{"id":"https://openalex.org/W4205587671","doi":"https://doi.org/10.23919/eusipco54536.2021.9616183","title":"Stability of Spherical Convolutional Neural Networks to Rotation Diffeomorphisms","display_name":"Stability of Spherical Convolutional Neural Networks to Rotation Diffeomorphisms","publication_year":2021,"publication_date":"2021-08-23","ids":{"openalex":"https://openalex.org/W4205587671","doi":"https://doi.org/10.23919/eusipco54536.2021.9616183"},"language":"en","primary_location":{"id":"doi:10.23919/eusipco54536.2021.9616183","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco54536.2021.9616183","pdf_url":null,"source":{"id":"https://openalex.org/S4363607854","display_name":"2021 29th European Signal Processing Conference (EUSIPCO)","issn_l":null,"issn":null,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 29th European Signal Processing Conference (EUSIPCO)","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/A5088013951","display_name":"Zhan Gao","orcid":"https://orcid.org/0000-0001-7250-7386"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhan Gao","raw_affiliation_strings":["Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, USA","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069506165","display_name":"Fernando Gama","orcid":"https://orcid.org/0000-0001-6117-8193"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fernando Gama","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078862959","display_name":"Alejandro Ribeiro","orcid":"https://orcid.org/0000-0003-4230-9906"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alejandro Ribeiro","raw_affiliation_strings":["Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, USA","institution_ids":["https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088013951"],"corresponding_institution_ids":["https://openalex.org/I79576946"],"apc_list":null,"apc_paid":null,"fwci":0.0653,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.36607143,"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":"1451","last_page":"1455"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9959999918937683,"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"}},"topics":[{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9959999918937683,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9934999942779541,"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/T10638","display_name":"Optical measurement and interference techniques","score":0.9930999875068665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/spherical-shell","display_name":"Spherical shell","score":0.714753270149231},{"id":"https://openalex.org/keywords/spherical-geometry","display_name":"Spherical geometry","score":0.5774341821670532},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.5261635184288025},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5207345485687256},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.4854729473590851},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.4764980673789978},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4642205238342285},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.46332165598869324},{"id":"https://openalex.org/keywords/spherical-harmonics","display_name":"Spherical harmonics","score":0.4386276304721832},{"id":"https://openalex.org/keywords/spherical-coordinate-system","display_name":"Spherical coordinate system","score":0.41501671075820923},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34671300649642944},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32395943999290466},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3224570155143738},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3102150559425354},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3088095188140869},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2653886079788208}],"concepts":[{"id":"https://openalex.org/C108280814","wikidata":"https://www.wikidata.org/wiki/Q12137","display_name":"Spherical shell","level":3,"score":0.714753270149231},{"id":"https://openalex.org/C77730005","wikidata":"https://www.wikidata.org/wiki/Q326905","display_name":"Spherical geometry","level":2,"score":0.5774341821670532},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.5261635184288025},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5207345485687256},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.4854729473590851},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.4764980673789978},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4642205238342285},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.46332165598869324},{"id":"https://openalex.org/C3768446","wikidata":"https://www.wikidata.org/wiki/Q877100","display_name":"Spherical