{"id":"https://openalex.org/W4386562941","doi":"https://doi.org/10.1137/22m1528756","title":"Convergence Analysis of Volumetric Stretch Energy Minimization and Its Associated Optimal Mass Transport","display_name":"Convergence Analysis of Volumetric Stretch Energy Minimization and Its Associated Optimal Mass Transport","publication_year":2023,"publication_date":"2023-09-08","ids":{"openalex":"https://openalex.org/W4386562941","doi":"https://doi.org/10.1137/22m1528756"},"language":"en","primary_location":{"id":"doi:10.1137/22m1528756","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1528756","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","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/A5034443841","display_name":"Tsung\u2010Ming Huang","orcid":"https://orcid.org/0000-0002-2505-2750"},"institutions":[{"id":"https://openalex.org/I134161618","display_name":"National Taiwan Normal University","ror":"https://ror.org/059dkdx38","country_code":"TW","type":"education","lineage":["https://openalex.org/I134161618"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Tsung-Ming Huang","raw_affiliation_strings":["Department of Mathematics, National Taiwan Normal University, Taipei, 116, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-2505-2750","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Taiwan Normal University, Taipei, 116, Taiwan","institution_ids":["https://openalex.org/I134161618"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002531402","display_name":"Wei-Hung Liao","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wei-Hung Liao","raw_affiliation_strings":["Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu, 300, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu, 300, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101337552","display_name":"Wen\u2010Wei Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wen-Wei Lin","raw_affiliation_strings":["Nanjing Center for Applied Mathematics, Nanjing 211135, People\u2019s Republic of China; Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nanjing Center for Applied Mathematics, Nanjing 211135, People\u2019s Republic of China; Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060158081","display_name":"Mei-Heng Yueh","orcid":"https://orcid.org/0000-0002-6873-5818"},"institutions":[{"id":"https://openalex.org/I134161618","display_name":"National Taiwan Normal University","ror":"https://ror.org/059dkdx38","country_code":"TW","type":"education","lineage":["https://openalex.org/I134161618"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Mei-Heng Yueh","raw_affiliation_strings":["Department of Mathematics, National Taiwan Normal University, Taipei, 116, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-6873-5818","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Taiwan Normal University, Taipei, 116, Taiwan","institution_ids":["https://openalex.org/I134161618"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006865040","display_name":"Shing\u2013Tung Yau","orcid":"https://orcid.org/0000-0003-3394-2187"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shing-Tung Yau","raw_affiliation_strings":["Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5508,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.59351275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"16","issue":"3","first_page":"1825","last_page":"1855"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9951000213623047,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9922999739646912,"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/computation","display_name":"Computation","score":0.6605983972549438},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6236228942871094},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.551055908203125},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5503451824188232},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.459126353263855},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.43982934951782227},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4370110332965851},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4275197386741638},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4269979000091553},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41417279839515686},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.4112565517425537},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13550755381584167}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6605983972549438},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6236228942871094},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.551055908203125},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5503451824188232},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.459126353263855},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.43982934951782227},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4370110332965851},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4275197386741638},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4269979000091553},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41417279839515686},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.4112565517425537},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13550755381584167},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1528756","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1528756","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7900000214576721,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320311041","display_name":"National Center for Theoretical Sciences","ror":"https://ror.org/02mfp0b67"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1621614599","https://openalex.org/W1753775462","https://openalex.org/W1906168790","https://openalex.org/W2018393413","https://openalex.org/W2021101386","https://openalex.org/W2052424080","https://openalex.org/W2052643735","https://openalex.org/W2068834636","https://openalex.org/W2094100343","https://openalex.org/W2100556411","https://openalex.org/W2143668817","https://openalex.org/W2180038452","https://openalex.org/W2434575306","https://openalex.org/W2465272462","https://openalex.org/W2735418187","https://openalex.org/W2751069891","https://openalex.org/W2953308089","https://openalex.org/W2962700762","https://openalex.org/W2962929605","https://openalex.org/W2963875852","https://openalex.org/W3008375286","https://openalex.org/W3048558702","https://openalex.org/W3181896412","https://openalex.org/W3186590563","https://openalex.org/W3187922971","https://openalex.org/W4224321202","https://openalex.org/W4246041266"],"related_works":["https://openalex.org/W2390829436","https://openalex.org/W1989791859","https://openalex.org/W2565094479","https://openalex.org/W602859758","https://openalex.org/W2006439817","https://openalex.org/W1971289376","https://openalex.org/W2379101322","https://openalex.org/W1992553864","https://openalex.org/W2776207444","https://openalex.org/W4231775656"],"abstract_inverted_index":{"Volumetric":[0],"stretch":[1,37,65],"energy":[2,38,66,95],"has":[3],"been":[4],"widely":[5],"applied":[6],"to":[7,41,52,79,85,158],"the":[8,71,91,94,103,106,117,127,130,148,160,177,180,185],"computation":[9,128],"of":[10,13,55,74,96,105,129,141,179,187],"volume-/mass-preserving":[11,49],"parameterizations":[12],"simply":[14],"connected":[15],"tetrahedral":[16],"mesh":[17],"models":[18],".":[19,75,98,153],"However,":[20],"this":[21,28],"approach":[22],"still":[23],"lacks":[24],"theoretical":[25,33,161],"support.":[26],"In":[27,99],"paper,":[29],"we":[30,101,120],"provide":[31],"a":[32,44,47,53,56,86,122,137],"foundation":[34],"for":[35,126,164],"volumetric":[36,64],"minimization":[39],"(VSEM)":[40],"show":[42,176],"that":[43],"map":[45,83,135],"is":[46,70,90],"precise":[48],"parameterization":[50],"from":[51,84,168],"region":[54],"specified":[57],"shape":[58],"if":[59,62],"and":[60,97,143],"only":[61],"its":[63],"reaches":[67],",":[68,142],"where":[69,89],"total":[72],"mass":[73,133],"We":[76],"use":[77],"VSEM":[78,107,118],"compute":[80],"an":[81],"-volume-/mass-preserving":[82,131],"unit":[87],"ball,":[88],"gap":[92],"between":[93],"addition,":[100],"prove":[102],"efficiency":[104],"algorithm":[108],"with":[109,136,145],"guaranteed":[110,138,149],"asymptotic":[111],"R-linear":[112],"convergence.":[113],"Furthermore,":[114],"based":[115],"on":[116],"algorithm,":[119,182],"propose":[121],"projected":[123],"gradient":[124],"method":[125],"optimal":[132],"transport":[134],"convergence":[139,150,162],"rate":[140,151],"combined":[144],"Nesterov-based":[146],"acceleration,":[147],"becomes":[152],"Numerical":[154],"experiments":[155,175],"are":[156],"presented":[157],"justify":[159],"behavior":[163],"various":[165],"examples":[166],"drawn":[167],"known":[169],"benchmark":[170],"models.":[171],"Moreover,":[172],"these":[173],"numerical":[174],"effectiveness":[178],"proposed":[181],"particularly":[183],"in":[184],"processing":[186],"3D":[188],"medical":[189],"MRI":[190],"brain":[191],"images.":[192]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}