{"id":"https://openalex.org/W4392697002","doi":"https://doi.org/10.3390/axioms13030185","title":"Improving Realism of Facial Interpolation and Blendshapes with Analytical Partial Differential Equation-Represented Physics","display_name":"Improving Realism of Facial Interpolation and Blendshapes with Analytical Partial Differential Equation-Represented Physics","publication_year":2024,"publication_date":"2024-03-12","ids":{"openalex":"https://openalex.org/W4392697002","doi":"https://doi.org/10.3390/axioms13030185"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13030185","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13030185","pdf_url":"https://www.mdpi.com/2075-1680/13/3/185/pdf?version=1710231638","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/3/185/pdf?version=1710231638","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113139443","display_name":"Sydney Day","orcid":null},"institutions":[{"id":"https://openalex.org/I9300472","display_name":"Bournemouth University","ror":"https://ror.org/05wwcw481","country_code":"GB","type":"education","lineage":["https://openalex.org/I9300472"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Sydney Day","raw_affiliation_strings":["Axis Studios, Glasgow G3 8EP, UK","National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Axis Studios, Glasgow G3 8EP, UK","institution_ids":[]},{"raw_affiliation_string":"National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK","institution_ids":["https://openalex.org/I9300472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052920166","display_name":"Zhidong Xiao","orcid":"https://orcid.org/0000-0003-1977-4674"},"institutions":[{"id":"https://openalex.org/I9300472","display_name":"Bournemouth University","ror":"https://ror.org/05wwcw481","country_code":"GB","type":"education","lineage":["https://openalex.org/I9300472"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Zhidong Xiao","raw_affiliation_strings":["National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK"],"raw_orcid":"https://orcid.org/0000-0003-1977-4674","affiliations":[{"raw_affiliation_string":"National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK","institution_ids":["https://openalex.org/I9300472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087575477","display_name":"Ehtzaz Chaudhry","orcid":"https://orcid.org/0000-0001-6797-3614"},"institutions":[{"id":"https://openalex.org/I9300472","display_name":"Bournemouth University","ror":"https://ror.org/05wwcw481","country_code":"GB","type":"education","lineage":["https://openalex.org/I9300472"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ehtzaz Chaudhry","raw_affiliation_strings":["National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK","institution_ids":["https://openalex.org/I9300472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055132842","display_name":"Matthew Hooker","orcid":"https://orcid.org/0000-0001-7515-693X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matthew Hooker","raw_affiliation_strings":["Axis Studios, Glasgow G3 8EP, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Axis Studios, Glasgow G3 8EP, UK","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017140258","display_name":"Xiaoqiang Zhu","orcid":"https://orcid.org/0000-0001-7486-0853"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoqiang Zhu","raw_affiliation_strings":["School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052361049","display_name":"Jian Chang","orcid":"https://orcid.org/0000-0003-4118-147X"},"institutions":[{"id":"https://openalex.org/I9300472","display_name":"Bournemouth University","ror":"https://ror.org/05wwcw481","country_code":"GB","type":"education","lineage":["https://openalex.org/I9300472"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jian Chang","raw_affiliation_strings":["National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK","institution_ids":["https://openalex.org/I9300472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014857926","display_name":"Andr\u00e9s Iglesias","orcid":"https://orcid.org/0000-0002-5672-8274"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Andr\u00e9s Iglesias","raw_affiliation_strings":["Department of Applied Mathematics and Computational Sciences, University of Cantabria, 39005 Santander, Spain"],"raw_orcid":"https://orcid.org/0000-0002-5672-8274","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computational Sciences, University of Cantabria, 39005 Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101850373","display_name":"Lihua You","orcid":"https://orcid.org/0000-0001-9738-4378"},"institutions":[{"id":"https://openalex.org/I9300472","display_name":"Bournemouth University","ror":"https://ror.org/05wwcw481","country_code":"GB","type":"education","lineage":["https://openalex.org/I9300472"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Lihua You","raw_affiliation_strings":["National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK","institution_ids":["https://openalex.org/I9300472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074858947","display_name":"Jianjun Zhang","orcid":"https://orcid.org/0000-0002-7069-5771"},"institutions":[{"id":"https://openalex.org/I9300472","display_name":"Bournemouth University","ror":"https://ror.org/05wwcw481","country_code":"GB","type":"education","lineage":["https://openalex.org/I9300472"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jianjun Zhang","raw_affiliation_strings":["National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK","institution_ids":["https://openalex.org/I9300472"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052920166","https://openalex.org/A5101850373"],"corresponding_institution_ids":["https://openalex.org/I9300472"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02007544,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"3","first_page":"185","last_page":"185"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11448","display_name":"Face recognition and analysis","score":0.9970999956130981,"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/T11448","display_name":"Face recognition and analysis","score":0.9970999956130981,"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/T11322","display_name":"Facial Rejuvenation and