{"id":"https://openalex.org/W2541908347","doi":"https://doi.org/10.1109/iccv.2009.5459164","title":"A linear formulation of shape from specular flow","display_name":"A linear formulation of shape from specular flow","publication_year":2009,"publication_date":"2009-09-01","ids":{"openalex":"https://openalex.org/W2541908347","doi":"https://doi.org/10.1109/iccv.2009.5459164","mag":"2541908347"},"language":"en","primary_location":{"id":"doi:10.1109/iccv.2009.5459164","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iccv.2009.5459164","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE 12th 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/A5005188518","display_name":"Guillermo D. Ca\u00f1as","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Guillermo D Canas","raw_affiliation_strings":["Harvard School of Engineering and Applied Sciences, Cambridge, USA"],"affiliations":[{"raw_affiliation_string":"Harvard School of Engineering and Applied Sciences, Cambridge, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085314974","display_name":"Yuriy Vasilyev","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuriy Vasilyev","raw_affiliation_strings":["Harvard School of Engineering and Applied Sciences, Cambridge, USA"],"affiliations":[{"raw_affiliation_string":"Harvard School of Engineering and Applied Sciences, Cambridge, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069464700","display_name":"Yair Adato","orcid":null},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Yair Adato","raw_affiliation_strings":["Computer Science Department, Ben-Gurion University of the Negev, Beersheba, Israel"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Ben-Gurion University of the Negev, Beersheba, Israel","institution_ids":["https://openalex.org/I124227911"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073071472","display_name":"Todd Zickler","orcid":"https://orcid.org/0000-0002-3853-1558"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Todd Zickler","raw_affiliation_strings":["Harvard School of Engineering and Applied Sciences, Cambridge, USA"],"affiliations":[{"raw_affiliation_string":"Harvard School of Engineering and Applied Sciences, Cambridge, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012875116","display_name":"Steven J. Gortler","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steven Gortler","raw_affiliation_strings":["Harvard School of Engineering and Applied Sciences, Cambridge, USA"],"affiliations":[{"raw_affiliation_string":"Harvard School of Engineering and Applied Sciences, Cambridge, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033109332","display_name":"Ohad Ben\u2010Shahar","orcid":"https://orcid.org/0000-0001-5346-152X"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ohad Ben-Shahar","raw_affiliation_strings":["Computer Science Department, Ben-Gurion University of the Negev, Beersheba, Israel"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Ben-Gurion University of the Negev, Beersheba, Israel","institution_ids":["https://openalex.org/I124227911"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5005188518"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.9367,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.94465268,"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":"191","last_page":"198"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9995999932289124,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/specular-reflection","display_name":"Specular reflection","score":0.8792495727539062},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.6702308654785156},{"id":"https://openalex.org/keywords/specular-highlight","display_name":"Specular highlight","score":0.6508444547653198},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.503574788570404},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.42445066571235657},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4027233123779297},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35226643085479736},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.34830066561698914},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3276328146457672},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3017682135105133},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2859421372413635},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.2556614875793457}],"concepts":[{"id":"https://openalex.org/C118381688","wikidata":"https://www.wikidata.org/wiki/Q1079524","display_name":"Specular reflection","level":2,"score":0.8792495727539062},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.6702308654785156},{"id":"https://openalex.org/C50045419","wikidata":"https://www.wikidata.org/wiki/Q7575328","display_name":"Specular