{"id":"https://openalex.org/W4380680758","doi":"https://doi.org/10.3389/fncom.2023.1189949","title":"Covariance properties under natural image transformations for the generalised Gaussian derivative model for visual receptive fields","display_name":"Covariance properties under natural image transformations for the generalised Gaussian derivative model for visual receptive fields","publication_year":2023,"publication_date":"2023-06-15","ids":{"openalex":"https://openalex.org/W4380680758","doi":"https://doi.org/10.3389/fncom.2023.1189949","pmid":"https://pubmed.ncbi.nlm.nih.gov/37398936"},"language":"en","primary_location":{"id":"doi:10.3389/fncom.2023.1189949","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fncom.2023.1189949","pdf_url":"https://www.frontiersin.org/articles/10.3389/fncom.2023.1189949/pdf","source":{"id":"https://openalex.org/S19778766","display_name":"Frontiers in Computational Neuroscience","issn_l":"1662-5188","issn":["1662-5188"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computational Neuroscience","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.frontiersin.org/articles/10.3389/fncom.2023.1189949/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054396186","display_name":"Tony Lindeberg","orcid":"https://orcid.org/0000-0002-9081-2170"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Tony Lindeberg","raw_affiliation_strings":["Computational Brain Science Lab, Division of Computational Science and Technology, KTH Royal Institute of Technology, Stockholm, Sweden"],"affiliations":[{"raw_affiliation_string":"Computational Brain Science Lab, Division of Computational Science and Technology, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054396186"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":{"value":2950,"currency":"USD","value_usd":2950},"apc_paid":{"value":2950,"currency":"USD","value_usd":2950},"fwci":0.8651,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.71333297,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"17","issue":null,"first_page":"1189949","last_page":"1189949"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10427","display_name":"Visual perception and processing mechanisms","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10427","display_name":"Visual perception and processing mechanisms","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9833999872207642,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12859","display_name":"Cell Image Analysis Techniques","score":0.9729999899864197,"subfield":{"id":"https://openalex.org/subfields/1304","display_name":"Biophysics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/receptive-field","display_name":"Receptive field","score":0.6913844347000122},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.6744740009307861},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5710117220878601},{"id":"https://openalex.org/keywords/covariance-operator","display_name":"Covariance operator","score":0.5271308422088623},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5021414756774902},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.4840223491191864},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.47905147075653076},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4537608027458191},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.4474678337574005},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4113057553768158},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36934131383895874},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3660728335380554},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16410812735557556},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10532695055007935},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09524807333946228}],"concepts":[{"id":"https://openalex.org/C19071747","wikidata":"https://www.wikidata.org/wiki/Q1755207","display_name":"Receptive field","level":2,"score":0.6913844347000122},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6744740009307861},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5710117220878601},{"id":"https://openalex.org/C103692563","wikidata":"https://www.wikidata.org/wiki/Q5178900","display_name":"Covariance