{"id":"https://openalex.org/W2146564297","doi":"https://doi.org/10.1137/070691231","title":"Estimation of Translation, Rotation, and Scaling between Noisy Images Using the Fourier\u2013Mellin Transform","display_name":"Estimation of Translation, Rotation, and Scaling between Noisy Images Using the Fourier\u2013Mellin Transform","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2146564297","doi":"https://doi.org/10.1137/070691231","mag":"2146564297"},"language":"en","primary_location":{"id":"doi:10.1137/070691231","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070691231","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","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/A5061972182","display_name":"J\u00e9r\u00e9mie Bigot","orcid":null},"institutions":[{"id":"https://openalex.org/I922237871","display_name":"Netherlands Institute for Radio Astronomy","ror":"https://ror.org/000k1q888","country_code":"NL","type":"other","lineage":["https://openalex.org/I2800991832","https://openalex.org/I4405262988","https://openalex.org/I922237871"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"J\u00e9r\u00e9mie Bigot","raw_affiliation_strings":["Jeremie.Bigot@math.ups-tlse.fr and Fabrice.Gamboa@math.ups-tlse.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jeremie.Bigot@math.ups-tlse.fr and Fabrice.Gamboa@math.ups-tlse.fr#TAB#","institution_ids":["https://openalex.org/I922237871"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039905527","display_name":"Fabrice Gamboa","orcid":"https://orcid.org/0000-0001-9779-4393"},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fabrice Gamboa","raw_affiliation_strings":["Paul Sabatier University;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Paul Sabatier University;","institution_ids":["https://openalex.org/I134560555"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008472172","display_name":"Myriam Vimond","orcid":"https://orcid.org/0000-0002-7722-9933"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Myriam Vimond","raw_affiliation_strings":["mvimond@ensai.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"mvimond@ensai.fr#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2848,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.93041335,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2","issue":"2","first_page":"614","last_page":"645"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9995999932289124,"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":0.9995999932289124,"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/T12549","display_name":"Image and Object Detection Techniques","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/T10531","display_name":"Advanced Vision and Imaging","score":0.9962000250816345,"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/translation","display_name":"Translation (biology)","score":0.7806926965713501},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.7141441106796265},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.68438720703125},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.6801111698150635},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6741068363189697},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.5531302690505981},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5340988039970398},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.49805426597595215},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4700305163860321},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46202951669692993},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45065826177597046},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.44349685311317444},{"id":"https://openalex.org/keywords/image-registration","display_name":"Image registration","score":0.42829832434654236},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4217497408390045},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.35910552740097046},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.33898216485977173},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2152479588985443},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16251340508460999},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10178428888320923},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.08076426386833191}],"concepts":[{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.7806926965713501},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.7141441106796265},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.68438720703125},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6801111698150635},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6741068363189697},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5531302690505981},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5340988039970398},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.49805426597595215},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4700305163860321},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46202951669692993},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45065826177597046},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.44349685311317444},{"id":"https://openalex.org/C166704113","wikidata":"https://www.wikidata.org/wiki/Q861092","display_name":"Image registration","level":3,"score":0.42829832434654236},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4217497408390045},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.35910552740097046},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.33898216485977173},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2152479588985443},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16251340508460999},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10178428888320923},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.08076426386833191},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070691231","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070691231","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00776806v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00776806","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Imaging Sciences, 2009, 2 (2), pp.614-645. ⟨10.1137/070691231⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W33507944","https://openalex.org/W1241854702","https://openalex.org/W1520822062","https://openalex.org/W1543495496","https://openalex.org/W1963623641","https://openalex.org/W1963943638","https://openalex.org/W1973337733","https://openalex.org/W1979887666","https://openalex.org/W1985415289","https://openalex.org/W1987450610","https://openalex.org/W1992244412","https://openalex.org/W2016373742","https://openalex.org/W2029026810","https://openalex.org/W2031937951","https://openalex.org/W2032882750","https://openalex.org/W2042695116","https://openalex.org/W2042941801","https://openalex.org/W2046401020","https://openalex.org/W2049686973","https://openalex.org/W2061543840","https://openalex.org/W2062483720","https://openalex.org/W2074745044","https://openalex.org/W2076114154","https://openalex.org/W2080558403","https://openalex.org/W2094718135","https://openalex.org/W2098727903","https://openalex.org/W2105456967","https://openalex.org/W2121549990","https://openalex.org/W2131372145","https://openalex.org/W2140798815","https://openalex.org/W2146932984","https://openalex.org/W2148416589","https://openalex.org/W2152035672","https://openalex.org/W2170167891","https://openalex.org/W3106303645","https://openalex.org/W4240093485"],"related_works":["https://openalex.org/W1603736412","https://openalex.org/W4304185162","https://openalex.org/W2061685118","https://openalex.org/W3006282800","https://openalex.org/W2462100143","https://openalex.org/W1770503332","https://openalex.org/W3125207769","https://openalex.org/W2577825108","https://openalex.org/W2949684406","https://openalex.org/W2140728006"],"abstract_inverted_index":{"In":[0],"this":[1,22],"paper":[2],"we":[3,81],"focus":[4],"on":[5,32,78],"extended":[6],"Euclidean":[7],"registration":[8,25],"of":[9,12,24,49,63,85,103],"a":[10,28,47,54,64],"set":[11,48],"noisy":[13],"images.":[14,50],"We":[15],"provide":[16],"an":[17],"appropriate":[18],"statistical":[19],"model":[20],"for":[21],"kind":[23],"problem,":[26],"and":[27,42,80,93],"new":[29],"criterion":[30,52],"based":[31,77],"Fourier-type":[33],"transforms":[34],"is":[35,53,76],"proposed":[36],"to":[37,45,98],"estimate":[38],"the":[39,61,70,83,86,100],"translation,":[40],"rotation,":[41],"scaling":[43],"parameters":[44],"align":[46],"This":[51],"two-step":[55],"procedure":[56],"which":[57,68],"does":[58],"not":[59],"require":[60],"use":[62],"reference":[65],"template":[66],"onto":[67],"all":[69],"images":[71],"are":[72,96],"aligned.":[73],"Our":[74],"approach":[75],"M-estimation,":[79],"prove":[82],"consistency":[84],"resulting":[87],"estimators.":[88],"A":[89],"small-scale":[90],"simulation":[91],"study":[92],"real":[94],"examples":[95],"used":[97],"illustrate":[99],"numerical":[101],"performances":[102],"our":[104],"procedure.":[105]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}