Surgery Techniques","score":0.9226999878883362,"subfield":{"id":"https://openalex.org/subfields/2708","display_name":"Dermatology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7397568821907043},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.568668007850647},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5184773802757263},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4507380723953247},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.44413599371910095},{"id":"https://openalex.org/keywords/realism","display_name":"Realism","score":0.44358181953430176},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3829260468482971},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.37379881739616394},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32660967111587524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3163934051990509},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.28138208389282227},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.14651557803153992},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.12021529674530029},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.07722261548042297},{"id":"https://openalex.org/keywords/orthodontics","display_name":"Orthodontics","score":0.055880963802337646}],"concepts":[{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7397568821907043},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.568668007850647},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5184773802757263},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4507380723953247},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.44413599371910095},{"id":"https://openalex.org/C543847140","wikidata":"https://www.wikidata.org/wiki/Q2642826","display_name":"Realism","level":2,"score":0.44358181953430176},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3829260468482971},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.37379881739616394},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32660967111587524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3163934051990509},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.28138208389282227},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.14651557803153992},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.12021529674530029},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.07722261548042297},{"id":"https://openalex.org/C29694066","wikidata":"https://www.wikidata.org/wiki/Q118301","display_name":"Orthodontics","level":1,"score":0.055880963802337646},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms13030185","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13030185","pdf_url":"https://www.mdpi.com/2075-1680/13/3/185/pdf?version=1710231638","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:eprints.bournemouth.ac.uk:39594","is_oa":true,"landing_page_url":null,"pdf_url":"https://eprints.bournemouth.ac.uk/39594/1/axioms-13-00185.pdf","source":{"id":"https://openalex.org/S4306400187","display_name":"Bournemouth University Research Online (Bournemouth University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9300472","host_organization_name":"Bournemouth University","host_organization_lineage":["https://openalex.org/I9300472"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:repositorio.unican.es:10902/36087","is_oa":true,"landing_page_url":"https://hdl.handle.net/10902/36087","pdf_url":"https://repositorio.unican.es/xmlui/bitstream/10902/36087/3/ImprovingRealismFacial.pdf","source":{"id":"https://openalex.org/S4306400398","display_name":"UCrea (University of Cantabria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13134134","host_organization_name":"Universidad de Cantabria","host_organization_lineage":["https://openalex.org/I13134134"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, 2024, 13(3), 185","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:9979e04e116e458bb951a2ac02345122","is_oa":false,"landing_page_url":"https://doaj.org/article/9979e04e116e458bb951a2ac02345122","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 3, p 185 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13030185","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13030185","pdf_url":"https://www.mdpi.com/2075-1680/13/3/185/pdf?version=1710231638","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1175115578","display_name":null,"funder_award_id":"AEI//10.13039/501100011033/","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G121809054","display_name":null,"funder_award_id":"MCIN/AEI/10","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G143639328","display_name":null,"funder_award_id":"AEI/10.13039/501100011033/FEDER","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G150483041","display_name":"PDE-based geometric modelling, image processing, and shape reconstruction","funder_award_id":"778035","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G1855990336","display_name":null,"funder_award_id":".13039/501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G210041235","display_name":null,"funder_award_id":"MCIN /AEI/ 10.13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2281333282","display_name":null,"funder_award_id":"MCIN / AEI /10.13039/501100011033","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2309174360","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G2390397592","display_name":null,"funder_award_id":"MCIN / AEI /10 .13039/501100011033/FEDER","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2585926585","display_name":null,"funder_award_id":"13039/501100011033/FEDER","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G2601397997","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2660406951","display_name":null,"funder_award_id":"/ AEI/10","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G300979063","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G34346518","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501 100 011 