harmonics","level":2,"score":0.4386276304721832},{"id":"https://openalex.org/C126990412","wikidata":"https://www.wikidata.org/wiki/Q203218","display_name":"Spherical coordinate system","level":2,"score":0.41501671075820923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34671300649642944},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32395943999290466},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3224570155143738},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3102150559425354},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3088095188140869},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2653886079788208},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C2781052500","wikidata":"https://www.wikidata.org/wiki/Q2230313","display_name":"Shell (structure)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/eusipco54536.2021.9616183","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco54536.2021.9616183","pdf_url":null,"source":{"id":"https://openalex.org/S4363607854","display_name":"2021 29th European Signal Processing Conference (EUSIPCO)","issn_l":null,"issn":null,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 29th European Signal Processing Conference (EUSIPCO)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.8100000023841858,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W625505059","https://openalex.org/W1579992943","https://openalex.org/W1617806327","https://openalex.org/W1920022804","https://openalex.org/W1986655361","https://openalex.org/W2049918078","https://openalex.org/W2082841340","https://openalex.org/W2111080752","https://openalex.org/W2115579991","https://openalex.org/W2129870696","https://openalex.org/W2148687996","https://openalex.org/W2160615084","https://openalex.org/W2334021688","https://openalex.org/W2576915720","https://openalex.org/W2591947811","https://openalex.org/W2744272590","https://openalex.org/W2796422723","https://openalex.org/W2898187790","https://openalex.org/W2962889053","https://openalex.org/W2963530975","https://openalex.org/W2963598163","https://openalex.org/W3091786697","https://openalex.org/W4253475706","https://openalex.org/W4288640779","https://openalex.org/W6636705262","https://openalex.org/W6640300118","https://openalex.org/W6734175935","https://openalex.org/W6746156960","https://openalex.org/W6756056079","https://openalex.org/W6757782795","https://openalex.org/W6769516661","https://openalex.org/W6783824477"],"related_works":["https://openalex.org/W70802032","https://openalex.org/W4239999982","https://openalex.org/W4321637725","https://openalex.org/W2125110984","https://openalex.org/W2099694762","https://openalex.org/W2024558872","https://openalex.org/W2810312732","https://openalex.org/W2091451126","https://openalex.org/W2598468016","https://openalex.org/W3087039205"],"abstract_inverted_index":{"Spherical":[0,39,73,90,109,140],"convolutional":[1],"neural":[2],"networks":[3],"(Spherical":[4],"CNNs)":[5],"learn":[6],"nonlinear":[7],"representations":[8],"from":[9],"spherical":[10,51,69,85,147],"signals.":[11],"These":[12],"are":[13,95],"mathematical":[14],"models":[15],"for":[16],"data":[17],"arising":[18],"in":[19,26,68,83,157],"3-D":[20,158],"objects":[21],"and":[22,31,34,87,131,135,137,161],"have":[23,71],"found":[24],"applications":[25],"computer":[27],"vision,":[28],"light":[29],"detection":[30],"ranging":[32],"(LIDAR),":[33],"planning":[35],"among":[36],"others.":[37],"The":[38],"CNN":[40,74,110],"comprises":[41],"a":[42,48,57],"cascade":[43],"of":[44,50,108,128,146],"layers,":[45],"each":[46],"with":[47,92],"series":[49],"convolutions":[52],"(spherical":[53],"filters)":[54],"followed":[55],"by":[56,112,118],"pointwise":[58],"nonlinearity.":[59],"This":[60,122],"paper":[61],"investigates":[62],"the":[63,84,105,113,119,126,129,132,143],"impact":[64],"that":[65,89,104],"structure":[66,145],"perturbations":[67,79],"signals":[70,148],"on":[72],"outputs.":[75],"We":[76,153],"consider":[77],"general":[78],"as":[80],"rotation":[81,166],"diffeomorphisms":[82],"surface,":[86],"show":[88],"CNNs":[91,141],"Lipschitz":[93],"filters":[94],"stable":[96,163],"to":[97,149,165],"such":[98],"perturbations.":[99],"In":[100],"particular,":[101],"we":[102],"establish":[103],"output":[106],"difference":[107],"induced":[111],"diffeomorphism":[114],"perturbation":[115,120],"is":[116],"bounded":[117],"size.":[121],"result":[123],"also":[124],"shows":[125],"role":[127],"nonlinearity":[130],"architecture":[133],"width":[134],"depth,":[136],"indicates":[138],"how":[139],"exploit":[142],"rotational":[144],"gain":[150],"superior":[151],"performance.":[152],"corroborate":[154],"theoretical":[155],"findings":[156],"object":[159],"classification,":[160],"observe":[162],"performance":[164],"diffeomorphisms.":[167]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}