{"id":"https://openalex.org/W4386655680","doi":"https://doi.org/10.48550/arxiv.2309.05575","title":"Anisotropic Diffusion Stencils: From Simple Derivations over Stability Estimates to ResNet Implementations","display_name":"Anisotropic Diffusion Stencils: From Simple Derivations over Stability Estimates to ResNet Implementations","publication_year":2023,"publication_date":"2023-09-11","ids":{"openalex":"https://openalex.org/W4386655680","doi":"https://doi.org/10.48550/arxiv.2309.05575"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2309.05575","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.05575","pdf_url":"https://arxiv.org/pdf/2309.05575","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2309.05575","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039895188","display_name":"Karl Schrader","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Schrader, Karl","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007086183","display_name":"Joachim Weickert","orcid":"https://orcid.org/0000-0002-8494-0045"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Weickert, Joachim","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054709660","display_name":"Michael Krause","orcid":"https://orcid.org/0000-0003-3315-974X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Krause, Michael","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039895188"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9846000075340271,"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/stencil","display_name":"Stencil","score":0.9744702577590942},{"id":"https://openalex.org/keywords/anisotropic-diffusion","display_name":"Anisotropic diffusion","score":0.4468560516834259},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43553411960601807},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.4159412682056427},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3441157937049866},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34148216247558594},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3350263237953186},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30723440647125244},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.2945460081100464},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.25355222821235657},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14939823746681213},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.13706400990486145},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.08885955810546875}],"concepts":[{"id":"https://openalex.org/C76752949","wikidata":"https://www.wikidata.org/wiki/Q7607499","display_name":"Stencil","level":2,"score":0.9744702577590942},{"id":"https://openalex.org/C203504353","wikidata":"https://www.wikidata.org/wiki/Q4765461","display_name":"Anisotropic diffusion","level":3,"score":0.4468560516834259},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43553411960601807},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4159412682056427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3441157937049866},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34148216247558594},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3350263237953186},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30723440647125244},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.2945460081100464},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.25355222821235657},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14939823746681213},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.13706400990486145},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.08885955810546875}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2309.05575","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.05575","pdf_url":"https://arxiv.org/pdf/2309.05575","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"doi:10.48550/arxiv.2309.05575","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2309.05575","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2309.05575","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.05575","pdf_url":"https://arxiv.org/pdf/2309.05575","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3105129168","https://openalex.org/W2804920739","https://openalex.org/W4316371992","https://openalex.org/W2186216222","https://openalex.org/W2392765154","https://openalex.org/W2008005532","https://openalex.org/W1971603802","https://openalex.org/W2564509292","https://openalex.org/W1795008753","https://openalex.org/W2131257462"],"abstract_inverted_index":{"Anisotropic":[0],"diffusion":[1,5,56],"processes":[2],"with":[3],"a":[4,20,36,44,71,99,134],"tensor":[6],"are":[7],"important":[8],"in":[9,125],"image":[10],"analysis,":[11],"physics,":[12],"and":[13,26,69,88,151],"engineering.":[14],"However,":[15],"their":[16,91],"numerical":[17],"approximation":[18],"has":[19],"strong":[21],"impact":[22],"on":[23,43,101,156],"dissipative":[24],"artefacts":[25],"deviations":[27],"from":[28],"rotation":[29],"invariance.":[30],"In":[31],"this":[32],"work,":[33],"we":[34,97],"study":[35],"large":[37],"family":[38,82],"of":[39,74,83,105,121,138],"finite":[40],"difference":[41],"discretisations":[42],"3":[45,47],"x":[46],"stencil.":[48,111],"We":[49],"derive":[50],"it":[51],"by":[52],"splitting":[53,131],"2-D":[54],"anisotropic":[55],"into":[57,142],"four":[58],"1-D":[59],"diffusions.":[60],"The":[61],"resulting":[62],"stencil":[63,81],"class":[64],"involves":[65],"one":[66],"free":[67],"parameter":[68],"covers":[70],"wide":[72],"range":[73],"existing":[75],"discretisations.":[76],"It":[77],"comprises":[78],"the":[79,102,106,110,126,139],"full":[80],"Weickert":[84],"et":[85],"al.":[86],"(2013)":[87],"shows":[89],"that":[90,118],"two":[92],"parameters":[93],"contain":[94],"redundancy.":[95],"Furthermore,":[96],"establish":[98],"bound":[100],"spectral":[103],"norm":[104],"matrix":[107],"corresponding":[108],"to":[109],"This":[112],"gives":[113],"time":[114],"step":[115],"size":[116],"limits":[117],"guarantee":[119],"stability":[120],"an":[122],"explicit":[123,140],"scheme":[124,141],"Euclidean":[127],"norm.":[128],"Our":[129],"directional":[130],"also":[132],"allows":[133],"very":[135],"natural":[136],"translation":[137],"ResNet":[143],"blocks.":[144],"Employing":[145],"neural":[146],"network":[147],"libraries":[148],"enables":[149],"simple":[150],"highly":[152],"efficient":[153],"parallel":[154],"implementations":[155],"GPUs.":[157]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}
