{"id":"https://openalex.org/W2977825555","doi":"https://doi.org/10.1109/isbi.2009.5193127","title":"4th order diffusion tensor interpolationwith divergence and curl constrained Bézier patches","display_name":"4th order diffusion tensor interpolationwith divergence and curl constrained Bézier patches","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2977825555","doi":"https://doi.org/10.1109/isbi.2009.5193127","mag":"2977825555"},"language":"en","primary_location":{"id":"doi:10.1109/isbi.2009.5193127","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isbi.2009.5193127","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro","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/A5028367824","display_name":"Inas A. Yassine","orcid":"https://orcid.org/0000-0003-1268-1555"},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Inas Yassine","raw_affiliation_strings":["Department of Computer Science and Electrical Engineering, West Virginia University, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Electrical Engineering, West Virginia University, USA","institution_ids":["https://openalex.org/I12097938"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090346230","display_name":"Tim McGraw","orcid":"https://orcid.org/0000-0001-6704-6351"},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tim McGraw","raw_affiliation_strings":["Department of Computer Science and Electrical Engineering, West Virginia University, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Electrical Engineering, West Virginia University, USA","institution_ids":["https://openalex.org/I12097938"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028367824"],"corresponding_institution_ids":["https://openalex.org/I12097938"],"apc_list":null,"apc_paid":null,"fwci":0.7004,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.75486592,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"56","issue":null,"first_page":"634","last_page":"637"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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/T10514","display_name":"Numerical methods in engineering","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10842","display_name":"Railway Engineering and Dynamics","score":0.95169997215271,"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/curl","display_name":"Curl (programming language)","score":0.6496309041976929},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6203916668891907},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6061838865280151},{"id":"https://openalex.org/keywords/tensor-field","display_name":"Tensor field","score":0.5869238376617432},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5567198991775513},{"id":"https://openalex.org/keywords/trilinear-interpolation","display_name":"Trilinear interpolation","score":0.5335123538970947},{"id":"https://openalex.org/keywords/cartesian-tensor","display_name":"Cartesian tensor","score":0.49046966433525085},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46734172105789185},{"id":"https://openalex.org/keywords/b\u00e9zier-curve","display_name":"B\u00e9zier curve","score":0.43496280908584595},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.42165905237197876},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40654119849205017},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.399189829826355},{"id":"https://openalex.org/keywords/tensor-density","display_name":"Tensor density","score":0.30867624282836914},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.2811368703842163},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2588736116886139},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.247187077999115},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22667327523231506},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08610370755195618}],"concepts":[{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.6496309041976929},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6203916668891907},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6061838865280151},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.5869238376617432},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5567198991775513},{"id":"https://openalex.org/C188325010","wikidata":"https://www.wikidata.org/wiki/Q861176","display_name":"Trilinear interpolation","level":4,"score":0.5335123538970947},{"id":"https://openalex.org/C64835786","wikidata":"https://www.wikidata.org/wiki/Q17004583","display_name":"Cartesian tensor","level":5,"score":0.49046966433525085},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46734172105789185},{"id":"https://openalex.org/C206423108","wikidata":"https://www.wikidata.org/wiki/Q214728","display_name":"B\u00e9zier curve","level":2,"score":0.43496280908584595},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.42165905237197876},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40654119849205017},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.399189829826355},{"id":"https://openalex.org/C148125525","wikidata":"https://www.wikidata.org/wiki/Q904927","display_name":"Tensor density","level":4,"score":0.30867624282836914},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.2811368703842163},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2588736116886139},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.247187077999115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22667327523231506},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08610370755195618},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isbi.2009.5193127","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isbi.2009.5193127","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1598557217","https://openalex.org/W1974849326","https://openalex.org/W1982675814","https://openalex.org/W1983052403","https://openalex.org/W1983496390","https://openalex.org/W2008025478","https://openalex.org/W2034966370","https://openalex.org/W2059640215","https://openalex.org/W2080065527","https://openalex.org/W2080626790","https://openalex.org/W2098549404","https://openalex.org/W2105595170","https://openalex.org/W2154869678","https://openalex.org/W2168108268","https://openalex.org/W4256688787","https://openalex.org/W6635900159"],"related_works":["https://openalex.org/W1965338607","https://openalex.org/W2403348579","https://openalex.org/W2981910625","https://openalex.org/W2186765725","https://openalex.org/W1990592457","https://openalex.org/W4360921185","https://openalex.org/W2785941732","https://openalex.org/W2765690628","https://openalex.org/W2607194831","https://openalex.org/W4320026073"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,56,77],"tensor":[3,36],"field":[4,27],"interpolation":[5,75],"method":[6,39],"based":[7],"on":[8,24],"tensor-valued":[9],"Bezier":[10],"patches.":[11],"The":[12,38],"control":[13,50],"points":[14,51],"of":[15,34,44,55],"the":[16,25,30,35,49,53],"patch":[17],"are":[18,61,71],"determined":[19],"by":[20,28],"imposing":[21],"physical":[22],"constraints":[23],"interpolated":[26],"constraining":[29],"divergence":[31],"and":[32,66,69,76],"curl":[33],"field.":[37],"generalizes":[40],"to":[41],"Cartesian":[42],"tensors":[43,68],"all":[45],"orders.":[46],"Solving":[47],"for":[48,63],"requires":[52],"solution":[54],"sparse":[57],"linear":[58,74],"system.":[59],"Results":[60],"presented":[62],"order":[64],"2":[65],"4":[67],"comparisons":[70],"made":[72],"with":[73],"previously":[78],"proposed":[79],"subdivision":[80],"scheme.":[81]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}