{"id":"https://openalex.org/W4308097370","doi":"https://doi.org/10.1109/euvip53989.2022.9922788","title":"CNN-based Euler\u2019s Elastica Inpainting with Deep Energy and Deep Image Prior","display_name":"CNN-based Euler\u2019s Elastica Inpainting with Deep Energy and Deep Image Prior","publication_year":2022,"publication_date":"2022-09-11","ids":{"openalex":"https://openalex.org/W4308097370","doi":"https://doi.org/10.1109/euvip53989.2022.9922788"},"language":"en","primary_location":{"id":"doi:10.1109/euvip53989.2022.9922788","is_oa":false,"landing_page_url":"https://doi.org/10.1109/euvip53989.2022.9922788","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 10th European Workshop on Visual Information Processing (EUVIP)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039895188","display_name":"Karl Schrader","orcid":null},"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":"Karl Schrader","raw_affiliation_strings":["Saarland University,Mathematical Image Analysis Group Faculty of Mathematics and Computer Science, Campus E1.7,Saarbrücken,Germany,66041"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland University,Mathematical Image Analysis Group Faculty of Mathematics and Computer Science, Campus E1.7,Saarbrücken,Germany,66041","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051997496","display_name":"Tobias Alt","orcid":"https://orcid.org/0000-0002-4451-9512"},"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":"Tobias Alt","raw_affiliation_strings":["Saarland University,Mathematical Image Analysis Group Faculty of Mathematics and Computer Science, Campus E1.7,Saarbrücken,Germany,66041"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland University,Mathematical Image Analysis Group Faculty of Mathematics and Computer Science, Campus E1.7,Saarbrücken,Germany,66041","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007086183","display_name":"Joachim Weickert","orcid":"https://orcid.org/0000-0002-8494-0045"},"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":"Joachim Weickert","raw_affiliation_strings":["Saarland University,Mathematical Image Analysis Group Faculty of Mathematics and Computer Science, Campus E1.7,Saarbrücken,Germany,66041"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland University,Mathematical Image Analysis Group Faculty of Mathematics and Computer Science, Campus E1.7,Saarbrücken,Germany,66041","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111882881","display_name":"Michael Ertel","orcid":null},"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":"Michael Ertel","raw_affiliation_strings":["Saarland University,Mathematical Image Analysis Group Faculty of Mathematics and Computer Science, Campus E1.7,Saarbrücken,Germany,66041"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland University,Mathematical Image Analysis Group Faculty of Mathematics and Computer Science, Campus E1.7,Saarbrücken,Germany,66041","institution_ids":["https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I91712215"],"apc_list":null,"apc_paid":null,"fwci":0.4061,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.60424943,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9955000281333923,"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"}},"topics":[{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9955000281333923,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9933000206947327,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9932000041007996,"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/inpainting","display_name":"Inpainting","score":0.9018359184265137},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.6140197515487671},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.6002604365348816},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5976936221122742},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.566909670829773},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.559538722038269},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5459732413291931},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5350547432899475},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5323567390441895},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.47349295020103455},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.44658923149108887},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43368399143218994},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37120139598846436},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.3433501422405243},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21155473589897156},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19945916533470154}],"concepts":[{"id":"https://openalex.org/C11727466","wikidata":"https://www.wikidata.org/wiki/Q1628157","display_name":"Inpainting","level":3,"score":0.9018359184265137},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.6140197515487671},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.6002604365348816},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5976936221122742},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.566909670829773},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.559538722038269},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5459732413291931},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5350547432899475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5323567390441895},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.47349295020103455},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.44658923149108887},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43368399143218994},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37120139598846436},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3433501422405243},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21155473589897156},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19945916533470154},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/euvip53989.2022.9922788","is_oa":false,"landing_page_url":"https://doi.org/10.1109/euvip53989.2022.9922788","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 10th European Workshop on Visual Information Processing (EUVIP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8600000143051147}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2380775572","https://openalex.org/W2213520135","https://openalex.org/W4242046654","https://openalex.org/W1504109132","https://openalex.org/W3134074939","https://openalex.org/W2117562399","https://openalex.org/W3174923100","https://openalex.org/W2244018504","https://openalex.org/W4298074124","https://openalex.org/W2374870846"],"abstract_inverted_index":{"Euler\u2019s":[0,83],"elastica":[1,169,189],"constitute":[2],"an":[3,11],"appealing":[4],"variational":[5,94],"image":[6,107],"inpainting":[7,81],"model.":[8],"It":[9,55,179],"minimises":[10],"energy":[12,89,95],"that":[13,62,79],"involves":[14],"the":[15,21,75,87,93,110,124,129,157],"total":[16],"variation":[17],"as":[18,20,96,115,198],"well":[19],"level":[22],"line":[23],"curvature.":[24],"These":[25],"components":[26],"are":[27,134],"transparent":[28],"and":[29,45,66,160],"make":[30],"it":[31,103,195,199],"attractive":[32],"for":[33,188],"shape":[34,143],"completion":[35],"tasks.":[36],"However,":[37],"its":[38],"gradient":[39],"flow":[40],"is":[41,52,56,180,196],"a":[42,71,105,116,164],"singular,":[43],"anisotropic,":[44],"nonlinear":[46],"PDE":[47],"of":[48],"fourth":[49],"order,":[50],"which":[51,91],"numerically":[53],"challenging:":[54],"difficult":[57],"to":[58,128],"find":[59],"efficient":[60],"algorithms":[61,140,187],"offer":[63],"sharp":[64,151],"edges":[65],"good":[67,147],"rotation":[68,148],"invariance.":[69],"As":[70],"remedy,":[72],"we":[73,101,154],"design":[74],"first":[76],"neural":[77,97,165,168],"algorithm":[78],"simulates":[80],"with":[82,104,138,150],"Elastica.":[84],"We":[85],"use":[86],"deep":[88,106],"concept":[90],"employs":[92],"network":[98,111],"loss.":[99],"Furthermore,":[100],"pair":[102],"prior":[108],"where":[109],"architecture":[112],"itself":[113],"acts":[114],"prior.":[117],"This":[118],"yields":[119],"better":[120],"inpaintings":[121],"by":[122],"steering":[123],"optimisation":[125],"trajectory":[126],"closer":[127],"desired":[130],"solution.":[131],"Our":[132,167],"results":[133],"qualitatively":[135],"on":[136,141],"par":[137],"state-of-the-art":[139],"elastica-based":[142],"completion.":[144],"They":[145],"combine":[146],"invariance":[149],"edges.":[152],"Moreover,":[153],"benefit":[155],"from":[156],"high":[158],"efficiency":[159],"effortless":[161],"parallelisation":[162],"within":[163],"framework.":[166],"approach":[170],"only":[171],"requires":[172,200],"3":[173,175],"\u00d7":[174],"central":[176],"difference":[177],"stencils.":[178],"thus":[181],"much":[182],"simpler":[183],"than":[184],"other":[185],"well-performing":[186],"inpainting.":[190],"Last":[191],"but":[192],"not":[193],"least,":[194],"unsupervised":[197],"no":[201],"ground":[202],"truth":[203],"training":[204],"data.":[205]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}