{"id":"https://openalex.org/W1597705134","doi":"https://doi.org/10.1007/978-3-7091-6867-7_1","title":"A semidiscrete nonlinear scale-space theory and its relation to the Perona\u2014Malik paradox","display_name":"A semidiscrete nonlinear scale-space theory and its relation to the Perona\u2014Malik paradox","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W1597705134","doi":"https://doi.org/10.1007/978-3-7091-6867-7_1","mag":"1597705134"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-7091-6867-7_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-7091-6867-7_1","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computer Vision","raw_type":"book-chapter"},"type":"book-chapter","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/A5012716651","display_name":"Joachim Weickert","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Joachim Weickert","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003819624","display_name":"Brahim Benhamouda","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brahim Benhamouda","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012716651"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0586,"has_fulltext":false,"cited_by_count":80,"citation_normalized_percentile":{"value":0.90631654,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9954000115394592,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9954000115394592,"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":0.9939000010490417,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9890000224113464,"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/mathematics","display_name":"Mathematics","score":0.7808849811553955},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6751788258552551},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6626900434494019},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5670539140701294},{"id":"https://openalex.org/keywords/scale-space","display_name":"Scale space","score":0.544061005115509},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5098018050193787},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4998762607574463},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.47462308406829834},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46197736263275146},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.17432627081871033},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1568925678730011}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7808849811553955},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6751788258552551},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6626900434494019},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5670539140701294},{"id":"https://openalex.org/C99102927","wikidata":"https://www.wikidata.org/wiki/Q3058184","display_name":"Scale space","level":4,"score":0.544061005115509},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5098018050193787},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4998762607574463},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.47462308406829834},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46197736263275146},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.17432627081871033},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1568925678730011},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"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":3,"locations":[{"id":"doi:10.1007/978-3-7091-6867-7_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-7091-6867-7_1","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computer Vision","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.46.7418","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.7418","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ti.uni-mannheim.de/ti/lehrstuehle/bmg/weickert/Papers/dag96.ps.gz","raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/080526a0-74cb-11db-bee9-02004c4f4f50","is_oa":false,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/080526a0-74cb-11db-bee9-02004c4f4f50","pdf_url":null,"source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Weickert , J & Benhamouda , B 1997 , A semidiscrete nonlinear scale-space theory and its relation to the Perona--Malik paradox . in Advances in computer vision . Springer , Wien , pp. 1-10 .","raw_type":"bookPart"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W44363806","https://openalex.org/W106081075","https://openalex.org/W1480546554","https://openalex.org/W1549562450","https://openalex.org/W1589429287","https://openalex.org/W1886510209","https://openalex.org/W1963743024","https://openalex.org/W2003342624","https://openalex.org/W2010557690","https://openalex.org/W2015004918","https://openalex.org/W2075332330","https://openalex.org/W2087369977","https://openalex.org/W2098314939","https://openalex.org/W2112328181","https://openalex.org/W2116609734","https://openalex.org/W2120959665","https://openalex.org/W2146052399","https://openalex.org/W2150134853","https://openalex.org/W2158547124","https://openalex.org/W2197960323","https://openalex.org/W3011612142","https://openalex.org/W3197550920","https://openalex.org/W4237306711","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2383807498","https://openalex.org/W2118964038","https://openalex.org/W100433498"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}