{"id":"https://openalex.org/W2089503490","doi":"https://doi.org/10.1137/s0036139994266311","title":"Invariant Geometric Evolutions of Surfaces and Volumetric Smoothing","display_name":"Invariant Geometric Evolutions of Surfaces and Volumetric Smoothing","publication_year":1997,"publication_date":"1997-02-01","ids":{"openalex":"https://openalex.org/W2089503490","doi":"https://doi.org/10.1137/s0036139994266311","mag":"2089503490"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139994266311","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139994266311","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://repository.gatech.edu/bitstreams/a81e2811-a20f-4548-b698-cd83f53c90c1/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012935165","display_name":"Allen Tannenbaum","orcid":"https://orcid.org/0000-0002-0567-5256"},"institutions":[{"id":"https://openalex.org/I4210115145","display_name":"University of Minnesota, Duluth","ror":"https://ror.org/01hy4qx27","country_code":"US","type":"education","lineage":["https://openalex.org/I4210115145"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Allen Tannenbaum","raw_affiliation_strings":["University of Minnesota, Duluth"],"affiliations":[{"raw_affiliation_string":"University of Minnesota, Duluth","institution_ids":["https://openalex.org/I4210115145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025218580","display_name":"Guillermo Sapiro","orcid":"https://orcid.org/0000-0001-9190-6964"},"institutions":[{"id":"https://openalex.org/I1324840837","display_name":"Hewlett-Packard (United States)","ror":"https://ror.org/059rn9488","country_code":"US","type":"company","lineage":["https://openalex.org/I1324840837"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guillermo Sapiro","raw_affiliation_strings":["Hewlett Packard"],"affiliations":[{"raw_affiliation_string":"Hewlett Packard","institution_ids":["https://openalex.org/I1324840837"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070840504","display_name":"Peter J. Olver","orcid":"https://orcid.org/0000-0001-6209-8777"},"institutions":[{"id":"https://openalex.org/I4210115145","display_name":"University of Minnesota, Duluth","ror":"https://ror.org/01hy4qx27","country_code":"US","type":"education","lineage":["https://openalex.org/I4210115145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter J. Olver","raw_affiliation_strings":["University of Minnesota, Duluth"],"affiliations":[{"raw_affiliation_string":"University of Minnesota, Duluth","institution_ids":["https://openalex.org/I4210115145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5012935165"],"corresponding_institution_ids":["https://openalex.org/I4210115145"],"apc_list":null,"apc_paid":null,"fwci":12.3912,"has_fulltext":true,"cited_by_count":94,"citation_normalized_percentile":{"value":0.99588086,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"57","issue":"1","first_page":"176","last_page":"194"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9966999888420105,"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":0.9911999702453613,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6776371598243713},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6476017236709595},{"id":"https://openalex.org/keywords/hypersurface","display_name":"Hypersurface","score":0.6351400017738342},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5782723426818848},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.547943651676178},{"id":"https://openalex.org/keywords/geometric-flow","display_name":"Geometric flow","score":0.542759120464325},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4800609052181244},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4557059705257416},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.45407283306121826},{"id":"https://openalex.org/keywords/affine-geometry-of-curves","display_name":"Affine geometry of curves","score":0.44612234830856323},{"id":"https://openalex.org/keywords/affine-space","display_name":"Affine space","score":0.38971346616744995},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3858758211135864},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37123391032218933},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.318002849817276},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.3084249496459961}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6776371598243713},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6476017236709595},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.6351400017738342},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5782723426818848},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.547943651676178},{"id":"https://openalex.org/C32209215","wikidata":"https://www.wikidata.org/wiki/Q5535483","display_name":"Geometric flow","level":3,"score":0.542759120464325},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4800609052181244},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4557059705257416},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.45407283306121826},{"id":"https://openalex.org/C202411454","wikidata":"https://www.wikidata.org/wiki/Q4688941","display_name":"Affine geometry of curves","level":4,"score":0.44612234830856323},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.38971346616744995},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3858758211135864},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37123391032218933},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.318002849817276},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3084249496459961},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036139994266311","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139994266311","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:smartech.gatech.edu:1853/32563","is_oa":true,"landing_page_url":"http://hdl.handle.net/1853/32563","pdf_url":"http://repository.gatech.edu/bitstreams/a81e2811-a20f-4548-b698-cd83f53c90c1/download","source":{"id":"https://openalex.org/S4377196313","display_name":"SMARTech