{"id":"https://openalex.org/W2117474834","doi":"https://doi.org/10.1109/tit.2009.2012997","title":"Testing for Image Symmetries\u2014With Application to Confocal Microscopy","display_name":"Testing for Image Symmetries\u2014With Application to Confocal Microscopy","publication_year":2009,"publication_date":"2009-03-19","ids":{"openalex":"https://openalex.org/W2117474834","doi":"https://doi.org/10.1109/tit.2009.2012997","mag":"2117474834"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2009.2012997","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2012997","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Information Theory","raw_type":"journal-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/A5044950412","display_name":"Nicolai Bissantz","orcid":"https://orcid.org/0000-0001-7301-4567"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Nicolai Bissantz","raw_affiliation_strings":["Faculty of Mathematics, Ruhr Universit\u00e4t Bochum, Bochum, Germany","Fac. of Math., Ruhr-Univ. Bochum, Bochum"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Ruhr Universit\u00e4t Bochum, Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]},{"raw_affiliation_string":"Fac. of Math., Ruhr-Univ. Bochum, Bochum","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024834862","display_name":"Hajo Holzmann","orcid":"https://orcid.org/0000-0003-4931-0061"},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hajo Holzmann","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Philipps-Universit\u00e4t Marburg, Marburg, Germany","Fac. of Math. & Comput. Sci., Philipps-Univ. Marburg, Marburg"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Philipps-Universit\u00e4t Marburg, Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]},{"raw_affiliation_string":"Fac. of Math. & Comput. Sci., Philipps-Univ. Marburg, Marburg","institution_ids":["https://openalex.org/I161103922"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016991767","display_name":"M. Pawlak","orcid":"https://orcid.org/0000-0003-2627-108X"},"institutions":[{"id":"https://openalex.org/I46247651","display_name":"University of Manitoba","ror":"https://ror.org/02gfys938","country_code":"CA","type":"education","lineage":["https://openalex.org/I46247651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Miroslaw Pawlak","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MAN, Canada","Dept. of Electr. & Comput. Eng., Univ. of Manitoba, Winnipeg, MB#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MAN, Canada","institution_ids":["https://openalex.org/I46247651"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., Univ. of Manitoba, Winnipeg, MB#TAB#","institution_ids":["https://openalex.org/I46247651"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044950412"],"corresponding_institution_ids":["https://openalex.org/I904495901"],"apc_list":null,"apc_paid":null,"fwci":1.9684,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.88046503,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"55","issue":"4","first_page":"1841","last_page":"1855"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.994700014591217,"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":0.994700014591217,"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/T12859","display_name":"Cell Image Analysis Techniques","score":0.9940999746322632,"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"}},{"id":"https://openalex.org/T13114","display_name":"Image Processing Techniques and Applications","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/computer-science","display_name":"Computer science","score":0.3557233214378357},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34821170568466187},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3298264741897583}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3557233214378357},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34821170568466187},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3298264741897583}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2009.2012997","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2012997","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W1509691074","https://openalex.org/W1562445908","https://openalex.org/W1616450149","https://openalex.org/W1963874316","https://openalex.org/W1986145324","https://openalex.org/W2000530451","https://openalex.org/W2011118115","https://openalex.org/W2011931375","https://openalex.org/W2012853725","https://openalex.org/W2017787659","https://