{"id":"https://openalex.org/W1997257485","doi":"https://doi.org/10.1007/s11075-014-9941-x","title":"Asymptotic error of cubic B-spline interpolation using prefiltering","display_name":"Asymptotic error of cubic B-spline interpolation using prefiltering","publication_year":2014,"publication_date":"2014-11-30","ids":{"openalex":"https://openalex.org/W1997257485","doi":"https://doi.org/10.1007/s11075-014-9941-x","mag":"1997257485"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-014-9941-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-014-9941-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-014-9941-x.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","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/s11075-014-9941-x.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057578282","display_name":"Yvonne Percan","orcid":null},"institutions":[{"id":"https://openalex.org/I102520234","display_name":"TH K\u00f6ln - University of Applied Sciences","ror":"https://ror.org/014nnvj65","country_code":"DE","type":"education","lineage":["https://openalex.org/I102520234"]},{"id":"https://openalex.org/I180923762","display_name":"University of Cologne","ror":"https://ror.org/00rcxh774","country_code":"DE","type":"education","lineage":["https://openalex.org/I180923762"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Yvonne Percan","raw_affiliation_strings":["Chair of Computer Science, University of Cologne, Weyertal 121, 50931, Cologne, Germany","Chair of Computer Science, University of Cologne, Cologne, Germany 50931#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Computer Science, University of Cologne, Weyertal 121, 50931, Cologne, Germany","institution_ids":["https://openalex.org/I180923762","https://openalex.org/I102520234"]},{"raw_affiliation_string":"Chair of Computer Science, University of Cologne, Cologne, Germany 50931#TAB#","institution_ids":["https://openalex.org/I180923762"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065331110","display_name":"Stefan Zellmann","orcid":"https://orcid.org/0000-0003-2880-9090"},"institutions":[{"id":"https://openalex.org/I102520234","display_name":"TH K\u00f6ln - University of Applied Sciences","ror":"https://ror.org/014nnvj65","country_code":"DE","type":"education","lineage":["https://openalex.org/I102520234"]},{"id":"https://openalex.org/I180923762","display_name":"University of Cologne","ror":"https://ror.org/00rcxh774","country_code":"DE","type":"education","lineage":["https://openalex.org/I180923762"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Stefan Zellmann","raw_affiliation_strings":["Chair of Computer Science, University of Cologne, Weyertal 121, 50931, Cologne, Germany","Chair of Computer Science, University of Cologne, Cologne, Germany 50931#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Computer Science, University of Cologne, Weyertal 121, 50931, Cologne, Germany","institution_ids":["https://openalex.org/I180923762","https://openalex.org/I102520234"]},{"raw_affiliation_string":"Chair of Computer Science, University of Cologne, Cologne, Germany 50931#TAB#","institution_ids":["https://openalex.org/I180923762"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040060768","display_name":"Ulrich Lang","orcid":"https://orcid.org/0000-0001-7166-0805"},"institutions":[{"id":"https://openalex.org/I102520234","display_name":"TH K\u00f6ln - University of Applied Sciences","ror":"https://ror.org/014nnvj65","country_code":"DE","type":"education","lineage":["https://openalex.org/I102520234"]},{"id":"https://openalex.org/I180923762","display_name":"University of Cologne","ror":"https://ror.org/00rcxh774","country_code":"DE","type":"education","lineage":["https://openalex.org/I180923762"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ulrich Lang","raw_affiliation_strings":["Chair of Computer Science, University of Cologne, Weyertal 121, 50931, Cologne, Germany","Chair of Computer Science, University of Cologne, Cologne, Germany 50931#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Computer Science, University of Cologne, Weyertal 121, 50931, Cologne, Germany","institution_ids":["https://openalex.org/I180923762","https://openalex.org/I102520234"]},{"raw_affiliation_string":"Chair of Computer Science, University of Cologne, Cologne, Germany 50931#TAB#","institution_ids":["https://openalex.org/I180923762"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065331110"],"corresponding_institution_ids":["https://openalex.org/I102520234","https://openalex.org/I180923762"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07007885,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":"1","first_page":"191","last_page":"203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9988999962806702,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9929999709129333,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/monotone-cubic-interpolation","display_name":"Monotone cubic interpolation","score":0.7095516324043274},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.7048907279968262},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6432040929794312},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5858302116394043},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.5113279223442078},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.50299471616745},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.48993033170700073},{"id":"https://openalex.org/keywords/b-spline","display_name":"B-spline","score":0.4848395586013794},{"id":"https://openalex.org/keywords/cubic-hermite-spline","display_name":"Cubic Hermite spline","score":0.4683645963668823},{"id":"https://openalex.org/keywords/bicubic-interpolation","display_name":"Bicubic