{"id":"https://openalex.org/W2170630345","doi":"https://doi.org/10.1109/tip.2009.2034693","title":"Squigraphs for Fine and Compact Modeling of 3-D Shapes","display_name":"Squigraphs for Fine and Compact Modeling of 3-D Shapes","publication_year":2009,"publication_date":"2009-10-16","ids":{"openalex":"https://openalex.org/W2170630345","doi":"https://doi.org/10.1109/tip.2009.2034693","mag":"2170630345","pmid":"https://pubmed.ncbi.nlm.nih.gov/19840911"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2009.2034693","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2009.2034693","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://orbilu.uni.lu/handle/10993/10589","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083368272","display_name":"Djamila Aouada","orcid":"https://orcid.org/0000-0002-7576-2064"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Djamila Aouada","raw_affiliation_strings":["Electrical and Computer Engineering Department,North Carolina State University, Raleigh, NC, 27695 USA. djamila.aouada@ieee.org","Electrical and Computer Engineering Department, North Carolina State University, Raleigh, NC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department,North Carolina State University, Raleigh, NC, 27695 USA. djamila.aouada@ieee.org","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"Electrical and Computer Engineering Department, North Carolina State University, Raleigh, NC, USA","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030154118","display_name":"Hamid Krim","orcid":"https://orcid.org/0000-0003-4971-1690"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hamid Krim","raw_affiliation_strings":["Electrical and Computer Engineering Department, North Carolina State University, Raleigh, NC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, North Carolina State University, Raleigh, NC, USA","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I137902535"],"apc_list":null,"apc_paid":null,"fwci":0.9389,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.77546754,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"19","issue":"2","first_page":"306","last_page":"321"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9993000030517578,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9932000041007996,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9878000020980835,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/morse-theory","display_name":"Morse theory","score":0.6586877107620239},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.632204532623291},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5393723249435425},{"id":"https://openalex.org/keywords/discriminative-model","display_name":"Discriminative model","score":0.5350488424301147},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5331878662109375},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5191856622695923},{"id":"https://openalex.org/keywords/geometric-shape","display_name":"Geometric shape","score":0.50022292137146},{"id":"https://openalex.org/keywords/shape-analysis","display_name":"Shape analysis (program analysis)","score":0.4735514223575592},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45363104343414307},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.41943731904029846},{"id":"https://openalex.org/keywords/geometric-primitive","display_name":"Geometric primitive","score":0.41577887535095215},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4124196767807007},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3947927951812744},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.39192628860473633},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2617484927177429},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22853630781173706},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15265923738479614}],"concepts":[{"id":"https://openalex.org/C156730297","wikidata":"https://www.wikidata.org/wiki/Q2296951","display_name":"Morse theory","level":2,"score":0.6586877107620239},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.632204532623291},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5393723249435425},{"id":"https://openalex.org/C97931131","wikidata":"https://www.wikidata.org/wiki/Q5282087","display_name":"Discriminative model","level":2,"score":0.5350488424301147},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5331878662109375},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5191856622695923},{"id":"https://openalex.org/C7305733","wikidata":"https://www.wikidata.org/wiki/Q207961","display_name":"Geometric shape","level":2,"score":0.50022292137146},{"id":"https://openalex.org/C112604564","wikidata":"https://www.wikidata.org/wiki/Q7489226","display_name":"Shape analysis (program analysis)","level":3,"score":0.4735514223575592},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45363104343414307},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.41943731904029846},{"id":"https://openalex.org/C181095308","wikidata":"https://www.wikidata.org/wiki/Q1541599","display_name":"Geometric primitive","level":2,"score":0.41577887535095215},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4124196767807007},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3947927951812744},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.39192628860473633},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2617484927177429},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22853630781173706},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15265923738479614},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C97686452","wikidata":"https://www.wikidata.org/wiki/Q7604153","display_name":"Static