openalex.org/W2018808115","https://openalex.org/W2031813546","https://openalex.org/W2035555425","https://openalex.org/W2035934910","https://openalex.org/W2045846905","https://openalex.org/W2049389371","https://openalex.org/W2049552229","https://openalex.org/W2056873774","https://openalex.org/W2069056675","https://openalex.org/W2069057356","https://openalex.org/W2074931146","https://openalex.org/W2086936614","https://openalex.org/W2093240266","https://openalex.org/W2098727903","https://openalex.org/W2099205439","https://openalex.org/W2112262460","https://openalex.org/W2116060068","https://openalex.org/W2118376687","https://openalex.org/W2119782970","https://openalex.org/W2128011810","https://openalex.org/W2128666678","https://openalex.org/W2133316672","https://openalex.org/W2134269439","https://openalex.org/W2137079931","https://openalex.org/W2141955292","https://openalex.org/W2144323727","https://openalex.org/W2146932984","https://openalex.org/W2147824893","https://openalex.org/W2156623445","https://openalex.org/W2156828901","https://openalex.org/W2159005573","https://openalex.org/W2163644233","https://openalex.org/W2796677525","https://openalex.org/W3013909613","https://openalex.org/W3124261078","https://openalex.org/W4206717629","https://openalex.org/W4230173782","https://openalex.org/W4232582992","https://openalex.org/W4244720582","https://openalex.org/W4247690975"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"Statistical":[0],"tests":[1,244],"are":[2,71,119,207,245],"introduced":[3],"for":[4,98],"checking":[5],"whether":[6,249],"an":[7,190],"image":[8,136],"function":[9,137,218],"<i":[10,14,18,27,31,35,39,46,61,103,107,111,123],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[11,15,19,28,32,36,40,43,47,50,62,104,108,112,124,127],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">f</i>":[12,105],"(":[13,106],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">x</i>":[16,33,41,109],",":[17,34,64,110],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">y</i>":[20,37,48,113],")":[21],"defined":[22],"on":[23,121],"the":[24,99,116,122,135,145,152,157,170,173,201,205,215,233,237,241,250,258],"unit":[25],"disc":[26],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">D</i>":[29,63],"={(":[30],"):":[38],"<sup":[42,49],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[44,51],"+":[45],"les":[52],"1}":[53],"is":[54,82,167,179,186,220],"invariant":[55,231],"under":[56,74,77,155,164],"certain":[57],"symmetry":[58,90,146,160],"transformations":[59],"of":[60,102,134,151,159,172,183,204,240],"given":[65],"that":[66],"discrete":[67],"and":[68,139,229],"noisy":[69],"data":[70],"observed.":[72],"Invariance":[73],"reflections":[75],"or":[76],"rotations":[78],"by":[79,188],"rational":[80],"angles":[81],"considered,":[83],"as":[84,86,96,161,163],"well":[85,162],"rotational":[87,213],"invariance.":[88],"These":[89],"relations":[91],"can":[92,253],"be":[93,255],"naturally":[94],"expressed":[95],"restrictions":[97],"Zernike":[100,131],"moments":[101],").":[114],"Therefore,":[115],"test":[117,153],"statistics":[118,154],"based":[120],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">L</i>":[125],"<sub":[126],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[128],"distance":[129],"between":[130],"series":[132],"estimates":[133],"itself":[138],"its":[140],"version":[141],"obtained":[142],"after":[143],"applying":[144],"transformation.":[147],"The":[148,181,243],"asymptotic":[149,174],"distribution":[150],"both":[156],"hypothesis":[158],"fixed":[165],"alternatives":[166],"derived.":[168],"Furthermore,":[169],"quality":[171],"approximations":[175],"via":[176],"simulation":[177],"studies":[178],"investigated.":[180,208],"usefulness":[182],"our":[184],"theory":[185],"verified":[187],"examining":[189],"important":[191],"problem":[192],"in":[193,200,257],"confocal":[194],"microscopy,":[195],"i.e.,":[196],"possible":[197],"imprecise":[198],"alignments":[199],"optical":[202,210,238],"path":[203],"microscope":[206],"For":[209],"systems":[211],"with":[212,223],"symmetry,":[214],"theoretical":[216],"point-spread":[217],"(PSF)":[219],"reflection":[221],"symmetric":[222],"respect":[224],"to":[225,247],"two":[226],"orthogonal":[227],"axes,":[228],"rotationally":[230],"if":[232],"detector":[234],"plane":[235,239],"matches":[236],"microscope.":[242],"used":[246],"investigate":[248],"required":[251],"symmetries":[252],"indeed":[254],"detected":[256],"empirical":[259],"PSF.":[260]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
