{"id":"https://openalex.org/W1844024880","doi":"https://doi.org/10.1137/15100518x","title":"Geodesics on Shape Spaces with Bounded Variation and Sobolev Metrics","display_name":"Geodesics on Shape Spaces with Bounded Variation and Sobolev Metrics","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W1844024880","doi":"https://doi.org/10.1137/15100518x","mag":"1844024880"},"language":"en","primary_location":{"id":"doi:10.1137/15100518x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15100518x","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/A5049240640","display_name":"Giacomo Nardi","orcid":"https://orcid.org/0009-0005-6498-8470"},"institutions":[{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Giacomo Nardi","raw_affiliation_strings":["CEntre de REcherches en MAth\u00e9matiques de la DEcision"],"affiliations":[{"raw_affiliation_string":"CEntre de REcherches en MAth\u00e9matiques de la DEcision","institution_ids":["https://openalex.org/I171048554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058651667","display_name":"Gabriel Peyr\u00e9","orcid":"https://orcid.org/0000-0002-4477-0387"},"institutions":[{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gabriel Peyr\u00e9","raw_affiliation_strings":["CEntre de REcherches en MAth\u00e9matiques de la DEcision"],"affiliations":[{"raw_affiliation_string":"CEntre de REcherches en MAth\u00e9matiques de la DEcision","institution_ids":["https://openalex.org/I171048554"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110944327","display_name":"Fran\u00e7ois\u2010Xavier Vialard","orcid":null},"institutions":[{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fran\u00e7ois-Xavier Vialard","raw_affiliation_strings":["CEntre de REcherches en MAth\u00e9matiques de la DEcision"],"affiliations":[{"raw_affiliation_string":"CEntre de REcherches en MAth\u00e9matiques de la DEcision","institution_ids":["https://openalex.org/I171048554"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5049240640"],"corresponding_institution_ids":["https://openalex.org/I171048554"],"apc_list":null,"apc_paid":null,"fwci":0.5925,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.74923193,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"9","issue":"1","first_page":"238","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8680180311203003},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.814287543296814},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5377656817436218},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.47935014963150024},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.42562156915664673},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.41200539469718933},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4114147424697876},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3772527575492859}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8680180311203003},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.814287543296814},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5377656817436218},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.47935014963150024},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.42562156915664673},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.41200539469718933},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4114147424697876},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3772527575492859}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15100518x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15100518x","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W571027346","https://openalex.org/W586270867","https://openalex.org/W1480714962","https://openalex.org/W1502786272","https://openalex.org/W1543220894","https://openalex.org/W1559874762","https://openalex.org/W1579576867","https://openalex.org/W1593038947","https://openalex.org/W1597381723","https://openalex.org/W1717953876","https://openalex.org/W1745126362","https://openalex.org/W1835013956","https://openalex.org/W1985368200","https://openalex.org/W1985415289","https://openalex.org/W1986964250","https://openalex.org/W1988167023","https://openalex.org/W1996822984","https://openalex.org/W1997015026","https://openalex.org/W2000594266","https://openalex.org/W2038261411","https://openalex.org/W2042899290","https://openalex.org/W2043786209","https://openalex.org/W2055834603","https://openalex.org/W2058190079","https://openalex.org/W2071570192","https://openalex.org/W2079808284","https://openalex.org/W2081834074","https://openalex.org/W2082119558","https://openalex.org/W2090903445","https://openalex.org/W2093976044","https://openalex.org/W2106518569","https://openalex.org/W2122415813","https://openalex.org/W2124968127","https://openalex.org/W2128962323","https://openalex.org/W2132630784","https://openalex.org/W2148890709","https://openalex.org/W2153358953","https://openalex.org/W2153562582","https://openalex.org/W2154084374","https://openalex.org/W2169071224","https://openalex.org/W2219403839","https://openalex.org/W2314511028","https://openalex.org/W2317715672","https://openalex.org/W2491089320","https://openalex.org/W2952530957","https://openalex.org/W2962812279","https://openalex.org/W2963431386","https://openalex.org/W2964177960","https://openalex.org/W3106241366","https://openalex.org/W3123533845","https://openalex.org/W3125879488","https://openalex.org/W4250800977"],"related_works":["https://openalex.org/W1978591761","https://openalex.org/W4287661821","https://openalex.org/W3133864228","https://openalex.org/W2941285539","https://openalex.org/W1579299075","https://openalex.org/W4206698794","https://openalex.org/W3089249579","https://openalex.org/W4286749417","https://openalex.org/W3126955880","https://openalex.org/W1982132340"],"abstract_inverted_index":{"This":[0,94,115],"paper":[1,56],"studies":[2],"the":[3,11,58,61,64,82,91,104,131,152,168,173],"space":[4,18,25,105,116],"of":[5,19,27,54,60,63,85,87,106,151,167],"$BV^2$":[6,12,177],"planar":[7],"curves":[8,42,107],"endowed":[9],"with":[10,108],"Finsler":[13,73],"metric":[14],"over":[15],"its":[16],"tangent":[17],"displacement":[20],"vector":[21],"fields.":[22],"Such":[23,75],"a":[24,76,118,147,158,164],"is":[26,57,78,123,134,137],"interest":[28],"for":[29,71,111],"applications":[30],"in":[31,142],"image":[32],"processing":[33],"and":[34,122,156,178],"computer":[35],"vision":[36],"because":[37],"it":[38],"enables":[39],"piecewise":[40,45],"regular":[41,46],"that":[43,130],"undergo":[44],"deformations,":[47],"such":[48,102],"as":[49,103],"articulations.":[50],"The":[51],"main":[52],"contribution":[53],"this":[55,72],"proof":[59],"existence":[62],"shortest":[65],"path":[66],"between":[67,176],"any":[68],"two":[69],"$BV^2$-curves":[70],"metric.":[74],"result":[77,128],"proved":[79],"by":[80],"applying":[81],"direct":[83],"method":[84,95,161],"calculus":[86],"variations":[88],"to":[89,99,139,162],"minimize":[90],"geodesic":[92,140,154],"energy.":[93,169],"applies":[96],"more":[97],"generally":[98],"similar":[100],"cases":[101],"$H^k$":[109],"metrics":[110],"$k\\geq":[112],"2$":[113],"integer.":[114],"has":[117],"strong":[119],"Riemannian":[120],"structure":[121],"geodesically":[124],"complete.":[125],"Thus,":[126],"our":[127],"shows":[129],"exponential":[132],"map":[133],"surjective,":[135],"which":[136],"complementary":[138],"completeness":[141],"infinite":[143],"dimensions.":[144],"We":[145],"propose":[146],"finite":[148],"element":[149],"discretization":[150],"minimal":[153],"problem,":[155],"use":[157],"gradient":[159],"descent":[160],"compute":[163],"stationary":[165],"point":[166],"Numerical":[170],"illustrations":[171],"show":[172],"qualitative":[174],"difference":[175],"$H^2$":[179],"geodesics.":[180]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}