{"id":"https://openalex.org/W4286231693","doi":"https://doi.org/10.48550/arxiv.2207.08925","title":"Image to Icosahedral Projection for $\\mathrm{SO}(3)$ Object Reasoning from Single-View Images","display_name":"Image to Icosahedral Projection for $\\mathrm{SO}(3)$ Object Reasoning from Single-View Images","publication_year":2022,"publication_date":"2022-07-18","ids":{"openalex":"https://openalex.org/W4286231693","doi":"https://doi.org/10.48550/arxiv.2207.08925"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2207.08925","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2207.08925","pdf_url":"https://arxiv.org/pdf/2207.08925","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2207.08925","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060590650","display_name":"David Klee","orcid":"https://orcid.org/0000-0003-1234-9755"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Klee, David","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050593664","display_name":"Ond\u0159ej B\u00ed\u017ea","orcid":"https://orcid.org/0000-0003-3390-8050"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Biza, Ondrej","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103163468","display_name":"Robert Platt","orcid":"https://orcid.org/0009-0001-2033-3473"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Platt, Robert","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5063254454","display_name":"Robin Walters","orcid":"https://orcid.org/0000-0002-9179-0321"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Walters, Robin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5060590650"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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":false,"primary_topic":{"id":"https://openalex.org/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9965999722480774,"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/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9965999722480774,"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/T11714","display_name":"Multimodal Machine Learning Applications","score":0.9962999820709229,"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.7628521919250488},{"id":"https://openalex.org/keywords/point-cloud","display_name":"Point cloud","score":0.656934916973114},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6514990925788879},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.6357927918434143},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6106536984443665},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.5992146730422974},{"id":"https://openalex.org/keywords/pose","display_name":"Pose","score":0.5367684364318848},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5017585754394531},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.477407842874527},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.4504863917827606},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29977601766586304},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20482981204986572},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16480043530464172}],"concepts":[{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.7628521919250488},{"id":"https://openalex.org/C131979681","wikidata":"https://www.wikidata.org/wiki/Q1899648","display_name":"Point cloud","level":2,"score":0.656934916973114},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6514990925788879},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.6357927918434143},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6106536984443665},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.5992146730422974},{"id":"https://openalex.org/C52102323","wikidata":"https://www.wikidata.org/wiki/Q1671968","display_name":"Pose","level":2,"score":0.5367684364318848},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5017585754394531},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.477407842874527},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.4504863917827606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29977601766586304},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20482981204986572},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16480043530464172},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2207.08925","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2207.08925","pdf_url":"https://arxiv.org/pdf/2207.08925","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2207.08925","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2207.08925","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2207.08925","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2207.08925","pdf_url":"https://arxiv.org/pdf/2207.08925","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3148895720","https://openalex.org/W2393913406","https://openalex.org/W30258475","https://openalex.org/W2356579025","https://openalex.org/W2736697936","https://openalex.org/W3211835374","https://openalex.org/W2548611373","https://openalex.org/W1601809778","https://openalex.org/W4320086129","https://openalex.org/W2798549588"],"abstract_inverted_index":{"Reasoning":[0],"about":[1],"3D":[2,31],"objects":[3],"based":[4,99],"on":[5,100],"2D":[6,53,89],"images":[7],"is":[8,48,122],"challenging":[9],"due":[10],"to":[11,30,125,133],"variations":[12],"in":[13,106,127],"appearance":[14],"caused":[15],"by":[16,108],"viewing":[17],"the":[18,67,113],"object":[19,26,72,134],"from":[20],"different":[21],"orientations.":[22],"Tasks":[23],"such":[24,35],"as":[25,36,44],"classification":[27,139],"are":[28,39],"invariant":[29],"rotations":[32],"and":[33,137,141],"other":[34],"pose":[37,135],"estimation":[38,136],"equivariant.":[40],"However,":[41],"imposing":[42],"equivariance":[43],"a":[45,62,96,110],"model":[46,64,121,132],"constraint":[47],"typically":[49],"not":[50,59],"possible":[51],"with":[52],"image":[54,68,115],"input":[55,86,114],"because":[56],"we":[57,94],"do":[58],"have":[60],"an":[61,117],"priori":[63],"of":[65,112],"how":[66],"changes":[69],"under":[70],"out-of-plane":[71],"rotations.":[73],"The":[74,119],"only":[75],"$\\mathrm{SO}(3)$-equivariant":[76],"models":[77],"that":[78,104,143],"currently":[79],"exist":[80],"require":[81],"point":[82],"cloud":[83],"or":[84],"voxel":[85],"rather":[87],"than":[88],"images.":[90],"In":[91],"this":[92,131],"paper,":[93],"propose":[95],"novel":[97],"architecture":[98],"icosahedral":[101],"group":[102],"convolutions":[103],"reasons":[105],"$\\mathrm{SO(3)}$":[107],"learning":[109],"projection":[111],"onto":[116],"icosahedron.":[118],"resulting":[120],"approximately":[123],"equivariant":[124],"rotation":[126],"$\\mathrm{SO}(3)$.":[128],"We":[129],"apply":[130],"shape":[138],"tasks":[140],"find":[142],"it":[144],"outperforms":[145],"reasonable":[146],"baselines.":[147],"Project":[148],"website:":[149],"\\url{https://dmklee.github.io/image2icosahedral}":[150]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2022-07-21T00:00:00"}