{"id":"https://openalex.org/W3130268568","doi":"https://doi.org/10.1007/s10444-021-09843-0","title":"Stable recovery of planar regions with algebraic boundaries in Bernstein form","display_name":"Stable recovery of planar regions with algebraic boundaries in Bernstein form","publication_year":2021,"publication_date":"2021-02-16","ids":{"openalex":"https://openalex.org/W3130268568","doi":"https://doi.org/10.1007/s10444-021-09843-0","mag":"3130268568"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-021-09843-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-021-09843-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-021-09843-0.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10444-021-09843-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068127736","display_name":"Costanza Conti","orcid":"https://orcid.org/0000-0001-6878-7784"},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Costanza Conti","raw_affiliation_strings":["DIEF, Universit\u00e0 di Firenze, Florence, Italy"],"affiliations":[{"raw_affiliation_string":"DIEF, Universit\u00e0 di Firenze, Florence, Italy","institution_ids":["https://openalex.org/I45084792"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072587563","display_name":"Mariantonia Cotronei","orcid":"https://orcid.org/0000-0003-4374-298X"},"institutions":[{"id":"https://openalex.org/I59725666","display_name":"University of Reggio Calabria","ror":"https://ror.org/041sz8d87","country_code":"IT","type":"education","lineage":["https://openalex.org/I59725666"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Mariantonia Cotronei","raw_affiliation_strings":["DIIES, Universit\u00e0 Mediterranea di Reggio Calabria, Reggio Calabria, Italy"],"affiliations":[{"raw_affiliation_string":"DIIES, Universit\u00e0 Mediterranea di Reggio Calabria, Reggio Calabria, Italy","institution_ids":["https://openalex.org/I59725666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042165292","display_name":"Demetrio Labate","orcid":"https://orcid.org/0000-0002-9718-789X"},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Demetrio Labate","raw_affiliation_strings":["Department of Mathematics, University of Houston, Houston, TX, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Houston, Houston, TX, USA","institution_ids":["https://openalex.org/I44461941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005630751","display_name":"Wilfredo Molina","orcid":"https://orcid.org/0000-0001-7233-4972"},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wilfredo Molina","raw_affiliation_strings":["Department of Mathematics, University of Houston, Houston, TX, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Houston, Houston, TX, USA","institution_ids":["https://openalex.org/I44461941"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5072587563"],"corresponding_institution_ids":["https://openalex.org/I59725666"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.1772,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.42764717,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"47","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9987000226974487,"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":0.9987000226974487,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9926999807357788,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9894999861717224,"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/mathematics","display_name":"Mathematics","score":0.7682329416275024},{"id":"https://openalex.org/keywords/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.7197175025939941},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.6153664588928223},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5787983536720276},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5303913950920105},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4885433614253998},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4806741178035736},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.43490588665008545},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42594075202941895},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.41910573840141296},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3944162130355835},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25625666975975037},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14963242411613464},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09252303838729858}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7682329416275024},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.7197175025939941},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.6153664588928223},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5787983536720276},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5303913950920105},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4885433614253998},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4806741178035736},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.43490588665008545},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42594075202941895},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.41910573840141296},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3944162130355835},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25625666975975037},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14963242411613464},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09252303838729858},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10444-021-09843-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-021-09843-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-021-09843-0.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:flore.unifi.it:2158/1240298","is_oa":true,"landing_page_url":"http://hdl.handle.net/2158/1240298","pdf_url":"http://hdl.handle.net/2158/1240298","source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10444-021-09843-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-021-09843-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-021-09843-0.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6587931529","display_name":null,"funder_award_id":"1720452","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7314263676","display_name":null,"funder_award_id":"DMS 1720487","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7482401565","display_name":null,"funder_award_id":"1720487","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/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320322648","display_name":"Universit\u00e0 degli Studi di Firenze","ror":"https://ror.org/04jr1s763"},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3130268568.pdf","grobid_xml":"https://content.openalex.org/works/W3130268568.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W629836974","https://openalex.org/W1522382323","https://openalex.org/W1659796361","https://openalex.org/W1971056102","https://openalex.org/W1977455827","https://openalex.org/W2002831093","https://openalex.org/W2018639632","https://openalex.org/W2026381294","https://openalex.org/W2035740370","https://openalex.org/W2055951450","https://openalex.org/W2073330885","https://openalex.org/W2077130908","https://openalex.org/W2096960845","https://openalex.org/W2098662489","https://openalex.org/W2102947781","https://openalex.org/W2105483458","https://openalex.org/W2110528969","https://openalex.org/W2118203826","https://openalex.org/W2125782250","https://openalex.org/W2149213383","https://openalex.org/W2154610756","https://openalex.org/W2157787988","https://openalex.org/W2158537680","https://openalex.org/W2159498975","https://openalex.org/W2199507604","https://openalex.org/W2252214922","https://openalex.org/W2288009986","https://openalex.org/W2792254744","https://openalex.org/W2955728274","https://openalex.org/W3028029859","https://openalex.org/W4230863024"],"related_works":["https://openalex.org/W1721599012","https://openalex.org/W2901858382","https://openalex.org/W4384273653","https://openalex.org/W1578479275","https://openalex.org/W91521151","https://openalex.org/W4224243588","https://openalex.org/W2361696322","https://openalex.org/W2302877070","https://openalex.org/W2043650433","https://openalex.org/W2081049694"],"abstract_inverted_index":{"Abstract":[0],"We":[1,133],"present":[2],"a":[3,11,17,48,61,74,95],"new":[4],"method":[5],"for":[6,54],"the":[7,80,83,88,105,135],"stable":[8],"reconstruction":[9,139],"of":[10,13,20,29,39,51,69,76,82,111,137],"class":[12],"binary":[14],"images":[15,23],"from":[16,141],"small":[18],"number":[19],"measurements.":[21],"The":[22,57],"we":[24,43,100],"consider":[25],"are":[26],"characteristic":[27],"functions":[28],"algebraic":[30,102],"domains,":[31],"that":[32],"is,":[33],"domains":[34],"defined":[35],"as":[36],"zero":[37],"loci":[38],"bivariate":[40,112],"polynomials,":[41],"and":[42,104,115,129,154],"assume":[44],"to":[45,59,73,85,125,131],"know":[46],"only":[47],"finite":[49],"set":[50,65,75],"uniform":[52],"samples":[53,143],"each":[55],"image.":[56],"solution":[58,90],"such":[60],"problem":[62],"can":[63],"be":[64],"up":[66],"in":[67,109],"terms":[68,110],"linear":[70],"equations":[71],"associated":[72],"image":[77,97,107],"moments.":[78],"However,":[79],"sensitivity":[81],"moments":[84,108],"noise":[86],"makes":[87],"numerical":[89,146],"highly":[91],"unstable.":[92],"To":[93],"derive":[94],"robust":[96,124],"recovery":[98],"algorithm,":[99],"represent":[101],"polynomials":[103,114],"corresponding":[106],"Bernstein":[113],"apply":[116],"polynomial-generating,":[117],"refinable":[118],"sampling":[119],"kernels.":[120],"This":[121],"approach":[122],"is":[123,150],"noise,":[126],"computationally":[127],"fast":[128],"simple":[130],"implement.":[132],"illustrate":[134],"performance":[136],"our":[138],"algorithm":[140],"noisy":[142],"through":[144],"extensive":[145],"experiments.":[147],"Our":[148],"code":[149],"released":[151],"open":[152],"source":[153],"freely":[155],"available.":[156]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
