{"id":"https://openalex.org/W6963969524","doi":"https://doi.org/10.2312/stag.20221253","title":"PC-GAU: PCA Basis of Scattered Gaussians for Shape Matching via Functional Maps","display_name":"PC-GAU: PCA Basis of Scattered Gaussians for Shape Matching via Functional Maps","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W6963969524","doi":"https://doi.org/10.2312/stag.20221253"},"language":"en","primary_location":{"id":"pmh:oai:boa.unimib.it:10281/495359","is_oa":false,"landing_page_url":"https://hdl.handle.net/10281/495359","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2312/stag.20221253","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Colombo, Michele","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Colombo, Michele","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Boracchi, Giacomo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Boracchi, Giacomo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Melzi, Simone","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Melzi, Simone","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.57096774,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.68804392,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T12713","display_name":"Forest Ecology and Biodiversity Studies","score":0.1753000020980835,"subfield":{"id":"https://openalex.org/subfields/1109","display_name":"Insect Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12713","display_name":"Forest Ecology and Biodiversity Studies","score":0.1753000020980835,"subfield":{"id":"https://openalex.org/subfields/1109","display_name":"Insect Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11753","display_name":"Forest Management and Policy","score":0.13230000436306,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"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/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.08049999922513962,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.7616999745368958},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.59170001745224},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.5899999737739563},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5841000080108643},{"id":"https://openalex.org/keywords/shape-analysis","display_name":"Shape analysis (program analysis)","score":0.5619999766349792},{"id":"https://openalex.org/keywords/functional-principal-component-analysis","display_name":"Functional principal component analysis","score":0.5612000226974487},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.5317999720573425},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5148000121116638},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4722999930381775}],"concepts":[{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.7616999745368958},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.59170001745224},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.5899999737739563},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5841000080108643},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5623999834060669},{"id":"https://openalex.org/C112604564","wikidata":"https://www.wikidata.org/wiki/Q7489226","display_name":"Shape analysis (program analysis)","level":3,"score":0.5619999766349792},{"id":"https://openalex.org/C71176878","wikidata":"https://www.wikidata.org/wiki/Q17014987","display_name":"Functional principal component analysis","level":3,"score":0.5612000226974487},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5511000156402588},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.5317999720573425},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5148000121116638},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4722999930381775},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4722999930381775},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.44279998540878296},{"id":"https://openalex.org/C129641003","wikidata":"https://www.wikidata.org/wiki/Q267189","display_name":"Active shape model","level":3,"score":0.4226999878883362},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3971000015735626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38449999690055847},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3774999976158142},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.34360000491142273},{"id":"https://openalex.org/C51820054","wikidata":"https://www.wikidata.org/wiki/Q5508814","display_name":"Functional data analysis","level":2,"score":0.310699999332428},{"id":"https://openalex.org/C45089102","wikidata":"https://www.wikidata.org/wiki/Q5693286","display_name":"Heat kernel signature","level":4,"score":0.304500013589859},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.2992999851703644},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.28999999165534973},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.2896000146865845},{"id":"https://openalex.org/C115051666","wikidata":"https://www.wikidata.org/wiki/Q6522493","display_name":"Ranging","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C2781195486","wikidata":"https://www.wikidata.org/wiki/Q289436","display_name":"Texture (cosmology)","level":3,"score":0.28060001134872437},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.2524000108242035},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:boa.unimib.it:10281/495359","is_oa":false,"landing_page_url":"https://hdl.handle.net/10281/495359","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:re.public.polimi.it:11311/1233524","is_oa":false,"landing_page_url":"https://hdl.handle.net/11311/1233524","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"doi:10.2312/stag.20221253","is_oa":true,"landing_page_url":"https://doi.org/10.2312/stag.20221253","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"doi:10.2312/stag.20221253","is_oa":true,"landing_page_url":"https://doi.org/10.2312/stag.20221253","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":""},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.45640048384666443}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Shape":[0],"matching":[1,148],"is":[2,32,70],"a":[3,23,122,164],"central":[4],"problem":[5],"in":[6,109,145,197],"geometry":[7],"processing":[8],"applications,":[9],"ranging":[10],"from":[11],"texture":[12],"transfer":[13],"to":[14,84,103,163,192],"statistical":[15],"shape":[16,132,147],"analysis.":[17],"The":[18,42],"functional":[19,49,61,106,124],"maps":[20,37,50,107,189],"framework":[21],"provides":[22],"compact":[24],"representation":[25],"of":[26,45,54,66,152,166,177],"correspondences":[27,89,115],"between":[28],"discrete":[29],"surfaces,":[30],"which":[31],"then":[33],"converted":[34],"into":[35,113],"point-wise":[36,114,188],"required":[38],"by":[39,157],"real-world":[40],"applications.":[41],"vast":[43],"majority":[44],"methods":[46],"based":[47],"on":[48,129,171],"involve":[51],"the":[52,55,60,67,78,87,105,110,130,142,153,172,198],"eigenfunctions":[53],"Laplace-Beltrami":[56],"Operator":[57],"(LB)":[58],"as":[59],"basis.":[62],"A":[63],"primary":[64],"drawback":[65],"LB":[68,111,143,193],"basis":[69,125,144,184],"that":[71,182],"its":[72],"energy":[73,127],"does":[74],"not":[75],"uniformly":[76],"cover":[77],"surface.":[79],"This":[80],"fact":[81],"gives":[82],"rise":[83],"regions":[85],"where":[86],"estimated":[88],"are":[90,116],"inaccurate,":[91],"typically":[92],"at":[93],"tiny":[94],"parts":[95],"and":[96],"protrusions.":[97],"For":[98],"this":[99],"reason,":[100],"state-of-the-art":[101],"procedures":[102],"convert":[104],"(represented":[108],"basis)":[112],"often":[117],"error-prone.":[118],"We":[119],"propose":[120],"PCGAU,":[121],"new":[123],"whose":[126],"spreads":[128],"whole":[131],"more":[133,186],"evenly":[134],"than":[135],"LB.":[136],"As":[137],"such,":[138],"PC-GAU":[139,150],"can":[140],"replace":[141],"existing":[146],"pipelines.":[149],"consists":[151],"principal":[154],"vectors":[155],"obtained":[156],"applying":[158],"Principal":[159],"Component":[160],"Analysis":[161],"(PCA)":[162],"dictionary":[165],"sparse":[167],"Gaussian":[168],"functions":[169],"scattered":[170],"surfaces.":[173],"Through":[174],"experimental":[175],"evaluation":[176],"established":[178],"benchmarks,":[179],"we":[180],"show":[181],"our":[183],"produces":[185],"accurate":[187],"\u2014-":[190],"compared":[191],"-":[194],"when":[195],"employed":[196],"same":[199],"shape-matching":[200],"pipeline.":[201]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