analysis","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2009.2034693","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2009.2034693","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Image Processing","raw_type":"journal-article"},{"id":"pmid:19840911","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/19840911","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 image processing : a publication of the IEEE Signal Processing Society","raw_type":null},{"id":"pmh:oai:orbilu.uni.lu:10993/10589","is_oa":true,"landing_page_url":"http://orbilu.uni.lu/handle/10993/10589","pdf_url":null,"source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Image Processing, 19, 306-321. IEEE (2010).","raw_type":null}],"best_oa_location":{"id":"pmh:oai:orbilu.uni.lu:10993/10589","is_oa":true,"landing_page_url":"http://orbilu.uni.lu/handle/10993/10589","pdf_url":null,"source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Image Processing, 19, 306-321. IEEE (2010).","raw_type":null},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.7400000095367432,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1486218565","https://openalex.org/W1543220894","https://openalex.org/W1590776313","https://openalex.org/W1602929451","https://openalex.org/W1995875735","https://openalex.org/W2005168270","https://openalex.org/W2005276292","https://openalex.org/W2007626594","https://openalex.org/W2023056405","https://openalex.org/W2025320551","https://openalex.org/W2061196326","https://openalex.org/W2088661553","https://openalex.org/W2089982566","https://openalex.org/W2090265155","https://openalex.org/W2093399550","https://openalex.org/W2099789128","https://openalex.org/W2102872744","https://openalex.org/W2104733593","https://openalex.org/W2110340327","https://openalex.org/W2112494174","https://openalex.org/W2118111890","https://openalex.org/W2122563626","https://openalex.org/W2124676244","https://openalex.org/W2133740040","https://openalex.org/W2137733660","https://openalex.org/W2138697915","https://openalex.org/W2146950091","https://openalex.org/W2156406284","https://openalex.org/W2158042553","https://openalex.org/W2164764562","https://openalex.org/W2165939338","https://openalex.org/W2172124895","https://openalex.org/W2295332248","https://openalex.org/W2914679068","https://openalex.org/W3099773806","https://openalex.org/W4205343085","https://openalex.org/W4213199372","https://openalex.org/W4234899042","https://openalex.org/W4235840289","https://openalex.org/W6629067189","https://openalex.org/W6656768927","https://openalex.org/W6675817216","https://openalex.org/W6680362723","https://openalex.org/W6684222857"],"related_works":["https://openalex.org/W2019779994","https://openalex.org/W2108807403","https://openalex.org/W3047674135","https://openalex.org/W2026545685","https://openalex.org/W2083793713","https://openalex.org/W1996895845","https://openalex.org/W2241205601","https://openalex.org/W2168632526","https://openalex.org/W3022249135","https://openalex.org/W2101115717"],"abstract_inverted_index":{"We":[0,113,145],"propose":[1],"to":[2,14,75,83,181,200],"superpose":[3],"global":[4,89],"topological":[5,110,174],"and":[6,18,47,87,157,166,175,216],"local":[7],"geometric":[8,131,176],"3-D":[9,23,30,98],"shape":[10,31,205],"descriptors":[11],"in":[12,63,173],"order":[13,236],"define":[15],"one":[16,165],"compact":[17],"discriminative":[19],"representation":[20,74,106],"for":[21,44,116],"a":[22,26,42,45,64,85,97,104,108,117,159,231],"object.":[24,99],"While":[25],"number":[27],"of":[28,50,71,96,120,137,150,234,237],"available":[29],"modeling":[32],"techniques":[33,224],"yield":[34],"satisfactory":[35],"object":[36],"classification":[37,198,215],"rates,":[38],"there":[39],"is":[40,103],"still":[41],"need":[43],"refined":[46],"efficient":[48],"identification/recognition":[49],"objects":[51],"among":[52],"the":[53,69,72,80,94,125,135,148,235],"same":[54],"class.":[55],"In":[56],"this":[57],"paper,":[58],"we":[59,78,128,168,179],"use":[60,114],"Morse":[61,81,138],"theory":[62],"two-phase":[65],"approach.":[66],"To":[67],"ensure":[68],"invariance":[70],"final":[73],"isometric":[76],"transforms,":[77],"choose":[79],"function":[82,91],"be":[84],"simple":[86],"intrinsic":[88],"geodesic":[90],"defined":[92],"on":[93],"surface":[95],"The":[100],"first":[101],"phase":[102,164],"coarse":[105],"through":[107],"reduced":[109],"Reeb":[111],"graph.":[112],"it":[115],"meaningful":[118],"decomposition":[119],"shapes":[121],"into":[122,153],"primitives.":[123],"During":[124],"second":[126],"phase,":[127],"add":[129],"detailed":[130],"information":[132,177],"by":[133,203],"tracking":[134],"evolution":[136],"function's":[139],"level":[140],"curves":[141,152],"along":[142],"each":[143],"primitive.":[144],"then":[146],"embed":[147],"manifold":[149],"these":[151],"[Formula:":[154],"see":[155,225],"text],":[156],"obtain":[158],"single":[160],"curve.":[161],"By":[162],"combining":[163],"two,":[167],"build":[169],"new":[170],"graphs":[171],"rich":[172],"that":[178,187],"refer":[180],"as":[182],"squigraphs.":[183],"Our":[184],"experiments":[185],"show":[186],"squigraphs":[188,229],"are":[189,219],"more":[190],"general":[191],"than":[192],"existing":[193],"techniques.":[194],"They":[195],"achieve":[196],"similar":[197],"rates":[199],"those":[201],"achieved":[202],"classical":[204],"descriptors.":[206],"Their":[207],"performance,":[208],"however,":[209],"becomes":[210],"clearly":[211],"superior":[212],"when":[213],"finer":[214],"identification":[217],"operations":[218],"targeted.":[220],"Indeed,":[221],"while":[222],"other":[223],"their":[226],"performances":[227],"dropping,":[228],"maintain":[230],"performance":[232],"rate":[233],"97%.":[238]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}