{"id":"https://openalex.org/W1996048318","doi":"https://doi.org/10.1109/msp.2002.1028349","title":"Diffusion PDEs on vector-valued images","display_name":"Diffusion PDEs on vector-valued images","publication_year":2002,"publication_date":"2002-09-01","ids":{"openalex":"https://openalex.org/W1996048318","doi":"https://doi.org/10.1109/msp.2002.1028349","mag":"1996048318"},"language":"en","primary_location":{"id":"doi:10.1109/msp.2002.1028349","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2002.1028349","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Magazine","raw_type":"journal-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/A5081478051","display_name":"David Tschumperl\u00e9","orcid":"https://orcid.org/0000-0003-3454-5079"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"D. Tschumperle","raw_affiliation_strings":["INRIA Sophia Antipolis","INRIA Sophia Antipolis,"],"affiliations":[{"raw_affiliation_string":"INRIA Sophia Antipolis","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"INRIA Sophia Antipolis,","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082632190","display_name":"Rachid Deriche","orcid":"https://orcid.org/0000-0002-4643-8417"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"R. Deriche","raw_affiliation_strings":["Computer and Biological Vision Group, INRIA Sophia Antipolis","[Computer and Biological Vision Group, INRIA Sophia Antipolis]"],"affiliations":[{"raw_affiliation_string":"Computer and Biological Vision Group, INRIA Sophia Antipolis","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"[Computer and Biological Vision Group, INRIA Sophia Antipolis]","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081478051"],"corresponding_institution_ids":["https://openalex.org/I1326498283"],"apc_list":null,"apc_paid":null,"fwci":5.7833,"has_fulltext":false,"cited_by_count":113,"citation_normalized_percentile":{"value":0.96798561,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"19","issue":"5","first_page":"16","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11105","display_name":"Advanced Image Processing Techniques","score":0.9976000189781189,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9976000189781189,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9959999918937683,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9950000047683716,"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/structure-tensor","display_name":"Structure tensor","score":0.558914840221405},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.534711480140686},{"id":"https://openalex.org/keywords/anisotropic-diffusion","display_name":"Anisotropic diffusion","score":0.5013341903686523},{"id":"https://openalex.org/keywords/image-restoration","display_name":"Image restoration","score":0.4885924458503723},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.46760454773902893},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46332213282585144},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4629349112510681},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4443697929382324},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4326375424861908},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.41439980268478394},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39169448614120483},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.3613676428794861},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.31362852454185486},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.2913873493671417},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12097612023353577}],"concepts":[{"id":"https://openalex.org/C113315163","wikidata":"https://www.wikidata.org/wiki/Q7625159","display_name":"Structure tensor","level":3,"score":0.558914840221405},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.534711480140686},{"id":"https://openalex.org/C203504353","wikidata":"https://www.wikidata.org/wiki/Q4765461","display_name":"Anisotropic diffusion","level":3,"score":0.5013341903686523},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.4885924458503723},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.46760454773902893},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46332213282585144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4629349112510681},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4443697929382324},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4326375424861908},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41439980268478394},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39169448614120483},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3613676428794861},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.31362852454185486},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.2913873493671417},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12097612023353577},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/msp.2002.1028349","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2002.1028349","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Magazine","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6100000143051147,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":69,"referenced_works":["https://openalex.org/W14724553","https://openalex.org/W92061280","https://openalex.org/W1480546554","https://openalex.org/W1506176942","https://openalex.org/W1536200267","https://openalex.org/W1549101196","https://openalex.org/W1553707579","https://openalex.org/W1563853427","https://openalex.org/W1564135739","https://openalex.org/W1571699948","https://openalex.org/W1572793615","https://openalex.org/W1581996658","https://openalex.org/W1604713470","https://openalex.org/W1825643916","https://openalex.org/W1966786995","https://openalex.org/W1969499601","https://openalex.org/W1972237939","https://openalex.org/W1983377470","https://openalex.org/W2016860730","https://openalex.org/W2019151455","https://openalex.org/W2027401313","https://openalex.org/W2039939700","https://openalex.org/W2043083428","https://openalex.org/W2054225369","https://openalex.org/W2057220024","https://openalex.org/W2066637591","https://openalex.org/W2079869572","https://openalex.org/W2087046122","https://openalex.org/W2097924771","https://openalex.org/W2098434088","https://openalex.org/W2099878763","https://openalex.org/W2103559027","https://openalex.org/W2104404402","https://openalex.org/W2105910985","https://openalex.org/W2107341511","https://openalex.org/W2110563224","https://openalex.org/W2114487471","https://openalex.org/W2117776696","https://openalex.org/W2121407523","https://openalex.org/W2122752532","https://openalex.org/W2126926806","https://openalex.org/W2130604180","https://openalex.org/W2146052399","https://openalex.org/W2147469781","https://openalex.org/W2148800344","https://openalex.org/W2150134853","https://openalex.org/W2152838595","https://openalex.org/W2155102938","https://openalex.org/W2155910912","https://openalex.org/W2163111080","https://openalex.org/W2165252576","https://openalex.org/W2168501356","https://openalex.org/W2265185874","https://openalex.org/W2294491857","https://openalex.org/W2295914420","https://openalex.org/W2295936755","https://openalex.org/W2464942957","https://openalex.org/W2493820185","https://openalex.org/W2521856874","https://openalex.org/W2914396913","https://openalex.org/W4249045480","https://openalex.org/W4285719527","https://openalex.org/W6600597339","https://openalex.org/W6631983884","https://openalex.org/W6632835288","https://openalex.org/W6633541420","https://openalex.org/W6697532585","https://openalex.org/W6719235211","https://openalex.org/W7000931787"],"related_works":["https://openalex.org/W2262332166","https://openalex.org/W2373529328","https://openalex.org/W2319782925","https://openalex.org/W2386523173","https://openalex.org/W2149396808","https://openalex.org/W2317217463","https://openalex.org/W2006843870","https://openalex.org/W1602455006","https://openalex.org/W1966786995","https://openalex.org/W2154534640"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"propose":[4,33],"a":[5,34,52],"local":[6,53],"and":[7,97],"geometric":[8],"point":[9],"of":[10,12,26,51,59],"view":[11],"vector":[13,27,36,54,68,80],"image":[14,41,99],"filtering":[15],"using":[16],"diffusion":[17,60],"PDEs.":[18],"It":[19],"allows":[20],"us":[21],"to":[22,71,77],"analyze":[23],"proposed":[24],"methods":[25],"data":[28],"regularization,":[29],"as":[30,32,91],"well":[31,38],"new":[35],"PDE,":[37],"adapted":[39],"for":[40,62,86],"restoration.":[42,100],"This":[43],"equation,":[44],"whose":[45],"key":[46],"feature":[47],"is":[48],"the":[49,57,84],"use":[50],"geometry,":[55],"combines":[56],"advantages":[58],"PDEs":[61],"noise":[63],"removing":[64],"but":[65],"also":[66],"uses":[67],"shock":[69],"filters":[70],"enhance":[72],"blurred":[73],"edges.":[74],"The":[75],"extension":[76],"norm":[78],"constrained":[79,89],"fields":[81],"can":[82],"be":[83],"start":[85],"other":[87],"well-known":[88],"problems,":[90],"optical":[92],"flow":[93],"computation,":[94],"orientation":[95],"analysis,":[96],"tensor":[98]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}