{"id":"https://openalex.org/W2500830068","doi":"https://doi.org/10.1080/13658816.2016.1162795","title":"Bias estimation and correction for triangle-based surface area calculations","display_name":"Bias estimation and correction for triangle-based surface area calculations","publication_year":2016,"publication_date":"2016-08-05","ids":{"openalex":"https://openalex.org/W2500830068","doi":"https://doi.org/10.1080/13658816.2016.1162795","mag":"2500830068"},"language":"en","primary_location":{"id":"doi:10.1080/13658816.2016.1162795","is_oa":false,"landing_page_url":"https://doi.org/10.1080/13658816.2016.1162795","pdf_url":null,"source":{"id":"https://openalex.org/S4210181446","display_name":"International Journal of Geographical Information Systems","issn_l":"0269-3798","issn":["0269-3798","1362-3087"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Geographical Information Science","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/A5073150732","display_name":"Shuqiang Xue","orcid":"https://orcid.org/0000-0001-8389-0085"},"institutions":[{"id":"https://openalex.org/I4210114963","display_name":"Chinese Academy of Surveying and Mapping","ror":"https://ror.org/02j693n47","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210114963"]},{"id":"https://openalex.org/I25355098","display_name":"Chang'an University","ror":"https://ror.org/05mxya461","country_code":"CN","type":"education","lineage":["https://openalex.org/I25355098"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuqiang Xue","raw_affiliation_strings":[",","Chinese Academy of Surveying and Mapping, Beijing, China","School of Geological and Surveying Engineering, Chang'an University, Xi'an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":",","institution_ids":[]},{"raw_affiliation_string":"Chinese Academy of Surveying and Mapping, Beijing, China","institution_ids":["https://openalex.org/I4210114963"]},{"raw_affiliation_string":"School of Geological and Surveying Engineering, Chang'an University, Xi'an, China","institution_ids":["https://openalex.org/I25355098"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111995588","display_name":"Yamin Dang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114963","display_name":"Chinese Academy of Surveying and Mapping","ror":"https://ror.org/02j693n47","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210114963"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yamin Dang","raw_affiliation_strings":["Chinese Academy of Surveying and Mapping, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese Academy of Surveying and Mapping, Beijing, China","institution_ids":["https://openalex.org/I4210114963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109448683","display_name":"Jiping Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114963","display_name":"Chinese Academy of Surveying and Mapping","ror":"https://ror.org/02j693n47","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210114963"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiping Liu","raw_affiliation_strings":["Chinese Academy of Surveying and Mapping, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese Academy of Surveying and Mapping, Beijing, China","institution_ids":["https://openalex.org/I4210114963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112861041","display_name":"Jinzhong Mi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114963","display_name":"Chinese Academy of Surveying and Mapping","ror":"https://ror.org/02j693n47","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210114963"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinzhong Mi","raw_affiliation_strings":["Chinese Academy of Surveying and Mapping, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese Academy of Surveying and Mapping, Beijing, China","institution_ids":["https://openalex.org/I4210114963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104271270","display_name":"Chun Dong","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114963","display_name":"Chinese Academy of Surveying and Mapping","ror":"https://ror.org/02j693n47","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210114963"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chun Dong","raw_affiliation_strings":["Chinese Academy of Surveying and Mapping, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese Academy of Surveying and Mapping, Beijing, China","institution_ids":["https://openalex.org/I4210114963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110209225","display_name":"Yingyan Cheng","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114963","display_name":"Chinese Academy of Surveying and Mapping","ror":"https://ror.org/02j693n47","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210114963"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yingyan Cheng","raw_affiliation_strings":["Chinese Academy of Surveying and Mapping, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese Academy of Surveying and