{"id":"https://openalex.org/W6907862102","doi":"https://doi.org/10.2312/sgp/sgp07/225-233","title":"Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation","display_name":"Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W6907862102","doi":"https://doi.org/10.2312/sgp/sgp07/225-233"},"language":"en","primary_location":{"id":"doi:10.2312/sgp/sgp07/225-233","is_oa":true,"landing_page_url":"https://doi.org/10.2312/sgp/sgp07/225-233","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"other","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2312/sgp/sgp07/225-233","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Rustamov, Raif M.","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rustamov, Raif M.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":null,"topics":[],"keywords":[{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.7124999761581421},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6258999705314636},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.5393999814987183},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.4959999918937683},{"id":"https://openalex.org/keywords/global-positioning-system","display_name":"Global Positioning System","score":0.47380000352859497},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4611999988555908},{"id":"https://openalex.org/keywords/discriminative-model","display_name":"Discriminative model","score":0.459199994802475},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4120999872684479}],"concepts":[{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.7124999761581421},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6258999705314636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5708000063896179},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.5393999814987183},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.4959999918937683},{"id":"https://openalex.org/C60229501","wikidata":"https://www.wikidata.org/wiki/Q18822","display_name":"Global Positioning System","level":2,"score":0.47380000352859497},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4611999988555908},{"id":"https://openalex.org/C97931131","wikidata":"https://www.wikidata.org/wiki/Q5282087","display_name":"Discriminative model","level":2,"score":0.459199994802475},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4120999872684479},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.40369999408721924},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.4009999930858612},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3628000020980835},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.36239999532699585},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3458999991416931},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32109999656677246},{"id":"https://openalex.org/C112604564","wikidata":"https://www.wikidata.org/wiki/Q7489226","display_name":"Shape analysis (program analysis)","level":3,"score":0.31209999322891235},{"id":"https://openalex.org/C57489055","wikidata":"https://www.wikidata.org/wiki/Q190046","display_name":"Ellipsoid","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30889999866485596},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.29190000891685486},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29010000824928284},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28529998660087585},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.25850000977516174},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C129641003","wikidata":"https://www.wikidata.org/wiki/Q267189","display_name":"Active shape model","level":3,"score":0.25619998574256897}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2312/sgp/sgp07/225-233","is_oa":true,"landing_page_url":"https://doi.org/10.2312/sgp/sgp07/225-233","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.2312/sgp/sgp07/225-233","is_oa":true,"landing_page_url":"https://doi.org/10.2312/sgp/sgp07/225-233","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"deformation":[1,83],"invariant":[2,84],"representation":[3,46],"of":[4,16,25,33,41,76],"surfaces,":[5],"the":[6,12,17,23,26,31,44,73,77],"GPS":[7,27,54,78],"embedding,":[8,79],"is":[9,37,47],"introduced":[10],"using":[11],"eigenvalues":[13],"and":[14,36,69,89,98],"eigenfunctions":[15],"Laplace-Beltrami":[18],"differential":[19],"operator.":[20],"Notably,":[21],"since":[22],"definition":[24],"embedding":[28,55],"completely":[29],"avoids":[30],"use":[32],"geodesic":[34],"distances,":[35],"based":[38],"on":[39],"objects":[40],"global":[42],"character,":[43],"obtained":[45],"robust":[48],"to":[49,59],"local":[50],"topology":[51],"changes.":[52],"The":[53],"captures":[56],"enough":[57],"information":[58],"handle":[60],"various":[61],"shape":[62,66,85],"processing":[63],"tasks":[64],"as":[65],"classification,":[67],"segmentation,":[68],"correspondence.":[70],"To":[71],"demonstrate":[72,90],"practical":[74],"relevance":[75],"we":[80],"introduce":[81],"a":[82],"descriptor":[86],"called":[87],"G2-distributions,":[88],"their":[91],"discriminative":[92],"power,":[93],"invariance":[94],"under":[95],"natural":[96],"deformations,":[97],"robustness.":[99]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-02-20T08:17:22.645390","created_date":"2025-10-10T00:00:00"}
