{"id":"https://openalex.org/W2035997109","doi":"https://doi.org/10.1109/tim.2011.2157720","title":"Experimental Verification of Formulas for Variances of Plane Parameters Fitted to Three-Dimensional Imaging Data","display_name":"Experimental Verification of Formulas for Variances of Plane Parameters Fitted to Three-Dimensional Imaging Data","publication_year":2011,"publication_date":"2011-07-07","ids":{"openalex":"https://openalex.org/W2035997109","doi":"https://doi.org/10.1109/tim.2011.2157720","mag":"2035997109"},"language":"en","primary_location":{"id":"doi:10.1109/tim.2011.2157720","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2011.2157720","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Instrumentation and Measurement","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/A5035875846","display_name":"Marek Franaszek","orcid":"https://orcid.org/0000-0003-4665-9268"},"institutions":[{"id":"https://openalex.org/I1321296531","display_name":"National Institute of Standards and Technology","ror":"https://ror.org/05xpvk416","country_code":"US","type":"funder","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marek Franaszek","raw_affiliation_strings":["National Institute of Standards and Technology, Gaithersburg, MD, USA","Nat. Inst. of Stand. & Technol., Gaithersburg, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Institute of Standards and Technology, Gaithersburg, MD, USA","institution_ids":["https://openalex.org/I1321296531"]},{"raw_affiliation_string":"Nat. Inst. of Stand. & Technol., Gaithersburg, MD, USA","institution_ids":["https://openalex.org/I1321296531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033670735","display_name":"Geraldine S. Cheok","orcid":"https://orcid.org/0000-0001-8335-1743"},"institutions":[{"id":"https://openalex.org/I1321296531","display_name":"National Institute of Standards and Technology","ror":"https://ror.org/05xpvk416","country_code":"US","type":"funder","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Geraldine S. Cheok","raw_affiliation_strings":["National Institute of Standards and Technology, Gaithersburg, MD, USA","Nat. Inst. of Stand. & Technol., Gaithersburg, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Institute of Standards and Technology, Gaithersburg, MD, USA","institution_ids":["https://openalex.org/I1321296531"]},{"raw_affiliation_string":"Nat. Inst. of Stand. & Technol., Gaithersburg, MD, USA","institution_ids":["https://openalex.org/I1321296531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072852232","display_name":"Kamel Saidi","orcid":"https://orcid.org/0000-0002-0098-7904"},"institutions":[{"id":"https://openalex.org/I1321296531","display_name":"National Institute of Standards and Technology","ror":"https://ror.org/05xpvk416","country_code":"US","type":"funder","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kamel S. Saidi","raw_affiliation_strings":["National Institute of Standards and Technology, Gaithersburg, MD, USA","Nat. Inst. of Stand. & Technol., Gaithersburg, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Institute of Standards and Technology, Gaithersburg, MD, USA","institution_ids":["https://openalex.org/I1321296531"]},{"raw_affiliation_string":"Nat. Inst. of Stand. & Technol., Gaithersburg, MD, USA","institution_ids":["https://openalex.org/I1321296531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1321296531"],"apc_list":null,"apc_paid":null,"fwci":0.5149,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.67994875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"61","issue":"1","first_page":"103","last_page":"110"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10638","display_name":"Optical measurement and interference techniques","score":0.9976000189781189,"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/T10638","display_name":"Optical measurement and interference techniques","score":0.9976000189781189,"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/T12019","display_name":"Calibration and Measurement Techniques","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/T11583","display_name":"Advanced Measurement and Metrology Techniques","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/mathematics","display_name":"Mathematics","score":0.6625553369522095},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5475930571556091},{"id":"https://openalex.org/keywords/standard-deviation","display_name":"Standard deviation","score":0.5413849353790283},{"id":"https://openalex.org/keywords/non-linear-least-squares","display_name":"Non-linear least squares","score":0.5071871280670166},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5022034645080566},{"id":"https://openalex.org/keywords/data-set","display_name":"Data