Mapping, Beijing, China","institution_ids":["https://openalex.org/I4210114963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039772620","display_name":"Xiaoqing Wang","orcid":"https://orcid.org/0000-0002-6660-8030"},"institutions":[{"id":"https://openalex.org/I4210141849","display_name":"National Administration of Surveying, Mapping and Geoinformation of China","ror":"https://ror.org/04z3map19","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210141849"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoqing Wang","raw_affiliation_strings":["National Geomatics Center of China, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Geomatics Center of China, Beijing, China","institution_ids":["https://openalex.org/I4210141849"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101836015","display_name":"Jun Wan","orcid":"https://orcid.org/0000-0003-0174-1145"},"institutions":[{"id":"https://openalex.org/I4210114963","display_name":"Chinese Academy of Surveying and Mapping","ror":"https://ror.org/02j693n47","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210114963"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Wan","raw_affiliation_strings":["Chinese Academy of Surveying and Mapping, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese Academy of Surveying and Mapping, Beijing, China","institution_ids":["https://openalex.org/I4210114963"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111995588"],"corresponding_institution_ids":["https://openalex.org/I4210114963"],"apc_list":null,"apc_paid":null,"fwci":1.7828,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.83449211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"30","issue":"11","first_page":"2155","last_page":"2170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10770","display_name":"Soil Geostatistics and Mapping","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12698","display_name":"3D Modeling in Geospatial Applications","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"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/monte-carlo-method","display_name":"Monte Carlo method","score":0.7134822607040405},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.6305484771728516},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.5639012455940247},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5084394812583923},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4976547062397003},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4737853705883026},{"id":"https://openalex.org/keywords/triangulated-irregular-network","display_name":"Triangulated irregular network","score":0.43712061643600464},{"id":"https://openalex.org/keywords/observational-error","display_name":"Observational error","score":0.4228725731372833},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4094299376010895},{"id":"https://openalex.org/keywords/digital-elevation-model","display_name":"Digital elevation model","score":0.3346777856349945},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2324066162109375},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.16854894161224365},{"id":"https://openalex.org/keywords/remote-sensing","display_name":"Remote sensing","score":0.16319015622138977},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12746527791023254}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.7134822607040405},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.6305484771728516},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5639012455940247},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5084394812583923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4976547062397003},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4737853705883026},{"id":"https://openalex.org/C131509275","wikidata":"https://www.wikidata.org/wiki/Q2296387","display_name":"Triangulated irregular network","level":3,"score":0.43712061643600464},{"id":"https://openalex.org/C19619285","wikidata":"https://www.wikidata.org/wiki/Q196372","display_name":"Observational error","level":2,"score":0.4228725731372833},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4094299376010895},{"id":"https://openalex.org/C181843262","wikidata":"https://www.wikidata.org/wiki/Q640492","display_name":"Digital elevation model","level":2,"score":0.3346777856349945},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2324066162109375},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.16854894161224365},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"score":0.16319015622138977},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12746527791023254},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/13658816.2016.1162795","is_oa":false,"landing_page_url":"https://doi.org/10.1080/13658816.2016.1162795","pdf_url":null,"source":{"id":"https://openalex.org/S4210181446","display_name":"International Journal of Geographical Information Systems","issn_l":"0269-3798","issn":["0269-3798","1362-3087"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Geographical