{"id":"https://openalex.org/W7202351283","doi":"https://doi.org/10.1111/cgf.70525","title":"Attention Based Optimization for 3D Shape Registration","display_name":"Attention Based Optimization for 3D Shape Registration","publication_year":2026,"publication_date":"2026-08-13","ids":{"openalex":"https://openalex.org/W7202351283","doi":"https://doi.org/10.1111/cgf.70525"},"language":"en","primary_location":{"id":"doi:10.1111/cgf.70525","is_oa":true,"landing_page_url":"https://doi.org/10.1111/cgf.70525","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1111/cgf.70525","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147136023","display_name":"A. Riva","orcid":"https://orcid.org/0009-0007-0177-0604"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"A. Riva","raw_affiliation_strings":["University of Milano\u2010Bicocca  Italy"],"raw_orcid":"https://orcid.org/0009-0007-0177-0604","affiliations":[{"raw_affiliation_string":"University of Milano\u2010Bicocca  Italy","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5144147404","display_name":"Olearo L.","orcid":null},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"L. Olearo","raw_affiliation_strings":["University of Milano\u2010Bicocca  Italy"],"raw_orcid":"https://orcid.org/0009-0000-7290-3549","affiliations":[{"raw_affiliation_string":"University of Milano\u2010Bicocca  Italy","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039565429","display_name":"Simone Melzi","orcid":"https://orcid.org/0000-0003-2790-9591"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"S. Melzi","raw_affiliation_strings":["University of Milano\u2010Bicocca  Italy"],"raw_orcid":"https://orcid.org/0000-0003-2790-9591","affiliations":[{"raw_affiliation_string":"University of Milano\u2010Bicocca  Italy","institution_ids":["https://openalex.org/I66752286"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I66752286"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":{"value":3710,"currency":"USD","value_usd":3710},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.87782447,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9398000240325928,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9398000240325928,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.008500000461935997,"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/T12417","display_name":"Morphological variations and asymmetry","score":0.003599999938160181,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/exploit","display_name":"Exploit","score":0.8276000022888184},{"id":"https://openalex.org/keywords/transformer","display_name":"Transformer","score":0.7039999961853027},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.578000009059906},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.5595999956130981},{"id":"https://openalex.org/keywords/pipeline","display_name":"Pipeline (software)","score":0.49050000309944153},{"id":"https://openalex.org/keywords/geometry-processing","display_name":"Geometry processing","score":0.4083999991416931},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.38510000705718994},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.36800000071525574},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.35109999775886536}],"concepts":[{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.8276000022888184},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7835999727249146},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.7039999961853027},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.578000009059906},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5767999887466431},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.5595999956130981},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.49050000309944153},{"id":"https://openalex.org/C2779521785","wikidata":"https://www.wikidata.org/wiki/Q5535529","display_name":"Geometry processing","level":3,"score":0.4083999991416931},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.38510000705718994},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.37549999356269836},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.36800000071525574},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C123657996","wikidata":"https://www.wikidata.org/wiki/Q12271","display_name":"Architecture","level":2,"score":0.34549999237060547},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.33809998631477356},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C3019007443","wikidata":"https://www.wikidata.org/wiki/Q568742","display_name":"3d model","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.3142000138759613},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.30790001153945923},{"id":"https://openalex.org/C108882727","wikidata":"https://www.wikidata.org/wiki/Q2991685","display_name":"Solid modeling","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C175309249","wikidata":"https://www.wikidata.org/wiki/Q725864","display_name":"Pipeline transport","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.29100000858306885},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C52622490","wikidata":"https://www.wikidata.org/wiki/Q1026626","display_name":"Feature