{"id":"https://openalex.org/W2791709203","doi":"https://doi.org/10.1109/tpami.2018.2803828","title":"Constant-Time Calculation of Zernike Moments for Detection with Rotational Invariance","display_name":"Constant-Time Calculation of Zernike Moments for Detection with Rotational Invariance","publication_year":2018,"publication_date":"2018-02-07","ids":{"openalex":"https://openalex.org/W2791709203","doi":"https://doi.org/10.1109/tpami.2018.2803828","mag":"2791709203","pmid":"https://pubmed.ncbi.nlm.nih.gov/29993477"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2018.2803828","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2018.2803828","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5011769936","display_name":"Aneta Bera","orcid":"https://orcid.org/0000-0002-0456-9451"},"institutions":[{"id":"https://openalex.org/I155313962","display_name":"West Pomeranian University of Technology in Szczecin","ror":"https://ror.org/0596m7f19","country_code":"PL","type":"education","lineage":["https://openalex.org/I155313962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Aneta Bera","raw_affiliation_strings":["Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland","West Pomeranian University of Technology, Szczecin, Poland"],"raw_orcid":"https://orcid.org/0000-0002-0456-9451","affiliations":[{"raw_affiliation_string":"Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland","institution_ids":["https://openalex.org/I155313962"]},{"raw_affiliation_string":"West Pomeranian University of Technology, Szczecin, Poland","institution_ids":["https://openalex.org/I155313962"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009725519","display_name":"Przemys\u0142aw Kl\u0119sk","orcid":"https://orcid.org/0000-0002-5579-187X"},"institutions":[{"id":"https://openalex.org/I155313962","display_name":"West Pomeranian University of Technology in Szczecin","ror":"https://ror.org/0596m7f19","country_code":"PL","type":"education","lineage":["https://openalex.org/I155313962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Przemyslaw Klesk","raw_affiliation_strings":["Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland","West Pomeranian University of Technology, Szczecin, Poland"],"raw_orcid":"https://orcid.org/0000-0002-5579-187X","affiliations":[{"raw_affiliation_string":"Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland","institution_ids":["https://openalex.org/I155313962"]},{"raw_affiliation_string":"West Pomeranian University of Technology, Szczecin, Poland","institution_ids":["https://openalex.org/I155313962"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050937436","display_name":"Dariusz Sychel","orcid":"https://orcid.org/0000-0001-9835-869X"},"institutions":[{"id":"https://openalex.org/I155313962","display_name":"West Pomeranian University of Technology in Szczecin","ror":"https://ror.org/0596m7f19","country_code":"PL","type":"education","lineage":["https://openalex.org/I155313962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Dariusz Sychel","raw_affiliation_strings":["Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland","West Pomeranian University of Technology, Szczecin, Poland"],"raw_orcid":"https://orcid.org/0000-0001-9835-869X","affiliations":[{"raw_affiliation_string":"Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland","institution_ids":["https://openalex.org/I155313962"]},{"raw_affiliation_string":"West Pomeranian University of Technology, Szczecin, Poland","institution_ids":["https://openalex.org/I155313962"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8021,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.8911846,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"41","issue":"3","first_page":"537","last_page":"551"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9994000196456909,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9994000196456909,"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/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9988999962806702,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9822999835014343,"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/zernike-polynomials","display_name":"Zernike polynomials","score":0.8790901899337769},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5482873320579529},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48817187547683716},{"id":"https://openalex.org/keywords/feature-extraction","display_name":"Feature extraction","score":0.4835069477558136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4580066204071045},{"id":"https://openalex.org/keywords/radon-transform","display_name":"Radon transform","score":0.45391446352005005},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4455820918083191},{"id":"https://openalex.org/keywords/rotational-invariance","display_name":"Rotational invariance","score":0.43025606870651245},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4275192618370056},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4153153896331787},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.36259377002716064},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.35597363114356995},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.09306323528289795}],"concepts":[{"id":"https://openalex.org/C92423082","wikidata":"https://www.wikidata.org/wiki/Q132146","display_name":"Zernike polynomials","level":3,"score":0.8790901899337769},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5482873320579529},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48817187547683716},{"id":"https://openalex.org/C52622490","wikidata":"https://www.wikidata.org/wiki/Q1026626","display_name":"Feature