Repository (Georgia Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130701444","host_organization_name":"Georgia Institute of Technology","host_organization_lineage":["https://openalex.org/I130701444"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:ADA455853","is_oa":false,"landing_page_url":"http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA455853","pdf_url":null,"source":{"id":"https://openalex.org/S4406923043","display_name":"Defense Technical Information Center (DTIC)","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":"DTIC","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:smartech.gatech.edu:1853/32563","is_oa":true,"landing_page_url":"http://hdl.handle.net/1853/32563","pdf_url":"http://repository.gatech.edu/bitstreams/a81e2811-a20f-4548-b698-cd83f53c90c1/download","source":{"id":"https://openalex.org/S4377196313","display_name":"SMARTech Repository (Georgia Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130701444","host_organization_name":"Georgia Institute of Technology","host_organization_lineage":["https://openalex.org/I130701444"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G177218894","display_name":null,"funder_award_id":"F49620","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1811648873","display_name":"Mathematical Sciences: Functional Analysis and the Robust   Control of Distributed and Nonlinear Systems","funder_award_id":"8811084","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1816446510","display_name":"Mathematical Sciences: Non-classical symmetries of          differential equations","funder_award_id":"9116672","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4664931440","display_name":"Mathematical Sciences: Structured and Nonlinear             Interpolation Methods for Robust System Synthesis","funder_award_id":"9122106","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5184800423","display_name":"Mathematical Sciences: Mathematical Physics and Continuum   Mechanics","funder_award_id":"9204192","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2089503490.pdf"},"referenced_works_count":64,"referenced_works":["https://openalex.org/W1482778848","https://openalex.org/W1489989365","https://openalex.org/W1491650242","https://openalex.org/W1498500832","https://openalex.org/W1498637939","https://openalex.org/W1503175024","https://openalex.org/W1509346826","https://openalex.org/W1553058023","https://openalex.org/W1553761880","https://openalex.org/W1562047587","https://openalex.org/W1565212980","https://openalex.org/W1566896733","https://openalex.org/W1573927207","https://openalex.org/W1580042292","https://openalex.org/W1587069887","https://openalex.org/W1595619062","https://openalex.org/W1605861909","https://openalex.org/W1607017601","https://openalex.org/W1643077812","https://openalex.org/W1875106494","https://openalex.org/W1973369053","https://openalex.org/W1973976434","https://openalex.org/W1980055624","https://openalex.org/W1983633249","https://openalex.org/W1991113069","https://openalex.org/W1991724846","https://openalex.org/W2002312729","https://openalex.org/W2009429030","https://openalex.org/W2032316144","https://openalex.org/W2034015214","https://openalex.org/W2036670771","https://openalex.org/W2045280866","https://openalex.org/W2055197673","https://openalex.org/W2065164181","https://openalex.org/W2067564695","https://openalex.org/W2072738093","https://openalex.org/W2082052570","https://openalex.org/W2083796387","https://openalex.org/W2085377048","https://openalex.org/W2086928772","https://openalex.org/W2088114053","https://openalex.org/W2094246409","https://openalex.org/W2109863423","https://openalex.org/W2110980766","https://openalex.org/W2111024532","https://openalex.org/W2111809232","https://openalex.org/W2112005670","https://openalex.org/W2116737017","https://openalex.org/W2120959665","https://openalex.org/W2133128448","https://openalex.org/W2139936470","https://openalex.org/W2146052399","https://openalex.org/W2150134853","https://openalex.org/W2161779468","https://openalex.org/W2166239864","https://openalex.org/W2171840999","https://openalex.org/W2333300544","https://openalex.org/W2611234013","https://openalex.org/W3014069877","https://openalex.org/W3022122637","https://openalex.org/W4229605890","https://openalex.org/W4229734144","https://openalex.org/W4244712874","https://openalex.org/W4247380397"],"related_works":["https://openalex.org/W2949158923","https://openalex.org/W1963689750","https://openalex.org/W2783831528","https://openalex.org/W2952835313","https://openalex.org/W2950162207","https://openalex.org/W4297775707","https://openalex.org/W2177808423","https://openalex.org/W1668619561","https://openalex.org/W2084943206","https://openalex.org/W4285236139"],"abstract_inverted_index":{"The":[0],"study":[1],"of":[2,11,34,48,58,104,110],"geometric":[3,32,39,68],"flows":[4],"for":[5,66,89],"smoothing,":[6],"multiscale":[7],"representation,":[8],"and":[9,13,36,50],"analysis":[10],"two-":[12],"three-dimensional":[14,93,111],"objects":[15],"has":[16],"received":[17],"much":[18],"attention":[19],"in":[20,92,107],"the":[21,31,46,55,63,84,97,108],"past":[22],"few":[23],"years.":[24],"In":[25],"this":[26],"paper,":[27],"we":[28,61,82],"first":[29],"survey":[30],"smoothing":[33],"curves":[35],"surfaces":[37,91],"via":[38],"heat-type":[40],"flows,":[41],"which":[42,71],"are":[43],"invariant":[44,73,87],"under":[45,74],"groups":[47],"Euclidean":[49],"affine":[51,86],"motions.":[52],"Second,":[53],"using":[54],"general":[56,64],"theory":[57],"differential":[59],"invariants,":[60],"determine":[62],"formula":[65],"a":[67,75],"hypersurface":[69],"evolution":[70],"is":[72],"prescribed":[76],"symmetry":[77],"group.":[78],"As":[79],"an":[80],"application,":[81],"present":[83],"simplest":[85],"flow":[88],"(convex)":[90],"space,":[94],"which,":[95],"like":[96],"affine-invariant":[98],"curve":[99],"shortening":[100],"flow,":[101],"will":[102],"be":[103],"fundamental":[105],"importance":[106],"processing":[109],"images.":[112]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}