{"id":"https://openalex.org/W2117672823","doi":"https://doi.org/10.1109/iccv.2007.4409024","title":"Shape from Focus and Defocus: Convexity, Quasiconvexity and Defocus-Invariant Textures","display_name":"Shape from Focus and Defocus: Convexity, Quasiconvexity and Defocus-Invariant Textures","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2117672823","doi":"https://doi.org/10.1109/iccv.2007.4409024","mag":"2117672823"},"language":"en","primary_location":{"id":"doi:10.1109/iccv.2007.4409024","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iccv.2007.4409024","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE 11th International Conference on Computer Vision","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/A5070940574","display_name":"Paolo Favaro","orcid":"https://orcid.org/0000-0003-3546-8247"},"institutions":[{"id":"https://openalex.org/I4210085930","display_name":"Heriot-Watt University Malaysia","ror":"https://ror.org/0059w0420","country_code":"MY","type":"education","lineage":["https://openalex.org/I4210085930"]},{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]}],"countries":["GB","MY"],"is_corresponding":true,"raw_author_name":"Paolo Favaro","raw_affiliation_strings":["Department of Electrical Engineering and Physics, Heriot-Watt University, Edinburgh, UK","Heriot-Watt University, Edinburgh"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Physics, Heriot-Watt University, Edinburgh, UK","institution_ids":["https://openalex.org/I32062511"]},{"raw_affiliation_string":"Heriot-Watt University, Edinburgh","institution_ids":["https://openalex.org/I4210085930"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070940574"],"corresponding_institution_ids":["https://openalex.org/I32062511","https://openalex.org/I4210085930"],"apc_list":null,"apc_paid":null,"fwci":1.7792,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.86951805,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13114","display_name":"Image Processing Techniques and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13114","display_name":"Image Processing Techniques and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9434000253677368,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9305999875068665,"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/convexity","display_name":"Convexity","score":0.8406610488891602},{"id":"https://openalex.org/keywords/quasiconvex-function","display_name":"Quasiconvex function","score":0.7032297253608704},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.6163756251335144},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6046476364135742},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5438942313194275},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4827222526073456},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42242878675460815},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32872724533081055},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.2140030860900879},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13826271891593933},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.09270340204238892},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.08854404091835022}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8406610488891602},{"id":"https://openalex.org/C80278974","wikidata":"https://www.wikidata.org/wiki/Q1126412","display_name":"Quasiconvex function","level":5,"score":0.7032297253608704},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.6163756251335144},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6046476364135742},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5438942313194275},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4827222526073456},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42242878675460815},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32872724533081055},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2140030860900879},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13826271891593933},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.09270340204238892},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.08854404091835022},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/iccv.2007.4409024","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iccv.2007.4409024","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE 11th International Conference on Computer Vision","raw_type":"proceedings-article"},{"id":"pmh:oai:boris.unibe.ch:105026","is_oa":false,"landing_page_url":"https://boris.unibe.ch/105026/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401086","display_name":"Bern Open Repository and Information System (University of Bern)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118564535","host_organization_name":"University of Bern","host_organization_lineage":["https://openalex.org/I118564535"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Favaro, Paolo (2007). Shape from Focus and Defocus: Convexity, Quasiconvexity and Defocus-Invariant Textures. In: 11th International Conference on Computer Vision (pp. 1-7). IEEE 10.1109/ICCV.2007.4409024 &lt;http://dx.doi.org/10.1109/ICCV.2007.4409024&gt;","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W153034902","https://openalex.org/W1506219486","https://openalex.org/W1956918427","https://openalex.org/W2020999234","https://openalex.org/W2033468335","https://openalex.org/W2041109737","https://openalex.org/W2046672499","https://openalex.org/W2047736581","https://openalex.org/W2064551963","https://openalex.org/W2065516294","https://openalex.org/W2113137767","https://openalex.org/W2136477411","https://openalex.org/W2143496191","https://openalex.org/W2143789285","https://openalex.org/W2150060382","https://openalex.org/W2160019548","https://openalex.org/W2166774562","https://openalex.org/W2911337866","https://openalex.org/W3003915866","https://openalex.org/W3013882592","https://openalex.org/W4249911582","https://openalex.org/W6630361849","https://openalex.org/W6641095792","https://openalex.org/W6680178729","https://openalex.org/W6758383647"],"related_works":["https://openalex.org/W2082424692","https://openalex.org/W2017555626","https://openalex.org/W1891397942","https://openalex.org/W2030128128","https://openalex.org/W2087192893","https://openalex.org/W1040893767","https://openalex.org/W2964001377","https://openalex.org/W1528932392","https://openalex.org/W4297813027","https://openalex.org/W3176060828"],"abstract_inverted_index":{"In":[0,36],"this":[1,46,78,139],"paper":[2],"we":[3,111],"analyze":[4],"the":[5,8,64,107],"convexity":[6],"and":[7,14,31,62,71,92,134,137],"quasiconvexity":[9],"of":[10,28,118],"shape":[11],"from":[12],"focus/defocus":[13],"image":[15],"restoration.":[16],"We":[17,75,101,126],"show":[18,102,127],"that":[19,103,120],"these":[20,44],"problems":[21],"are":[22],"strictly":[23],"quasiconvex":[24],"for":[25,34],"a":[26,88,96,116],"family":[27],"Bregman's":[29],"divergences,":[30],"in":[32],"particular":[33],"least-squares.":[35],"addition":[37],"to":[38,43,52,129,144],"giving":[39],"novel":[40],"analytical":[41],"insight":[42],"problems,":[45],"study":[47],"can":[48,56,141],"be":[49,142],"readily":[50],"exploited":[51],"design":[53],"algorithms:":[54,84],"One":[55],"do":[57,121],"away":[58],"with":[59],"global":[60,97,108],"minimizers":[61],"obtain":[63],"same":[65],"optimal":[66],"solution":[67],"by":[68,80],"employing":[69],"simple":[70],"efficient":[72],"local":[73,89],"methods.":[74],"experimentally":[76],"validate":[77],"investigation":[79],"comparing":[81],"two":[82],"minimization":[83],"one":[85],"based":[86,94],"on":[87,95],"method":[90,98],"(gradient-flow)":[91],"another":[93],"(graph":[99],"cuts).":[100],"both":[104],"algorithms":[105],"find":[106],"optimum.":[109],"Finally,":[110],"fully":[112],"characterize":[113],"defocus-invariant":[114,133],"textures,":[115],"class":[117],"textures":[119,131],"not":[122],"allow":[123],"depth":[124,147],"recovery.":[125],"how":[128,138],"decompose":[130],"into":[132],"defocus-varying":[135],"components,":[136],"decomposition":[140],"used":[143],"dramatically":[145],"improve":[146],"estimates.":[148]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