extraction","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C129641003","wikidata":"https://www.wikidata.org/wiki/Q267189","display_name":"Active shape model","level":3,"score":0.2802000045776367},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.26190000772476196},{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.2606000006198883},{"id":"https://openalex.org/C112604564","wikidata":"https://www.wikidata.org/wiki/Q7489226","display_name":"Shape analysis (program analysis)","level":3,"score":0.25519999861717224}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1111/cgf.70525","is_oa":true,"landing_page_url":"https://doi.org/10.1111/cgf.70525","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1111/cgf.70525","is_oa":true,"landing_page_url":"https://doi.org/10.1111/cgf.70525","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321610","display_name":"Universit\u00e0 degli Studi di Milano-Bicocca","ror":"https://ror.org/01ynf4891"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W2047161559","https://openalex.org/W2050204708","https://openalex.org/W2091791686","https://openalex.org/W2100657858","https://openalex.org/W2555859288","https://openalex.org/W2585039351","https://openalex.org/W2619671517","https://openalex.org/W2786201971","https://openalex.org/W2805390168","https://openalex.org/W2963653041","https://openalex.org/W2987431950","https://openalex.org/W3049594084","https://openalex.org/W3083261328","https://openalex.org/W3087291937","https://openalex.org/W3119708198","https://openalex.org/W3127333286","https://openalex.org/W3159359216","https://openalex.org/W3159926201","https://openalex.org/W3193639655","https://openalex.org/W3199042658","https://openalex.org/W4214612132","https://openalex.org/W4312788538","https://openalex.org/W4313045638","https://openalex.org/W4313143242","https://openalex.org/W4375929246","https://openalex.org/W4386065784","https://openalex.org/W4388979610","https://openalex.org/W4399769808","https://openalex.org/W4402667891","https://openalex.org/W4402704536","https://openalex.org/W4405128543","https://openalex.org/W4412673776","https://openalex.org/W4415798239","https://openalex.org/W7133184786","https://openalex.org/W7133236665","https://openalex.org/W7196929644"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Transformers":[1],"are":[2],"sequence\u2010to\u2010sequence":[3],"architectures":[4],"originally":[5],"designed":[6],"to":[7,41,92,120,124,196],"handle":[8],"structurally":[9],"rigid":[10],"and":[11,17,30,60,126,142,152,186],"order\u2010sensitive":[12],"data,":[13],"such":[14,52],"as":[15,53,69,80,149,174,213],"text":[16],"images.":[18],"At":[19],"their":[20],"core,":[21],"they":[22],"exploit":[23,169],"the":[24,78,89,99,114,131,162,166,170,175,210],"attention":[25,117,197],"mechanism,":[26],"which":[27],"is":[28],"permutation\u2010equivariant":[29],"relies":[31],"on":[32,113],"computing":[33],"token\u2010to\u2010token":[34,122],"relationships.":[35],"These":[36],"models":[37],"have":[38],"been":[39],"applied":[40],"3D":[42,64,200],"geometry":[43,65],"in":[44],"several":[45],"instances,":[46],"achieving":[47],"discrete":[48],"success":[49],"across":[50],"tasks":[51],"shape":[54,58,85,94,184,218],"generation,":[55],"segmentation,":[56],"classification,":[57],"matching,":[59],"registration.":[61],"While":[62],"existing":[63],"methods":[66],"use":[67,115],"transformers":[68],"traditional":[70],"learners,":[71],"we":[72,111,168],"present":[73],"an":[74,81,206,214],"approach":[75,195,207],"that":[76,140,208],"reinterprets":[77],"transformer":[79,211],"optimization":[82],"pipeline":[83,216],"for":[84,101,198,217],"correspondence.":[86],"By":[87],"fitting":[88],"model":[90],"directly":[91,173],"a":[93,106,191],"pair,":[95],"our":[96,203],"method":[97],"eliminates":[98],"need":[100],"large":[102],"training":[103,225],"datasets,":[104],"providing":[105],"category\u2010agnostic":[107],"solution.":[108],"In":[109],"particular,":[110],"focus":[112],"of":[116,133,158,165],"weights,":[118],"tailored":[119],"encode":[121],"information,":[123],"inject":[125],"extract":[127],"point\u2010to\u2010point":[128],"information":[129],"during":[130],"processing":[132],"one":[134],"or":[135],"more":[136],"meshes.":[137],"We":[138],"demonstrate,":[139],"self\u2010":[141],"cross\u2010attention":[143,171],"mechanisms":[144],"can,":[145],"by":[146],"design,":[147],"serve":[148],"feature":[150],"extractors":[151],"matching":[153,185],"solvers,":[154],"respectively.":[155],"Furthermore,":[156],"instead":[157],"deriving":[159],"correspondence":[160],"from":[161],"final":[163],"output":[164],"network,":[167],"weights":[172],"permutation":[176],"matrix.":[177],"This":[178],"framework":[179],"not":[180],"only":[181],"achieves":[182],"robust":[183],"registration":[187],"but":[188],"also":[189],"provides":[190],"theoretically":[192],"grounded,":[193],"interpretable":[194],"unstructured":[199],"data.":[201,226],"Notably,":[202],"work":[204],"represents":[205],"leverages":[209],"architecture":[212],"end\u2010to\u2010end":[215],"correspondence,":[219],"operating":[220],"effectively":[221],"without":[222],"requiring":[223],"additional":[224]},"counts_by_year":[],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2026-08-14T00:00:00"}