extraction","level":2,"score":0.4835069477558136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4580066204071045},{"id":"https://openalex.org/C197231052","wikidata":"https://www.wikidata.org/wiki/Q979829","display_name":"Radon transform","level":2,"score":0.45391446352005005},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4455820918083191},{"id":"https://openalex.org/C33098168","wikidata":"https://www.wikidata.org/wiki/Q108537107","display_name":"Rotational invariance","level":2,"score":0.43025606870651245},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4275192618370056},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4153153896331787},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.36259377002716064},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.35597363114356995},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.09306323528289795},{"id":"https://openalex.org/C165699331","wikidata":"https://www.wikidata.org/wiki/Q461533","display_name":"Wavefront","level":2,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2018.2803828","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2018.2803828","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:29993477","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29993477","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":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4317403233","display_name":null,"funder_award_id":"2016/21/B/ST6/01495","funder_id":"https://openalex.org/F4320322650","funder_display_name":"Narodowym Centrum Nauki"}],"funders":[{"id":"https://openalex.org/F4320322650","display_name":"Narodowym Centrum Nauki","ror":"https://ror.org/03ha2q922"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1579279110","https://openalex.org/W1964201132","https://openalex.org/W1964725559","https://openalex.org/W1973977441","https://openalex.org/W2011974067","https://openalex.org/W2024046085","https://openalex.org/W2035062046","https://openalex.org/W2051262919","https://openalex.org/W2081944396","https://openalex.org/W2087546568","https://openalex.org/W2105709288","https://openalex.org/W2108734443","https://openalex.org/W2115763357","https://openalex.org/W2136235502","https://openalex.org/W2141955292","https://openalex.org/W2143425433","https://openalex.org/W2144460703","https://openalex.org/W2146880335","https://openalex.org/W2161969291","https://openalex.org/W2164598857","https://openalex.org/W2168501771","https://openalex.org/W2172100293","https://openalex.org/W2184781617","https://openalex.org/W2200201590","https://openalex.org/W2247274765","https://openalex.org/W2619270659","https://openalex.org/W4213116910","https://openalex.org/W4253999777","https://openalex.org/W4285719527","https://openalex.org/W6691127938"],"related_works":["https://openalex.org/W2547138831","https://openalex.org/W2061580049","https://openalex.org/W1997638723","https://openalex.org/W2067788074","https://openalex.org/W2183108721","https://openalex.org/W2073465494","https://openalex.org/W1989910702","https://openalex.org/W2128407262","https://openalex.org/W2389707563","https://openalex.org/W2356513325"],"abstract_inverted_index":{"We":[0,55,93,124],"construct":[1],"a":[2,37,185],"set":[3],"of":[4,52,72,81,97,103,108,112,138,149,152,175],"special":[5],"complex-valued":[6],"integral":[7,65,105,109,142],"images":[8,66],"and":[9,43,67,86,131],"an":[10,89],"algorithm":[11],"that":[12],"allows":[13],"to":[14,62],"calculate":[15],"Zernike":[16,130],"moments":[17,134],"fast,":[18],"namely":[19],"in":[20,83,115,135,178],"constant":[21],"time.":[22],"The":[23],"technique":[24],"is":[25,34,47,88],"suitable":[26],"for":[27],"dense":[28],"detection":[29,150],"procedures,":[30],"where":[31,44],"the":[32,50,63,70,79,84,98,136,159,163,168,189,194],"image":[33,59],"scanned":[35],"by":[36,162],"sliding":[38],"window":[39,85],"at":[40,49],"multiple":[41],"scales,":[42],"rotational":[45],"invariance":[46],"required":[48],"level":[51],"each":[53,73],"window.":[54],"assume":[56],"no":[57],"preliminary":[58],"segmentation.":[60],"Owing":[61],"proposed":[64,160],"binomial":[68],"expansions,":[69],"extraction":[71],"feature":[74,116],"does":[75],"not":[76],"depend":[77],"on":[78,121,158],"number":[80,102,111],"pixels":[82],"thereby":[87],"<inline-formula><tex-math":[90,196],"notation=\"LaTeX\">$O(1)$</tex-math></inline-formula>":[91],"calculation.":[92],"analyze":[94],"algorithmic":[95],"properties":[96],"proposition,":[99],"such":[100],"as:":[101],"needed":[104],"images,":[106,110],"complex-conjugacy":[107],"operations":[113],"involved":[114],"extraction,":[117],"speed-up":[118],"possibilities":[119],"based":[120],"lookup":[122],"tables.":[123],"also":[125],"point":[126],"out":[127],"connections":[128],"between":[129],"orthogonal":[132],"Fourier\u2013Mellin":[133],"context":[137],"computations":[139],"backed":[140],"with":[141,173],"images.":[143],"Finally,":[144],"we":[145],"demonstrate":[146],"three":[147],"examples":[148,174],"tasks":[151],"varying":[153],"difficulty.":[154],"Detectors":[155],"are":[156],"trained":[157],"features":[161],"RealBoost":[164],"algorithm.":[165],"When":[166],"learning,":[167],"classifiers":[169],"get":[170],"acquainted":[171],"only":[172],"target":[176],"objects":[177],"their":[179],"upright":[180],"position":[181],"or":[182],"rotated":[183],"within":[184],"limited":[186],"range.":[187],"At":[188],"testing":[190],"stage,":[191],"generalization":[192],"onto":[193],"full":[195],"notation=\"LaTeX\">$360^\\circ$</tex-math></inline-formula>":[197],"angle":[198],"takes":[199],"place":[200],"automatically.":[201]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}