operator","level":3,"score":0.5271308422088623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5021414756774902},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.4840223491191864},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.47905147075653076},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4537608027458191},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.4474678337574005},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4113057553768158},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36934131383895874},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3660728335380554},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16410812735557556},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10532695055007935},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09524807333946228},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3389/fncom.2023.1189949","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fncom.2023.1189949","pdf_url":"https://www.frontiersin.org/articles/10.3389/fncom.2023.1189949/pdf","source":{"id":"https://openalex.org/S19778766","display_name":"Frontiers in Computational Neuroscience","issn_l":"1662-5188","issn":["1662-5188"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computational Neuroscience","raw_type":"journal-article"},{"id":"pmid:37398936","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37398936","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in computational neuroscience","raw_type":null},{"id":"pmh:oai:DiVA.org:kth-327330","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-327330","pdf_url":"https://kth.diva-portal.org/smash/get/diva2:1758831/FULLTEXT02","source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","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":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pubmedcentral.nih.gov:10311448","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10311448","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10311448/pdf/fncom-17-1189949.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Front Comput Neurosci","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:7ae911714ddf47f6adcbf065a6b32698","is_oa":true,"landing_page_url":"https://doaj.org/article/7ae911714ddf47f6adcbf065a6b32698","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Frontiers in Computational Neuroscience, Vol 17 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3389/fncom.2023.1189949","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fncom.2023.1189949","pdf_url":"https://www.frontiersin.org/articles/10.3389/fncom.2023.1189949/pdf","source":{"id":"https://openalex.org/S19778766","display_name":"Frontiers in Computational Neuroscience","issn_l":"1662-5188","issn":["1662-5188"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computational Neuroscience","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2564771978","display_name":null,"funder_award_id":"2022-02969","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G5240272414","display_name":null,"funder_award_id":"2022-0296","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G6250578322","display_name":null,"funder_award_id":"2018-03586","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G712881263","display_name":null,"funder_award_id":"2018-","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"}],"funders":[{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4380680758.pdf"},"referenced_works_count":92,"referenced_works":["https://openalex.org/W104847522","https://openalex.org/W1594088999","https://openalex.org/W1678355425","https://openalex.org/W1734554626","https://openalex.org/W1840528424","https://openalex.org/W1914401667","https://openalex.org/W1951259116","https://openalex.org/W1954638517","https://openalex.org/W1965673217","https://openalex.org/W1970269179","https://openalex.org/W1970554717","https://openalex.org/W1984757472","https://openalex.org/W1986327281","https://openalex.org/W1997781091","https://openalex.org/W2003334469","https://openalex.org/W2006598994","https://openalex.org/W2010548775","https://openalex.org/W2022735534","https://openalex.org/W2023539733","https://openalex.org/W2025520018","https://openalex.org/W2026543737","https://openalex.org/W2041616184","https://openalex.org/W2052196865","https://openalex.org/W2055339315","https://openalex.org/W2056459831","https://openalex.org/W2060487744","https://openalex.org/W2062184596","https://openalex.org/W2063248482","https://openalex.org/W2075165262","https://openalex.org/W2078396259","https://openalex.org/W2090871504","https://openalex.org/W2103212315","https://openalex.org/W2105464873","https://openalex.org/W2110121211","https://openalex.org/W2116360511","https://openalex.org/W2117731089","https://openalex.org/W2122672396","https://openalex.org/W2130841080","https://openalex.org/W2136127238","https://openalex.org/W2138100172","https://openalex.org/W2142756981","https://openalex.org/W2143659673","https://openalex.org/W2144063100","https://openalex.org/W2145889472","https://openalex.org/W2146758052","https://openalex.org/W2149194912","https://openalex.org/W2151035455","https://openalex.org/W2162950292","https://openalex.org/W2165087100","https://openalex.org/W2166130385","https://openalex.org/W2261689926","https://openalex.org/W2336807537","https://openalex.org/W2527076004","https://openalex.org/W2552934535","https://openalex.org/W2581415955","https://openalex.org/W2656417304","https://openalex.org/W2779379590","https://openalex.org/W2947599954","https://openalex.org/W2981512247","https://openalex.org/W2982238751","https://openalex.org/W2996406751","https://openalex.org/W3038121656","https://openalex.org/W3106050203","https://openalex.org/W3109158212","https://openalex.org/W3120249005","https://openalex.org/W3120530331","https://openalex.org/W3121375137","https://openalex.org/W3121439520","https://openalex.org/W3171742925","https://openalex.org/W3196312384","https://openalex.org/W3203623872","https://openalex.org/W4210308843","https://openalex.org/W4230819937","https://openalex.org/W4244723818","https://openalex.org/W4256349509","https://openalex.org/W4280518161","https://openalex.org/W4287125263","https://openalex.org/W4292676217","https://openalex.org/W4292949594","https://openalex.org/W4310572212","https://openalex.org/W4317780962","https://openalex.org/W4362458506","https://openalex.org/W4364386926","https://openalex.org/W4367000048","https://openalex.org/W4375959281","https://openalex.org/W6706457818","https://openalex.org/W6763710644","https://openalex.org/W6768563538","https://openalex.org/W6769209158","https://openalex.org/W6792213754","https://openalex.org/W6796492147","https://openalex.org/W6845473225"],"related_works":["https://openalex.org/W2386803684","https://openalex.org/W1971337326","https://openalex.org/W2073389045","https://openalex.org/W3178402891","https://openalex.org/W651058035","https://openalex.org/W143964308","https://openalex.org/W2101252966","https://openalex.org/W2013574807","https://openalex.org/W1502180380","https://openalex.org/W1982271221"],"abstract_inverted_index":{"The":[0],"property":[1],"of":[2,25,49,63,76,150,165,176,188,211,223,226,234,259,277,290],"covariance,":[3],"also":[4],"referred":[5],"to":[6,30,46,54,155,162,273],"as":[7,40,182,184,251,253],"equivariance,":[8],"means":[9],"that":[10,22,138],"an":[11],"image":[12,17,28,34,44,52,144,169,238,242,294,299],"operator":[13,29,53],"is":[14,104],"well-behaved":[15],"under":[16,121,191,240],"transformations,":[18,124,127,300],"in":[19,67,79,90,99,148,200,282],"the":[20,23,27,42,47,51,55,80,85,100,107,151,156,168,196,201,204,212,221,224,232,267,271,275,278,283,288],"sense":[21],"result":[24,39],"applying":[26,41,50],"a":[31,37,61,71,139],"transformed":[32],"input":[33],"gives":[35],"essentially":[36],"similar":[38],"same":[43],"transformation":[45],"output":[48],"original":[56],"image.":[57],"This":[58],"paper":[59],"presents":[60],"theory":[62,214],"geometric":[64,93,303],"covariance":[65,119,135,304],"properties":[66,95,120,136],"vision,":[68,217],"developed":[69],"for":[70,113,215,255],"generalised":[72,109,157],"Gaussian":[73,110,158],"derivative":[74,111,159],"model":[75,112],"receptive":[77,115,152,229,260,280],"fields":[78,116,153,230,281],"primary":[81,284],"visual":[82,101,114,228,285],"cortex":[83,286],"and":[84,130,145,170,198,203,231,236,292],"lateral":[86],"geniculate":[87],"nucleus,":[88],"which,":[89],"turn,":[91],"enable":[92],"invariance":[94],"at":[96],"higher":[97],"levels":[98],"hierarchy.":[102],"It":[103],"shown":[105],"how":[106],"studied":[108],"obeys":[117],"true":[118],"spatial":[122,125,235,291],"scaling":[123,132],"affine":[126],"Galilean":[128],"transformations":[129],"temporal":[131],"transformations.":[133,243],"These":[134],"imply":[137],"vision":[140],"system,":[141],"based":[142,301],"on":[143,302],"video":[146,171],"measurements":[147],"terms":[149],"according":[154],"model,":[160],"can,":[161],"first":[163],"order":[164],"approximation,":[166],"handle":[167],"deformations":[172],"between":[173,185,195,220],"multiple":[174,186],"views":[175,187],"objects":[177,197],"delimited":[178],"by":[179,208,297],"smooth":[180],"surfaces,":[181],"well":[183,252],"spatio-temporal":[189,237,293],"events,":[190],"varying":[192],"relative":[193],"motions":[194],"events":[199],"world":[202],"observer.":[205],"We":[206],"conclude":[207],"describing":[209],"implications":[210],"presented":[213,268],"biological":[216,227,249,279],"regarding":[218],"connections":[219],"variabilities":[222,233,289],"shapes":[225,276],"structures":[239,295],"natural":[241,298],"Specifically,":[244],"we":[245],"formulate":[246],"experimentally":[247],"testable":[248],"hypotheses":[250],"needs":[254],"measuring":[256],"population":[257],"statistics":[258],"field":[261],"characteristics,":[262],"originating":[263],"from":[264,266],"predictions":[265],"theory,":[269],"concerning":[270],"extent":[272],"which":[274],"span":[287],"induced":[296],"properties.":[305]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}
