{"id":"https://openalex.org/W2781511202","doi":"https://doi.org/10.1080/00207160.2017.1423292","title":"Anomalous diffusion, dilation, and erosion in image processing","display_name":"Anomalous diffusion, dilation, and erosion in image processing","publication_year":2018,"publication_date":"2018-01-03","ids":{"openalex":"https://openalex.org/W2781511202","doi":"https://doi.org/10.1080/00207160.2017.1423292","mag":"2781511202"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2017.1423292","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1423292","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://juser.fz-juelich.de/record/861213","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030657709","display_name":"Andreas Kleefeld","orcid":"https://orcid.org/0000-0001-8324-821X"},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Andreas Kleefeld","raw_affiliation_strings":["Forschungszentrum J\u00fclich GmbH, J\u00fclich Supercomputing Centre, J\u00fclich, Germany"],"raw_orcid":"https://orcid.org/0000-0001-8324-821X","affiliations":[{"raw_affiliation_string":"Forschungszentrum J\u00fclich GmbH, J\u00fclich Supercomputing Centre, J\u00fclich, Germany","institution_ids":["https://openalex.org/I171892758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051193971","display_name":"Sophia Vorderw\u00fclbecke","orcid":null},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sophia Vorderw\u00fclbecke","raw_affiliation_strings":["Forschungszentrum J\u00fclich GmbH, J\u00fclich Supercomputing Centre, J\u00fclich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Forschungszentrum J\u00fclich GmbH, J\u00fclich Supercomputing Centre, J\u00fclich, Germany","institution_ids":["https://openalex.org/I171892758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038254582","display_name":"Bernhard Burgeth","orcid":"https://orcid.org/0000-0001-6602-6201"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bernhard Burgeth","raw_affiliation_strings":["Department of Mathematics and Computer Science, Saarland University, Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Saarland University, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030657709"],"corresponding_institution_ids":["https://openalex.org/I171892758"],"apc_list":null,"apc_paid":null,"fwci":0.1334,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.43452588,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"95","issue":"6-7","first_page":"1375","last_page":"1393"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.9955000281333923,"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/discretization","display_name":"Discretization","score":0.7556741237640381},{"id":"https://openalex.org/keywords/dilation","display_name":"Dilation (metric space)","score":0.7360235452651978},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.7287230491638184},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6793667078018188},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5189856886863708},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5170326828956604},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.4889010488986969},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.47506090998649597},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.4746934771537781},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.4377148151397705},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.4337092638015747},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3938225209712982},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.37872520089149475},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1756039261817932}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7556741237640381},{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.7360235452651978},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.7287230491638184},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6793667078018188},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5189856886863708},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5170326828956604},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.4889010488986969},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.47506090998649597},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.4746934771537781},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.4377148151397705},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.4337092638015747},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3938225209712982},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.37872520089149475},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1756039261817932},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/00207160.2017.1423292","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1423292","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:juser.fz-juelich.de:844935","is_oa":false,"landing_page_url":"http://juser.fz-juelich.de/record/844935","pdf_url":null,"source":{"id":"https://openalex.org/S4306401090","display_name":"JuSER (Forschungszentrum J\u00fclich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I171892758","host_organization_name":"Forschungszentrum J\u00fclich","host_organization_lineage":["https://openalex.org/I171892758"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International journal of computer mathematics 95(6-7), 1375 - 1393 (2018). doi:10.1080/00207160.2017.1423292 special issue: \"Advances on Computational Fractional Partial Differential Equations\"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:juser.fz-juelich.de:861213","is_oa":true,"landing_page_url":"http://juser.fz-juelich.de/record/861213","pdf_url":null,"source":{"id":"https://openalex.org/S4306401090","display_name":"JuSER (Forschungszentrum J\u00fclich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I171892758","host_organization_name":"Forschungszentrum J\u00fclich","host_organization_lineage":["https://openalex.org/I171892758"],"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":"SIAM Conference on Computational Science and Engineering, CSE 2019, Spokane, United States of America, 2019-02-25 - 2019-03-01","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:juser.fz-juelich.de:861213","is_oa":true,"landing_page_url":"http://juser.fz-juelich.de/record/861213","pdf_url":null,"source":{"id":"https://openalex.org/S4306401090","display_name":"JuSER (Forschungszentrum J\u00fclich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I171892758","host_organization_name":"Forschungszentrum J\u00fclich","host_organization_lineage":["https://openalex.org/I171892758"],"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":"SIAM Conference on Computational Science and Engineering, CSE 2019, Spokane, United States of America, 2019-02-25 - 2019-03-01","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[{"score":0.6100000143051147,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W253046551","https://openalex.org/W1501211933","https://openalex.org/W1561442812","https://openalex.org/W1608344871","https://openalex.org/W1653522820","https://openalex.org/W1779031210","https://openalex.org/W1991113069","https://openalex.org/W1995504856","https://openalex.org/W2000434452","https://openalex.org/W2005114389","https://openalex.org/W2012872284","https://openalex.org/W2022685032","https://openalex.org/W2022735534","https://openalex.org/W2031041142","https://openalex.org/W2031366974","https://openalex.org/W2066533951","https://openalex.org/W2068928911","https://openalex.org/W2070438803","https://openalex.org/W2073018140","https://openalex.org/W2091613684","https://openalex.org/W2093834886","https://openalex.org/W2105795805","https://openalex.org/W2109863423","https://openalex.org/W2114093641","https://openalex.org/W2121534722","https://openalex.org/W2129098897","https://openalex.org/W2133279414","https://openalex.org/W2134837756","https://openalex.org/W2147910047","https://openalex.org/W2150134853","https://openalex.org/W2253836808","https://openalex.org/W2259227674","https://openalex.org/W2518477744","https://openalex.org/W2610857016","https://openalex.org/W2788774855","https://openalex.org/W2998023265","https://openalex.org/W3099393693","https://openalex.org/W4293515545"],"related_works":["https://openalex.org/W2030146312","https://openalex.org/W3125365929","https://openalex.org/W2009939145","https://openalex.org/W2509889981","https://openalex.org/W2607759403","https://openalex.org/W3165417076","https://openalex.org/W2107140857","https://openalex.org/W4323344139","https://openalex.org/W2067855936","https://openalex.org/W1660413260"],"abstract_inverted_index":{"In":[0],"this":[1,110],"paper,":[2],"anomalous":[3],"sub-":[4],"and":[5,13,49,68,82,91,107],"super-diffusion":[6],"arising":[7],"in":[8,44,50],"image":[9],"processing":[10],"is":[11,14,42,63,84],"considered":[12],"modelled":[15],"by":[16,86],"a":[17,28,87],"diffusion":[18],"equation":[19,41,79],"with":[20,46,52],"fractional":[21,88],"time":[22,51,73,89],"derivative.":[23],"It":[24],"might":[25],"serve":[26],"as":[27],"building":[29],"block":[30],"for":[31],"the":[32,53,72,76,100],"construction":[33],"of":[34,75],"various":[35],"filters.":[36],"The":[37],"resulting":[38],"partial":[39,77],"differential":[40,78],"discretized":[43],"space":[45],"centred":[47],"differences":[48],"explicit":[54],"or":[55],"implicit":[56],"Euler":[57],"method,":[58],"respectively.":[59],"A":[60,104],"numerical":[61,102],"investigation":[62],"performed":[64],"to":[65],"illustrate":[66],"new":[67,96],"interesting":[69],"results.":[70,103],"Additionally,":[71],"derivative":[74,90],"describing":[80],"dilation":[81],"erosion":[83],"replaced":[85],"then":[92],"solved":[93],"numerically.":[94],"Interesting":[95],"questions":[97],"arise":[98],"from":[99],"presented":[101],"short":[105],"summary":[106],"outlook":[108],"conclude":[109],"article.":[111]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