set","score":0.47899577021598816},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.4502057135105133},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4486897587776184},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4384566843509674},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40597301721572876},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.3591602146625519},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20111113786697388}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6625553369522095},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5475930571556091},{"id":"https://openalex.org/C22679943","wikidata":"https://www.wikidata.org/wiki/Q159375","display_name":"Standard deviation","level":2,"score":0.5413849353790283},{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.5071871280670166},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5022034645080566},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.47899577021598816},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.4502057135105133},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4486897587776184},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4384566843509674},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40597301721572876},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3591602146625519},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20111113786697388},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tim.2011.2157720","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tim.2011.2157720","pdf_url":null,"source":{"id":"https://openalex.org/S10892749","display_name":"IEEE Transactions on Instrumentation and Measurement","issn_l":"0018-9456","issn":["0018-9456","1557-9662"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Instrumentation and Measurement","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W326804598","https://openalex.org/W1413993273","https://openalex.org/W1501188762","https://openalex.org/W2022480405","https://openalex.org/W2041303354","https://openalex.org/W2105285489","https://openalex.org/W2125996276","https://openalex.org/W2140649816","https://openalex.org/W2165657894","https://openalex.org/W2315214008","https://openalex.org/W2320962057","https://openalex.org/W2498000451","https://openalex.org/W2608909760","https://openalex.org/W2784917123","https://openalex.org/W2785051599","https://openalex.org/W2793192660","https://openalex.org/W4242841269","https://openalex.org/W4285719527","https://openalex.org/W4300945981","https://openalex.org/W6611341176","https://openalex.org/W6629757974","https://openalex.org/W6680862331","https://openalex.org/W6723672520","https://openalex.org/W6737014416","https://openalex.org/W6747572719","https://openalex.org/W6748280388","https://openalex.org/W6749424742"],"related_works":["https://openalex.org/W2026673180","https://openalex.org/W1959514624","https://openalex.org/W200101083","https://openalex.org/W2939592218","https://openalex.org/W2359835307","https://openalex.org/W327962130","https://openalex.org/W1997338499","https://openalex.org/W2589353378","https://openalex.org/W4378552425","https://openalex.org/W4380487384"],"abstract_inverted_index":{"Nonlinear":[0],"least":[1],"squares":[2],"method":[3],"is":[4,59,143],"applied":[5],"to":[6,10,61,92],"fit":[7],"a":[8,34,134],"plane":[9,127],"3-D":[11],"imaging":[12],"data.":[13],"Two":[14],"different":[15],"error":[16,78,108],"functions":[17],"used":[18],"in":[19,111,156],"fitting":[20],"are":[21,30,110,140,152],"tested:":[22],"orthogonal":[23,77],"and":[24],"directional.":[25],"Variances":[26],"of":[27,64,124],"fitted":[28,126],"parameters":[29],"calculated":[31,84,95,101,117],"either":[32],"from":[33,68,96,102,118,133,148],"single":[35,135],"data":[36],"set":[37],"using":[38,86],"derived":[39],"earlier":[40],"analytical":[41],"formulas":[42,89,103,139],"or":[43],"by":[44,85],"repeating":[45],"the":[46,49,54,57,62,65,69,76,82,87,93,106,115,122,125,149,157],"scans":[47,147],"at":[48],"same":[50,150],"experimental":[51],"settings.":[52],"In":[53],"latter":[55],"case,":[56],"variance":[58],"equal":[60],"square":[63],"standard":[66],"deviation":[67],"repeated":[70],"scans.":[71,98,120],"The":[72,99],"results":[73],"show":[74],"that":[75],"function":[79,109],"severely":[80],"underestimates":[81],"variances":[83,94,100,123],"mathematical":[88],"when":[90,137],"compared":[91],"multiple":[97,119,146],"based":[104],"on":[105],"directional":[107],"good":[112],"agreement":[113],"with":[114],"estimates":[116],"Thus,":[121],"parameter":[128],"can":[129],"be":[130],"determined":[131],"correctly":[132],"scan":[136],"proper":[138],"used.":[141],"This":[142],"important":[144],"because":[145],"location":[151],"typically":[153],"not":[154],"performed":[155],"field.":[158]},"counts_by_year":[{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
