{"id":"https://openalex.org/W2081807893","doi":"https://doi.org/10.1137/s0036139997327174","title":"Viscosity Solutions and Convergence of Monotone Schemes for Synthetic Aperture Radar Shape-from-Shading Equations with Discontinuous Intensities","display_name":"Viscosity Solutions and Convergence of Monotone Schemes for Synthetic Aperture Radar Shape-from-Shading Equations with Discontinuous Intensities","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2081807893","doi":"https://doi.org/10.1137/s0036139997327174","mag":"2081807893"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139997327174","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139997327174","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","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/A5063032058","display_name":"Daniel N. Ostrov","orcid":null},"institutions":[{"id":"https://openalex.org/I16269868","display_name":"Santa Clara University","ror":"https://ror.org/03ypqe447","country_code":"US","type":"education","lineage":["https://openalex.org/I16269868"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daniel N. Ostrov","raw_affiliation_strings":["Santa Clara University, Santa Clara, CA"],"affiliations":[{"raw_affiliation_string":"Santa Clara University, Santa Clara, CA","institution_ids":["https://openalex.org/I16269868"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5063032058"],"corresponding_institution_ids":["https://openalex.org/I16269868"],"apc_list":null,"apc_paid":null,"fwci":3.1987,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.91191983,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"59","issue":"6","first_page":"2060","last_page":"2085"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9789000153541565,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/eikonal-equation","display_name":"Eikonal equation","score":0.7406113743782043},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6226123571395874},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6207924485206604},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5916391611099243},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5173670649528503},{"id":"https://openalex.org/keywords/synthetic-aperture-radar","display_name":"Synthetic aperture radar","score":0.4912692904472351},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.4407334625720978},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.4405059218406677},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.42711177468299866},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.38532882928848267},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08721724152565002}],"concepts":[{"id":"https://openalex.org/C40375134","wikidata":"https://www.wikidata.org/wiki/Q1303846","display_name":"Eikonal equation","level":2,"score":0.7406113743782043},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6226123571395874},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6207924485206604},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5916391611099243},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5173670649528503},{"id":"https://openalex.org/C87360688","wikidata":"https://www.wikidata.org/wiki/Q740686","display_name":"Synthetic aperture radar","level":2,"score":0.4912692904472351},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.4407334625720978},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.4405059218406677},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.42711177468299866},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.38532882928848267},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08721724152565002},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036139997327174","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139997327174","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:bibcyt.ucla.edu.ve:T070300009647/8","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300009647/8&Nombrebd=Bciucla","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W153353184","https://openalex.org/W1978484312","https://openalex.org/W1986838484","https://openalex.org/W2012872284","https://openalex.org/W2027438381","https://openalex.org/W2035643168","https://openalex.org/W2053208684","https://openalex.org/W2057462050","https://openalex.org/W2061123497","https://openalex.org/W2118304946","https://openalex.org/W2171530698","https://openalex.org/W2749408143","https://openalex.org/W3021722416"],"related_works":["https://openalex.org/W40509887","https://openalex.org/W2211241880","https://openalex.org/W2797290608","https://openalex.org/W2884664122","https://openalex.org/W2053914471","https://openalex.org/W2038591586","https://openalex.org/W4200633479","https://openalex.org/W2129691545","https://openalex.org/W1994663289","https://openalex.org/W4226303482"],"abstract_inverted_index":{"The":[0],"shape-from-shading":[1],"(SFS)":[2],"equation":[3,46,61],"relating":[4],"u(y,r),":[5],"the":[6,15,24,41,58,72,129,132,155],"unknown":[7],"(angular)":[8],"height":[9,50],"of":[10,89,101],"a":[11,77,122],"surface,":[12,25],"to":[13,54,95,121,131,151],"I(y,r),":[14],"known":[16],"synthetic":[17],"aperture":[18],"radar":[19,60,84,133],"(SAR)":[20],"intensity":[21,56,91],"data":[22],"from":[23],"is":[26,76],"I":[27,75],"=":[28],"\\frac{u_r^2}{\\sqrt{1+u_r^2+u_y^2}},":[29],"where":[30,74],"y":[31],"and":[32,36,138],"r":[33],"are":[34],"axial":[35],"radial":[37],"cylindrical":[38],"coordinates.":[39],"Unlike":[40],"more":[42],"common":[43,123,143],"eikonal":[44],"SFS":[45],"which":[47,80,125],"relates":[48],"surface":[49],"in":[51,83],"Cartesian":[52],"coordinates":[53],"optical/photographic":[55],"data,":[57],"above":[59],"can":[62],"be":[63],"transformed":[64],"into":[65],"Hamilton--Jacobi":[66],"Cauchy":[67],"form:":[68],"ur+g(I,uy)=0.":[69],"We":[70,104,111],"explore":[71],"case":[73],"discontinuous":[78],"function,":[79],"occurs":[81],"commonly":[82],"data.":[85],"By":[86],"considering":[87],"sequences":[88,100,108,119],"continuous":[90],"functions":[92],"that":[93,106,115,117,140],"converge":[94,120,150],"I,":[96],"we":[97,126,136],"obtain":[98],"corresponding":[99],"viscosity":[102],"solutions.":[103],"prove":[105],"these":[107,118],"must":[109,149],"converge.":[110],"also":[112],"establish":[113,137],"conditions":[114],"guarantee":[116],"limit,":[124],"define":[127],"as":[128,154],"solution":[130,153],"equation.":[134],"Finally,":[135],"demonstrate":[139],"when":[141],"this":[142,152],"limit":[144],"exists,":[145],"monotone":[146],"numerical":[147],"schemes":[148],"mesh":[156],"size":[157],"decreases.":[158]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