033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3681454997","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4042783231","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G425668148","display_name":null,"funder_award_id":".13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G430777504","display_name":null,"funder_award_id":"10.13039/501100011033/","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G434337789","display_name":null,"funder_award_id":"HORIZON2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5080475149","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5421974903","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G553349141","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033.","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G586857820","display_name":null,"funder_award_id":"501100011033/FEDER","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5876459773","display_name":null,"funder_award_id":"EP/L016540/1","funder_id":"https://openalex.org/F4320338169","funder_display_name":"Centre for Digital Entertainment"},{"id":"https://openalex.org/G6151357664","display_name":null,"funder_award_id":"AEI 10.13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6372227679","display_name":"EPSRC Centre for Doctoral Training in Digital Entertainment","funder_award_id":"EP/L016540/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7092617787","display_name":null,"funder_award_id":"PID2021-127073OB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7391727506","display_name":null,"funder_award_id":"10.13039/501100011033/FEDER","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G846842501","display_name":null,"funder_award_id":"MCIN/AEI/10.13039 /501100011033/FEDER","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G897484643","display_name":null,"funder_award_id":"MCIN /AEI /10.13039","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G99296377","display_name":null,"funder_award_id":"/AEI/10.13039/ 501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null},{"id":"https://openalex.org/F4320338169","display_name":"Centre for Digital Entertainment","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4392697002.pdf"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W1498580944","https://openalex.org/W1709848863","https://openalex.org/W1933831357","https://openalex.org/W1978476222","https://openalex.org/W1983776370","https://openalex.org/W2024680211","https://openalex.org/W2034881292","https://openalex.org/W2038198107","https://openalex.org/W2055849012","https://openalex.org/W2096076356","https://openalex.org/W2104539097","https://openalex.org/W2122549197","https://openalex.org/W2124917223","https://openalex.org/W2130829492","https://openalex.org/W2131681761","https://openalex.org/W2135666716","https://openalex.org/W2138672947","https://openalex.org/W2149403983","https://openalex.org/W2170653751","https://openalex.org/W2186047126","https://openalex.org/W2236592196","https://openalex.org/W2401751489","https://openalex.org/W2471962767","https://openalex.org/W2484111965","https://openalex.org/W2519683295","https://openalex.org/W2617644139","https://openalex.org/W2739069563","https://openalex.org/W2920864629","https://openalex.org/W3034008956","https://openalex.org/W3212423753","https://openalex.org/W4206002877","https://openalex.org/W4210806018","https://openalex.org/W4211056820","https://openalex.org/W4220797971","https://openalex.org/W4233118564","https://openalex.org/W4246969505","https://openalex.org/W4249872381","https://openalex.org/W4308494346","https://openalex.org/W4388007690","https://openalex.org/W6622638115","https://openalex.org/W6644369777","https://openalex.org/W6646398240","https://openalex.org/W6654258287","https://openalex.org/W6679290147","https://openalex.org/W6679371156","https://openalex.org/W6807474319","https://openalex.org/W6888776147"],"related_works":["https://openalex.org/W2387507339","https://openalex.org/W4206705773","https://openalex.org/W4288093576","https://openalex.org/W2980071750","https://openalex.org/W2354172195","https://openalex.org/W2515413930","https://openalex.org/W4367666133","https://openalex.org/W2785590221","https://openalex.org/W2351745915","https://openalex.org/W2029287765"],"abstract_inverted_index":{"How":[0],"to":[1,34,69,108,147,167,219],"create":[2,109,148],"realistic":[3,37,197,203],"shapes":[4,9,68,146],"by":[5,152],"interpolating":[6,143],"two":[7,66,144],"known":[8,67,145],"for":[10],"facial":[11,38,222,237],"blendshapes":[12],"has":[13],"not":[14],"been":[15],"investigated":[16],"in":[17,142],"the":[18,47,55,63,71,90,105,117,129,135,138,154,159,168,195,208,215,228],"existing":[19],"literature.":[20],"In":[21],"this":[22,42],"paper,":[23],"we":[24,44,83,133,213],"propose":[25,84],"a":[26,85,120,221],"physics-based":[27,72,236],"mathematical":[28,73,87,106,130],"model":[29,74,107],"and":[30,59,96,111,124,163,172,177,187,225],"its":[31],"analytical":[32,126,140,161,181],"solutions":[33,127,141,162,182],"obtain":[35],"more":[36,202,232],"shape":[39,150,155,170,198],"changes.":[40],"To":[41],"end,":[43],"first":[45],"introduce":[46,102],"internal":[48],"force":[49,92],"of":[50,57,65,89,116,128,137],"elastic":[51],"beam":[52],"bending":[53],"into":[54,104],"equation":[56],"motion":[58],"integrate":[60],"it":[61,103],"with":[62,76,94,158,207],"constraints":[64],"develop":[70,220],"represented":[75,93],"dynamic":[77,114],"partial":[78],"differential":[79],"equations":[80],"(PDEs).":[81],"Second,":[82],"unified":[86],"expression":[88],"external":[91],"linear":[95,110,165,176,210],"various":[97,112,178],"nonlinear":[98,113,179],"time-dependent":[99],"Fourier":[100],"series,":[101],"deformations":[115],"curves":[118],"defining":[119],"human":[121],"face":[122],"model,":[123],"derive":[125],"model.":[131],"Third,":[132],"evaluate":[134],"realism":[136],"obtained":[139,160,206],"new":[149],"changes":[151,156,171],"comparing":[153],"calculated":[157],"geometric":[164,209],"interpolation":[166,193,218],"ground-truth":[169],"conclude":[173],"that":[174,227],"among":[175],"PDE-based":[180,189,192,217],"named":[183],"as":[184],"linear,":[185],"quadratic,":[186],"cubic":[188],"interpolation,":[190],"quadratic":[191,216],"creates":[194],"most":[196],"changes,":[199],"which":[200],"are":[201],"than":[204,234],"those":[205],"interpolation.":[211],"Finally,":[212],"use":[214],"blendshape":[223],"method":[224],"demonstrate":[226],"proposed":[229],"approach":[230],"is":[231],"efficient":[233],"numerical":[235],"blendshapes.":[238]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