highlight","level":3,"score":0.6508444547653198},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.503574788570404},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.42445066571235657},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4027233123779297},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35226643085479736},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.34830066561698914},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3276328146457672},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3017682135105133},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2859421372413635},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.2556614875793457}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/iccv.2009.5459164","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iccv.2009.5459164","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE 12th International Conference on Computer Vision","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.152.2859","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.152.2859","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eecs.harvard.edu/~zickler/papers/LinearSFSF_ICCV2009.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.739.7893","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.739.7893","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.bgu.ac.il/%7Eben-shahar/Publications/2009-Canas_Vasilyev_Adato_Zickler_Gortler_and_Ben_Shahar-A_Linear_Formulation_of_Shape_from_Specular_Flow.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.6499999761581421,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W83777946","https://openalex.org/W1227273861","https://openalex.org/W1539790409","https://openalex.org/W1546634626","https://openalex.org/W1867429401","https://openalex.org/W1999562192","https://openalex.org/W2015578497","https://openalex.org/W2019929483","https://openalex.org/W2028898066","https://openalex.org/W2079877940","https://openalex.org/W2107067501","https://openalex.org/W2117656188","https://openalex.org/W2132139399","https://openalex.org/W2142147923","https://openalex.org/W2158915925","https://openalex.org/W2159817251","https://openalex.org/W2170555925","https://openalex.org/W2265179103","https://openalex.org/W2912864153","https://openalex.org/W3106893712","https://openalex.org/W6603445503","https://openalex.org/W6627965806","https://openalex.org/W6639126518","https://openalex.org/W6693196668","https://openalex.org/W6758747957"],"related_works":["https://openalex.org/W2175900582","https://openalex.org/W2081408094","https://openalex.org/W2135509629","https://openalex.org/W1611976505","https://openalex.org/W3141300019","https://openalex.org/W2101266052","https://openalex.org/W913384303","https://openalex.org/W2098050270","https://openalex.org/W3035953197","https://openalex.org/W2738091825"],"abstract_inverted_index":{"When":[0],"a":[1,12,34,101,106,155],"curved":[2],"mirror-like":[3],"surface":[4,54],"moves":[5,151],"relative":[6],"to":[7,29,89,105,131,154],"its":[8],"environment,":[9],"it":[10],"induces":[11],"motion":[13,128],"field-or":[14],"specular":[15,25,62,113,139,162],"flow-":[16],"on":[17,67,79],"the":[18,30,110,120],"image":[19],"plane":[20],"that":[21,100,164],"observes":[22],"it.":[23],"This":[24,93,116],"flow":[26,63,114,163],"is":[27,41],"related":[28],"mirror's":[31],"shape":[32,111,130,160,179],"through":[33],"non-linear":[35],"partial":[36],"differential":[37],"equation,":[38],"and":[39,46,70,123,129,174],"there":[40],"interest":[42],"in":[43,91,170],"understanding":[44],"when":[45,142],"how":[47],"this":[48,59],"equation":[49],"can":[50],"be":[51,132],"solved":[52],"for":[53,125,158],"shape.":[55],"Existing":[56],"analyses":[57],"of":[58,109],"`shape":[60],"from":[61,112,134,161,181],"equation'":[64],"have":[65,73],"focused":[66],"closed-form":[68],"solutions,":[69],"while":[71],"they":[72],"yielded":[74],"insight,":[75],"their":[76],"critical":[77],"reliance":[78],"externally-provided":[80,144],"initial":[81,145],"conditions":[82,146],"and/or":[83],"specific":[84],"motions":[85,169],"makes":[86],"them":[87],"difficult":[88],"apply":[90],"practice.":[92],"paper":[94],"resolves":[95],"these":[96],"issues.":[97],"We":[98],"show":[99],"suitable":[102],"reparameterization":[103],"leads":[104],"linear":[107],"formulation":[108,117],"equation.":[115],"radically":[118],"simplifies":[119],"reconstruction":[121],"process":[122],"allows,":[124],"example,":[126],"both":[127],"recovered":[133],"as":[135,137],"few":[136],"two":[138],"flows":[140],"even":[141],"no":[143],"are":[147],"available.":[148],"Our":[149],"analysis":[150],"us":[152],"closer":[153],"practical":[156],"method":[157],"recovering":[159],"operates":[165],"under":[166],"arbitrary,":[167],"unknown":[168,171],"illumination":[172],"environments":[173],"does":[175],"not":[176],"require":[177],"additional":[178],"information":[180],"other":[182],"sources.":[183]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