interpolation","score":0.44588130712509155},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.339731365442276},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32917582988739014},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2609461545944214},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2541848421096802},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.20175930857658386},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.18746569752693176},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.14549759030342102},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10471552610397339}],"concepts":[{"id":"https://openalex.org/C64485984","wikidata":"https://www.wikidata.org/wiki/Q4044484","display_name":"Monotone cubic interpolation","level":5,"score":0.7095516324043274},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.7048907279968262},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6432040929794312},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5858302116394043},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.5113279223442078},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.50299471616745},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.48993033170700073},{"id":"https://openalex.org/C15945459","wikidata":"https://www.wikidata.org/wiki/Q2083109","display_name":"B-spline","level":2,"score":0.4848395586013794},{"id":"https://openalex.org/C84607441","wikidata":"https://www.wikidata.org/wiki/Q1537263","display_name":"Cubic Hermite spline","level":5,"score":0.4683645963668823},{"id":"https://openalex.org/C49608258","wikidata":"https://www.wikidata.org/wiki/Q611705","display_name":"Bicubic interpolation","level":4,"score":0.44588130712509155},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.339731365442276},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32917582988739014},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2609461545944214},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2541848421096802},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.20175930857658386},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.18746569752693176},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.14549759030342102},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10471552610397339},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11075-014-9941-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-014-9941-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-014-9941-x.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:USBKOELN.ub.uni-koeln.de:39455","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400371","display_name":"K\u00f6lner Universit\u00e4ts PublikationsServer (Universit\u00e4t zu K\u00f6ln)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210115942","host_organization_name":"Rhenish Institute for Environmental Research","host_organization_lineage":["https://openalex.org/I4210115942"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.1007/s11075-014-9941-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-014-9941-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-014-9941-x.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.6600000262260437}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1997257485.pdf","grobid_xml":"https://content.openalex.org/works/W1997257485.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W108990048","https://openalex.org/W1483681246","https://openalex.org/W1979965865","https://openalex.org/W1987278426","https://openalex.org/W2003410902","https://openalex.org/W2025711175","https://openalex.org/W2050921210","https://openalex.org/W2087175825","https://openalex.org/W2094507611","https://openalex.org/W2097661764","https://openalex.org/W2110057212","https://openalex.org/W2111794246","https://openalex.org/W2130017280","https://openalex.org/W2142467640","https://openalex.org/W2156241772","https://openalex.org/W2157494358","https://openalex.org/W2158842967","https://openalex.org/W2543920651","https://openalex.org/W2988564852","https://openalex.org/W3150857940","https://openalex.org/W4256596898"],"related_works":["https://openalex.org/W2899709058","https://openalex.org/W4289304019","https://openalex.org/W2381865570","https://openalex.org/W2062768614","https://openalex.org/W2900445293","https://openalex.org/W2117487173","https://openalex.org/W4250117113","https://openalex.org/W2350415687","https://openalex.org/W2380799314","https://openalex.org/W2806075104"],"abstract_inverted_index":{"A":[0],"popular":[1],"class":[2],"of":[3,49,59,106,110,119,141],"reconstruction":[4,108,143],"filters":[5],"that":[6,27,55,95,123,132],"are":[7],"used":[8],"in":[9,76],"signal":[10],"and":[11,131],"image":[12],"processing":[13],"is":[14,24,34,124],"based":[15,125],"on":[16,126],"cubic":[17,41,73,112],"B-splines.":[18],"One":[19],"reason":[20],"for":[21],"their":[22],"popularity":[23],"the":[25,56,72,80,97,103,107,111,120,138],"fact":[26],"they":[28],"can":[29,44,62,86],"be":[30,45,63,88],"efficiently":[31],"implemented.":[32],"This":[33],"specifically":[35],"true":[36],"with":[37,71],"modern":[38],"GPUs":[39],"where":[40],"B-spline":[42,74,113],"filtering":[43,70],"implemented":[46],"by":[47,90],"means":[48],"linearly":[50],"interpolating":[51],"texture":[52],"fetches":[53],"so":[54],"actual":[57],"number":[58],"memory":[60],"accesses":[61],"significantly":[64],"reduced.":[65],"The":[66,84],"curve":[67],"obtained":[68],"from":[69],"does":[75],"general":[77],"not":[78],"interpolate":[79],"original":[81,98],"data":[82,99],"set.":[83,100],"latter":[85],"however":[87],"achieved":[89],"applying":[91],"a":[92,117,127],"prefiltering":[93],"step":[94],"transforms":[96],"We":[101],"study":[102],"asymptotic":[104],"behavior":[105],"error":[109],"interpolation":[114],"filter":[115],"using":[116],"state":[118],"art":[121],"method":[122],"Taylor":[128],"series":[129],"expansion":[130],"was":[133],"carefully":[134],"adjusted":[135],"to":[136],"accommodate":[137],"infinite":[139],"support":[140],"this":[142],"filter.":[144]},"counts_by_year":[],"updated_date":"2026-06-16T07:32:37.131356","created_date":"2025-10-10T00:00:00"}
