift":[157],"it":[158],"universal":[161],"covering":[162],"space,":[163],"obtain":[165],"transformation":[168],"corresponding":[169],"loop.":[176],"geodesic":[180],"inside":[181],"axis":[187],"transformation,":[191],"Theories":[197],"algorithms":[199],"are":[200,207],"explained":[201],"thoroughly":[202],"details.":[204],"Experimental":[205],"results":[206],"reported":[208],"show":[210],"efficiency":[212],"efficacy":[214],"algorithm.":[217],"applied":[225],"detection":[228],"comparison.":[231]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}