{"id":"https://openalex.org/W3189175238","doi":"https://doi.org/10.1137/21m143772x","title":"An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging","display_name":"An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging","publication_year":2022,"publication_date":"2022-04-01","ids":{"openalex":"https://openalex.org/W3189175238","doi":"https://doi.org/10.1137/21m143772x","mag":"3189175238"},"language":"en","primary_location":{"id":"doi:10.1137/21m143772x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m143772x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5100458836","display_name":"Hao Liu","orcid":"https://orcid.org/0000-0002-7504-9859"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hao Liu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101951979","display_name":"Xue\u2010Cheng Tai","orcid":"https://orcid.org/0000-0003-3359-9104"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xue-Cheng Tai","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056887719","display_name":"Roland Glowinski","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roland Glowinski","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100458836"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6012,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.88708974,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"44","issue":"2","first_page":"A935","last_page":"A963"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9968000054359436,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.7433918118476868},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6833476424217224},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6334394812583923},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.6312978267669678},{"id":"https://openalex.org/keywords/gaussian-curvature","display_name":"Gaussian curvature","score":0.61160808801651},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5480355620384216},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.49903225898742676},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.478482186794281},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4681311845779419},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.449587345123291},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3844299912452698},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3697654604911804},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36352023482322693},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1774078905582428},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1419563591480255},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0834413468837738}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7433918118476868},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6833476424217224},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6334394812583923},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6312978267669678},{"id":"https://openalex.org/C16140857","wikidata":"https://www.wikidata.org/wiki/Q945953","display_name":"Gaussian curvature","level":3,"score":0.61160808801651},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5480355620384216},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.49903225898742676},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.478482186794281},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4681311845779419},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.449587345123291},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3844299912452698},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3697654604911804},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36352023482322693},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1774078905582428},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1419563591480255},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0834413468837738},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m143772x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m143772x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1730190705","display_name":null,"funder_award_id":"12300819","funder_id":"https://openalex.org/F4320320955","funder_display_name":"Hong Kong Baptist University"},{"id":"https://openalex.org/G1835434695","display_name":null,"funder_award_id":"RC-FNRA-IG/19-20/SCI/01","funder_id":"https://openalex.org/F4320320955","funder_display_name":"Hong Kong Baptist University"},{"id":"https://openalex.org/G293159644","display_name":null,"funder_award_id":"RG(R)-RC/17-18/02-MATH","funder_id":"https://openalex.org/F4320320955","funder_display_name":"Hong Kong Baptist University"},{"id":"https://openalex.org/G3384263218","display_name":null,"funder_award_id":"179356","funder_id":"https://openalex.org/F4320320955","funder_display_name":"Hong Kong Baptist University"},{"id":"https://openalex.org/G840645771","display_name":null,"funder_award_id":"162784","funder_id":"https://openalex.org/F4320320955","funder_display_name":"Hong Kong Baptist University"}],"funders":[{"id":"https://openalex.org/F4320320955","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W599684198","https://openalex.org/W1596118678","https://openalex.org/W1970535101","https://openalex.org/W1971042117","https://openalex.org/W1974705324","https://openalex.org/W1981220339","https://openalex.org/W1996724333","https://openalex.org/W2017088210","https://openalex.org/W2027560386","https://openalex.org/W2043146490","https://openalex.org/W2067788981","https://openalex.org/W2081468024","https://openalex.org/W2090427126","https://openalex.org/W2092663520","https://openalex.org/W2103559027","https://openalex.org/W2104804805","https://openalex.org/W2114175003","https://openalex.org/W2114722947","https://openalex.org/W2125676375","https://openalex.org/W2130118020","https://openalex.org/W2133665775","https://openalex.org/W2142874675","https://openalex.org/W2146842127","https://openalex.org/W2236372174","https://openalex.org/W2344964557","https://openalex.org/W2529571905","https://openalex.org/W2569134578","https://openalex.org/W2580772840","https://openalex.org/W2623012778","https://openalex.org/W2781330866","https://openalex.org/W2794620576","https://openalex.org/W2801076785","https://openalex.org/W2890917923","https://openalex.org/W2893817145","https://openalex.org/W2900512984","https://openalex.org/W2944916379","https://openalex.org/W2955730445","https://openalex.org/W2963814976","https://openalex.org/W2963942766","https://openalex.org/W2969671405","https://openalex.org/W2981253580","https://openalex.org/W2983861835","https://openalex.org/W2996409188","https://openalex.org/W3034707487","https://openalex.org/W3093196859","https://openalex.org/W3096366476","https://openalex.org/W3104544580","https://openalex.org/W3120501852","https://openalex.org/W3124553318","https://openalex.org/W3168159543","https://openalex.org/W4245463005","https://openalex.org/W4254446689"],"related_works":["https://openalex.org/W3215570221","https://openalex.org/W4308065694","https://openalex.org/W4295655570","https://openalex.org/W4226297850","https://openalex.org/W2376037591","https://openalex.org/W2350536225","https://openalex.org/W4213275102","https://openalex.org/W73664651","https://openalex.org/W3171720365","https://openalex.org/W1974092275"],"abstract_inverted_index":{"Gaussian":[0,24,49,61],"curvature":[1,50,62],"is":[2,76,97,126],"an":[3,43],"important":[4],"geometric":[5],"property":[6],"of":[7,22,60,87,132],"surfaces,":[8],"which":[9],"has":[10],"been":[11],"used":[12],"broadly":[13],"in":[14,36],"mathematical":[15],"modeling.":[16],"Due":[17],"to":[18,99,129],"the":[19,23,57,80,83,105,130],"full":[20,58],"nonlinearity":[21,59],"curvature,":[25],"efficient":[26,121],"numerical":[27],"methods":[28],"for":[29,46,82],"models":[30],"based":[31],"on":[32,143],"it":[33],"are":[34],"uncommon":[35],"literature.":[37],"In":[38,52],"this":[39],"article,":[40],"we":[41,55],"propose":[42],"operator-splitting":[44],"method":[45,125],"a":[47,88,113],"general":[48],"model.":[51],"our":[53],"method,":[54],"decouple":[56],"from":[63],"differential":[64],"operators":[65],"by":[66,102,120],"introducing":[67],"two":[68],"matrix-":[69],"and":[70,136,146],"vector-valued":[71],"functions.":[72],"The":[73,93,123],"optimization":[74],"problem":[75],"then":[77],"converted":[78],"into":[79],"search":[81],"steady":[84],"state":[85],"solution":[86,116],"time":[89,100],"dependent":[90],"PDE":[91,95],"system.":[92],"above":[94],"system":[96],"well-suited":[98],"discretization":[101],"operator":[103],"splitting,":[104],"subproblems":[106],"encountered":[107],"at":[108],"each":[109],"fractional":[110],"step":[111],"having":[112],"closed":[114],"form":[115],"or":[117],"being":[118,138],"solvable":[119],"algorithms.":[122],"proposed":[124],"not":[127],"sensitive":[128],"choice":[131],"parameters,":[133],"its":[134],"efficiency":[135],"performances":[137],"demonstrated":[139],"via":[140],"systematic":[141],"experiments":[142],"surface":[144],"smoothing":[145],"image":[147],"denoising.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