Information Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5627956924","display_name":null,"funder_award_id":"41504020","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7406939605","display_name":"\u5b9a\u4f4d\u65b9\u7a0b\u975e\u7ebf\u6027\u5e73\u5dee\u4e0e(\u52a8\u6001)\u5b9a\u4f4d\u6784\u578b\u7814\u7a76","funder_award_id":"41104018","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W63280359","https://openalex.org/W156823488","https://openalex.org/W182452766","https://openalex.org/W603018635","https://openalex.org/W1506818537","https://openalex.org/W1545396084","https://openalex.org/W1682212122","https://openalex.org/W1846598612","https://openalex.org/W1965544000","https://openalex.org/W1968728426","https://openalex.org/W1998935517","https://openalex.org/W2001891730","https://openalex.org/W2005575398","https://openalex.org/W2015446807","https://openalex.org/W2015450134","https://openalex.org/W2016241235","https://openalex.org/W2024058386","https://openalex.org/W2032748399","https://openalex.org/W2036583159","https://openalex.org/W2037322760","https://openalex.org/W2062328845","https://openalex.org/W2081215147","https://openalex.org/W2085235746","https://openalex.org/W2085715291","https://openalex.org/W2090265020","https://openalex.org/W2094168997","https://openalex.org/W2114746181","https://openalex.org/W2117662933","https://openalex.org/W2119534769","https://openalex.org/W2122884007","https://openalex.org/W2124475118","https://openalex.org/W2127695578","https://openalex.org/W2134248412","https://openalex.org/W2142959563","https://openalex.org/W2178700827","https://openalex.org/W2365480673","https://openalex.org/W2373795654","https://openalex.org/W2502455623","https://openalex.org/W2602444692","https://openalex.org/W2903571355","https://openalex.org/W3201423827","https://openalex.org/W4231126268","https://openalex.org/W4237198128","https://openalex.org/W4241924757","https://openalex.org/W4247834712"],"related_works":["https://openalex.org/W2188653007","https://openalex.org/W3151972826","https://openalex.org/W2951077607","https://openalex.org/W3150210773","https://openalex.org/W4292583799","https://openalex.org/W1514009816","https://openalex.org/W2754066691","https://openalex.org/W2808790646","https://openalex.org/W1765347834","https://openalex.org/W3028282378"],"abstract_inverted_index":{"The":[0,142,236],"calculation":[1],"of":[2,10,16,23,219],"surface":[3,35,41,56,63,88,104,124,221,256,270],"area":[4,22,36,57,64,125,222,257,271],"is":[5,65,70,144,208],"meaningful":[6],"for":[7],"a":[8,39,71,92,119,148,171,182,200],"variety":[9],"space-filling":[11],"phenomena,":[12],"e.g.,":[13],"the":[14,34,46,54,62,75,84,87,102,110,114,122,127,131,139,159,163,176,196,212,217,220,229,232,242,248,263,268,275],"packing":[15],"plants":[17],"or":[18],"animals":[19],"within":[20],"an":[21,254],"land.":[24],"With":[25],"Digital":[26],"Elevation":[27],"Model":[28],"(DEM)":[29],"data":[30,77,116,133],"we":[31,90,190],"can":[32,134,152,223,258],"calculate":[33],"by":[37,45,96,137,147,155,227,241,247,261],"using":[38,138],"continuous":[40],"model,":[42],"such":[43],"as":[44,53],"Triangulated":[47],"Irregular":[48],"Network":[49],"(TIN).":[50],"However,":[51],"just":[52],"triangle-based":[55,103,123,269],"discussed":[58],"in":[59,86,113,118,121,130],"this":[60],"paper,":[61],"generally":[66],"biased":[67],"because":[68],"it":[69],"nonlinear":[72,98,205],"mapping":[73],"about":[74,175],"DEM":[76,115,132,177,276],"which":[78,151],"contain":[79],"measurement":[80,178,197],"errors.":[81],"To":[82],"reduce":[83],"bias":[85,94,120,143,201,214,230,265],"area,":[89],"propose":[91],"second-order":[93,213],"correction":[95],"applying":[97],"error":[99,206],"propagation":[100,207],"to":[101],"area.":[105],"This":[106],"process":[107],"reveals":[108],"that":[109,253],"random":[111],"errors":[112,129],"result":[117],"while":[126],"systematic":[128],"be":[135,153,224,259],"reduced":[136],"height":[140],"differences.":[141],"theoretically":[145],"given":[146],"probability":[149],"integral":[150,161],"approximated":[154],"numerical":[156,160,249],"approaches":[157,169],"including":[158],"and":[162,180,246],"Monte":[164,243],"Carlo":[165,244],"method;":[166],"but":[167],"these":[168],"need":[170],"theoretical":[172],"distribution":[173],"assumption":[174],"errors,":[179],"have":[181,192],"very":[183],"high":[184],"computational":[185],"cost.":[186],"In":[187],"most":[188],"cases,":[189],"only":[191],"variance":[193,218,234],"information":[194],"on":[195,204,211],"errors;":[198],"thus,":[199],"estimation":[202,215,266],"based":[203],"proposed.":[209],"Based":[210],"proposed,":[216],"improved":[225],"immediately":[226],"removing":[228,262],"from":[231,267,274],"original":[233],"estimation.":[235],"main":[237],"results":[238],"are":[239],"verified":[240],"method":[245],"integral.":[250],"They":[251],"show":[252],"unbiased":[255],"obtained":[260],"proposed":[264],"originally":[272],"calculated":[273],"data.":[277]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2}],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2025-10-10T00:00:00"}