{"id":"https://openalex.org/W2113945082","doi":"https://doi.org/10.1109/iccv.2007.4409142","title":"Fast Invariant Riemannian DT-MRI Regularization","display_name":"Fast Invariant Riemannian DT-MRI Regularization","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2113945082","doi":"https://doi.org/10.1109/iccv.2007.4409142","mag":"2113945082"},"language":"en","primary_location":{"id":"doi:10.1109/iccv.2007.4409142","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iccv.2007.4409142","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE 11th 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/A5027868086","display_name":"Yaniv Gur","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Yaniv Gur","raw_affiliation_strings":["Department of Applied Mathematics, Tel-Aviv University, Tel-Aviv, Israel","Tel Aviv University Tel Aviv"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Tel-Aviv University, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University Tel Aviv","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030076264","display_name":"Nir Sochen","orcid":"https://orcid.org/0000-0001-7805-5560"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Nir Sochen","raw_affiliation_strings":["Department of Applied Mathematics, Tel-Aviv University, Tel-Aviv, Israel","Tel Aviv University Tel Aviv"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Tel-Aviv University, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University Tel Aviv","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027868086"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":1.416,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.82360896,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"4485","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6188636422157288},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5305042266845703},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.44407832622528076},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4263330101966858},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.42037859559059143},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30705133080482483},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.10971274971961975}],"concepts":[{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6188636422157288},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5305042266845703},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.44407832622528076},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4263330101966858},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42037859559059143},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30705133080482483},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.10971274971961975},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iccv.2007.4409142","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iccv.2007.4409142","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE 11th International Conference on Computer Vision","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":24,"referenced_works":["https://openalex.org/W572198187","https://openalex.org/W620218924","https://openalex.org/W1506743325","https://openalex.org/W1508718704","https://openalex.org/W1525296983","https://openalex.org/W1549842019","https://openalex.org/W1555486060","https://openalex.org/W1588783123","https://openalex.org/W1604713470","https://openalex.org/W1887970033","https://openalex.org/W1983496390","https://openalex.org/W2008025478","https://openalex.org/W2026366832","https://openalex.org/W2028402761","https://openalex.org/W2112473379","https://openalex.org/W2164355691","https://openalex.org/W2612417255","https://openalex.org/W3038054700","https://openalex.org/W4210919084","https://openalex.org/W4242893675","https://openalex.org/W6619527138","https://openalex.org/W6631724637","https://openalex.org/W6737448088","https://openalex.org/W7000931787"],"related_works":["https://openalex.org/W1978572805","https://openalex.org/W2383807498","https://openalex.org/W1997992934","https://openalex.org/W1987225439","https://openalex.org/W4238188170","https://openalex.org/W2125114371","https://openalex.org/W2019977573","https://openalex.org/W2149980199","https://openalex.org/W3125766170","https://openalex.org/W2040641410"],"abstract_inverted_index":{"We":[0,75,171],"present":[1],"regularization":[2],"by":[3,160,174],"invariant":[4,167,224],"denoising/smoothing":[5],"of":[6,22,43,51,53,85,104,113,145,157,162,169,198,208],"Diffusion":[7],"Tensor":[8],"MRI":[9],"(DTI).":[10],"Our":[11],"solution":[12],"to":[13,71,195],"the":[14,28,49,77,96,105,114,146,155,166,176,179,185,196,199,202,235],"problem":[15],"emerges":[16],"from":[17],"a":[18,37,60,64,91,139,151,221],"pure":[19],"geometric":[20],"point":[21],"view.":[23],"The":[24,41,205,218],"image":[25,58],"domain":[26],"and":[27,34,67,89,130,232],"image's":[29],"values":[30],"are":[31],"combined":[32],"together":[33],"described":[35],"as":[36,182,184,230,234],"(mathematical)":[38],"fiber":[39,55,106],"bundle.":[40,56],"space":[42,50,80,156],"all":[44],"possible":[45],"DT":[46,57],"images":[47],"is":[48,59,108,216,220,227],"sections":[52,103],"this":[54,241],"map":[61],"that":[62,173],"attaches":[63],"three-dimensional":[65],"symmetric":[66,141],"positive-definite":[68],"(SPD)":[69],"matrix":[70],"each":[72],"volume":[73],"element.":[74],"treat":[76],"more":[78],"general":[79,132],"P":[81,118,125,133],"<sub":[82,119,126,134],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[83,120,127,135],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sub>":[84,121,136],"n-dimensional":[86],"SPD":[87],"matrices":[88],"introduce":[90],"natural":[92,115],"GL(n)-invariant":[93,152],"metric":[94,101,116],"via":[95,201,211],"underlying":[97],"algebraic":[98],"structure.":[99],"A":[100],"over":[102,154],"bundle":[107],"induced":[109,203],"then":[110],"in":[111,131],"terms":[112],"on":[117,243],".":[122],"This":[123],"turns":[124],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">3</sub>":[128],"tensors,":[129,137],"into":[138],"Riemannian":[140],"spaces.":[142],"By":[143],"means":[144],"Beltrami":[147],"framework":[148,242],"we":[149,164,239],"define":[150],"functional":[153],"sections.":[158],"Then,":[159],"calculus":[161],"variations":[163],"derive":[165],"equations":[168],"motion.":[170],"show":[172],"choosing":[175],"Iwasawa":[177],"coordinates":[178,191],"analytical":[180],"calculations":[181],"well":[183],"numerical":[186,206],"implementation":[187,207],"become":[188],"simple.":[189],"These":[190],"evolve":[192],"with":[193],"respect":[194],"geometry":[197],"section":[200],"metric.":[204],"these":[209],"flows":[210],"standard":[212],"finite":[213],"difference":[214],"schemes":[215],"straightforward.":[217],"result":[219],"full":[222],"GL(n)":[223],"algorithm":[225],"which":[226],"at":[228],"least":[229],"fast":[231],"efficient":[233],"Log-Euclidean":[236],"method.":[237],"Finally,":[238],"demonstrate":[240],"real":[244],"DTI":[245],"data.":[246]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
