{"id":"https://openalex.org/W2139762693","doi":"https://doi.org/10.1109/tpami.1986.4767807","title":"Regularization of Inverse Visual Problems Involving Discontinuities","display_name":"Regularization of Inverse Visual Problems Involving Discontinuities","publication_year":1986,"publication_date":"1986-07-01","ids":{"openalex":"https://openalex.org/W2139762693","doi":"https://doi.org/10.1109/tpami.1986.4767807","mag":"2139762693"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.1986.4767807","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1986.4767807","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Transactions on Pattern Analysis and Machine Intelligence","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/A5034397232","display_name":"Demetri Terzopoulos","orcid":null},"institutions":[{"id":"https://openalex.org/I4210090857","display_name":"Schlumberger (United States)","ror":"https://ror.org/009m79n22","country_code":"US","type":"company","lineage":["https://openalex.org/I4210090857","https://openalex.org/I4210092184"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Demetri Terzopoulos","raw_affiliation_strings":["Schlumberger Palo Alto Research, Palo Alto, CA, USA","Schlumberger Palo Alto Research, 3340 Hillview Ave., Palo Alto, CA 94304"],"affiliations":[{"raw_affiliation_string":"Schlumberger Palo Alto Research, Palo Alto, CA, USA","institution_ids":["https://openalex.org/I4210090857"]},{"raw_affiliation_string":"Schlumberger Palo Alto Research, 3340 Hillview Ave., Palo Alto, CA 94304","institution_ids":["https://openalex.org/I4210090857"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034397232"],"corresponding_institution_ids":["https://openalex.org/I4210090857"],"apc_list":null,"apc_paid":null,"fwci":38.0947,"has_fulltext":false,"cited_by_count":766,"citation_normalized_percentile":{"value":0.99861802,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"PAMI-8","issue":"4","first_page":"413","last_page":"424"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","score":0.9988999962806702,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9988999962806702,"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":0.992900013923645,"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/T10638","display_name":"Optical measurement and interference techniques","score":0.9914000034332275,"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/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.7938475012779236},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7110702991485596},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.6239053606987},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5949772000312805},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4773849844932556},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.462016224861145},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.45660191774368286},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4563101530075073},{"id":"https://openalex.org/keywords/backus\u2013gilbert-method","display_name":"Backus\u2013Gilbert method","score":0.4412981867790222},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.41725248098373413},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3766538202762604},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.26612329483032227},{"id":"https://openalex.org/keywords/regularization-perspectives-on-support-vector-machines","display_name":"Regularization perspectives on support vector machines","score":0.2146642506122589},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.1445195972919464},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.12379944324493408},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11933696269989014}],"concepts":[{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.7938475012779236},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7110702991485596},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6239053606987},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5949772000312805},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4773849844932556},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.462016224861145},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.45660191774368286},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4563101530075073},{"id":"https://openalex.org/C27872270","wikidata":"https://www.wikidata.org/wiki/Q4839810","display_name":"Backus\u2013Gilbert method","level":5,"score":0.4412981867790222},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.41725248098373413},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3766538202762604},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26612329483032227},{"id":"https://openalex.org/C141718189","wikidata":"https://www.wikidata.org/wiki/Q7309628","display_name":"Regularization perspectives on support vector machines","level":4,"score":0.2146642506122589},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.1445195972919464},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.12379944324493408},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11933696269989014},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tpami.1986.4767807","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1986.4767807","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W63727357","https://openalex.org/W111967242","https://openalex.org/W120125598","https://openalex.org/W625539078","https://openalex.org/W1481069933","https://openalex.org/W1558233590","https://openalex.org/W1563853427","https://openalex.org/W1578255497","https://openalex.org/W1601420106","https://openalex.org/W1631253743","https://openalex.org/W1645522763","https://openalex.org/W1736170383","https://openalex.org/W1973092800","https://openalex.org/W1978319702","https://openalex.org/W2002355073","https://openalex.org/W2003945700","https://openalex.org/W2013745774","https://openalex.org/W2020999234","https://openalex.org/W2022140147","https://openalex.org/W2022231604","https://openalex.org/W2024060531","https://openalex.org/W2062023095","https://openalex.org/W2068179746","https://openalex.org/W2074797641","https://openalex.org/W2081873601","https://openalex.org/W2085877024","https://openalex.org/W2095945391","https://openalex.org/W2103565112","https://openalex.org/W2109863423","https://openalex.org/W2112165068","https://openalex.org/W2112246162","https://openalex.org/W2118623924","https://openalex.org/W2121203842","https://openalex.org/W2130859329","https://openalex.org/W2133155955","https://openalex.org/W2149846618","https://openalex.org/W2150629612","https://openalex.org/W2165200356","https://openalex.org/W2172960773","https://openalex.org/W2800394774","https://openalex.org/W3021591933","https://openalex.org/W3089381401","https://openalex.org/W3141390961","https://openalex.org/W3142915818","https://openalex.org/W4246727630","https://openalex.org/W4302428745","https://openalex.org/W6633541420"],"related_works":["https://openalex.org/W2366023887","https://openalex.org/W2030398504","https://openalex.org/W1989857057","https://openalex.org/W2615123869","https://openalex.org/W2055767387","https://openalex.org/W2374214022","https://openalex.org/W3134728064","https://openalex.org/W2387685679","https://openalex.org/W2347781941","https://openalex.org/W45494237"],"abstract_inverted_index":{"Inverse":[0],"problems,":[1],"such":[2],"as":[3,23,110],"the":[4,63,79,100],"reconstruction":[5,56,120],"problems":[6,121],"that":[7,38,122],"arise":[8],"in":[9],"early":[10],"vision,":[11,104],"tend":[12],"to":[13,50,118],"be":[14,21,107],"mathematically":[15],"ill-posed.":[16],"Through":[17],"regularization,":[18,52],"they":[19,105],"may":[20,106],"reformulated":[22],"well-posed":[24],"variational":[25],"principles":[26],"whose":[27],"solutions":[28],"are":[29,116],"computable.":[30],"Standard":[31],"regularization":[32],"theory":[33],"employs":[34],"quadratic":[35],"stabilizing":[36,86],"functionals":[37,87],"impose":[39],"global":[40,131],"smoothness":[41,132],"constraints":[42,115,133],"on":[43],"possible":[44],"solutions.":[45],"Discontinuities":[46],"present":[47],"serious":[48],"difficulties":[49],"standard":[51],"however,":[53],"since":[54],"their":[55],"requires":[57],"a":[58,71],"precise":[59],"spatial":[60],"control":[61,81,97],"over":[62,82],"smoothing":[64],"properties":[65],"of":[66,74,102,109],"stabilizers.":[67],"This":[68],"paper":[69],"proposes":[70],"general":[72],"class":[73],"controlled-continuity":[75,111],"stabilizers":[76],"which":[77,130],"provide":[78],"necessary":[80],"smoothness.":[83],"These":[84,113],"nonquadratic":[85],"comprise":[88],"multiple":[89],"generalized":[90],"spline":[91],"kernels":[92],"combined":[93],"with":[94],"(noncontinuous)":[95],"continuity":[96],"functions.":[98],"In":[99],"context":[101],"computational":[103],"thought":[108],"constraints.":[112],"generic":[114],"applicable":[117],"visual":[119],"involve":[123],"both":[124],"continuous":[125],"regions":[126],"and":[127],"discontinuities,":[128],"for":[129],"fail.":[134]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
