{"id":"https://openalex.org/W1131800792","doi":"https://doi.org/10.2312/pe/vmv/vmv12/143-150","title":"Cyclic Numerical Time Integration in Variational Non-Rigid Image Registration based on Quadratic Regularisation","display_name":"Cyclic Numerical Time Integration in Variational Non-Rigid Image Registration based on Quadratic Regularisation","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1131800792","doi":"https://doi.org/10.2312/pe/vmv/vmv12/143-150","mag":"1131800792"},"language":"en","primary_location":{"id":"doi:10.2312/pe/vmv/vmv12/143-150","is_oa":true,"landing_page_url":"https://doi.org/10.2312/pe/vmv/vmv12/143-150","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2312/pe/vmv/vmv12/143-150","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017333493","display_name":"Andreas Mang","orcid":"https://orcid.org/0000-0003-4605-3290"},"institutions":[{"id":"https://openalex.org/I9341345","display_name":"University of L\u00fcbeck","ror":"https://ror.org/00t3r8h32","country_code":"DE","type":"education","lineage":["https://openalex.org/I9341345"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Mang, Andreas","raw_affiliation_strings":["University of L\u00fcbeck, L\u00fcbeck, Germany"],"affiliations":[{"raw_affiliation_string":"University of L\u00fcbeck, L\u00fcbeck, Germany","institution_ids":["https://openalex.org/I9341345"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010066068","display_name":"Tina A. Schuetz","orcid":null},"institutions":[{"id":"https://openalex.org/I9341345","display_name":"University of L\u00fcbeck","ror":"https://ror.org/00t3r8h32","country_code":"DE","type":"education","lineage":["https://openalex.org/I9341345"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Schuetz, Tina Anne","raw_affiliation_strings":["University of L\u00fcbeck, L\u00fcbeck, Germany"],"affiliations":[{"raw_affiliation_string":"University of L\u00fcbeck, L\u00fcbeck, Germany","institution_ids":["https://openalex.org/I9341345"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054589273","display_name":"Stefan Becker","orcid":"https://orcid.org/0000-0002-5333-3162"},"institutions":[{"id":"https://openalex.org/I9341345","display_name":"University of L\u00fcbeck","ror":"https://ror.org/00t3r8h32","country_code":"DE","type":"education","lineage":["https://openalex.org/I9341345"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Becker, Stefan","raw_affiliation_strings":["University of L\u00fcbeck, L\u00fcbeck, Germany"],"affiliations":[{"raw_affiliation_string":"University of L\u00fcbeck, L\u00fcbeck, Germany","institution_ids":["https://openalex.org/I9341345"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038388778","display_name":"Alina Toma","orcid":"https://orcid.org/0000-0003-2212-2896"},"institutions":[{"id":"https://openalex.org/I9341345","display_name":"University of L\u00fcbeck","ror":"https://ror.org/00t3r8h32","country_code":"DE","type":"education","lineage":["https://openalex.org/I9341345"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Toma, Alina","raw_affiliation_strings":["University of L\u00fcbeck, L\u00fcbeck, Germany"],"affiliations":[{"raw_affiliation_string":"University of L\u00fcbeck, L\u00fcbeck, Germany","institution_ids":["https://openalex.org/I9341345"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075608266","display_name":"Thorsten M. Buzug","orcid":"https://orcid.org/0000-0002-0399-8043"},"institutions":[{"id":"https://openalex.org/I9341345","display_name":"University of L\u00fcbeck","ror":"https://ror.org/00t3r8h32","country_code":"DE","type":"education","lineage":["https://openalex.org/I9341345"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Buzug, Thorsten M.","raw_affiliation_strings":["University of L\u00fcbeck, L\u00fcbeck, Germany"],"affiliations":[{"raw_affiliation_string":"University of L\u00fcbeck, L\u00fcbeck, Germany","institution_ids":["https://openalex.org/I9341345"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5017333493"],"corresponding_institution_ids":["https://openalex.org/I9341345"],"apc_list":null,"apc_paid":null,"fwci":0.2767,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.52979235,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"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/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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9927999973297119,"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/quadratic-equation","display_name":"Quadratic equation","score":0.6593599319458008},{"id":"https://openalex.org/keywords/image-registration","display_name":"Image registration","score":0.5843191146850586},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4821131229400635},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.46562737226486206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44829678535461426},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44075673818588257},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43954014778137207},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39997047185897827},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39769190549850464},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3569764792919159},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23692965507507324}],"concepts":[{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6593599319458008},{"id":"https://openalex.org/C166704113","wikidata":"https://www.wikidata.org/wiki/Q861092","display_name":"Image registration","level":3,"score":0.5843191146850586},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4821131229400635},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.46562737226486206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44829678535461426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44075673818588257},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43954014778137207},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39997047185897827},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39769190549850464},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3569764792919159},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23692965507507324}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2312/pe/vmv/vmv12/143-150","is_oa":true,"landing_page_url":"https://doi.org/10.2312/pe/vmv/vmv12/143-150","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.2312/pe/vmv/vmv12/143-150","is_oa":true,"landing_page_url":"https://doi.org/10.2312/pe/vmv/vmv12/143-150","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1533758240","https://openalex.org/W1534099420","https://openalex.org/W1564699816","https://openalex.org/W1579634341","https://openalex.org/W1585416137","https://openalex.org/W1960717653","https://openalex.org/W1968642437","https://openalex.org/W1973888842","https://openalex.org/W1988567899","https://openalex.org/W2041398617","https://openalex.org/W2045484730","https://openalex.org/W2045696825","https://openalex.org/W2051820877","https://openalex.org/W2078466655","https://openalex.org/W2084932145","https://openalex.org/W2090301223","https://openalex.org/W2090808267","https://openalex.org/W2093252491","https://openalex.org/W2099801199","https://openalex.org/W2109859915","https://openalex.org/W2123723083","https://openalex.org/W2142853128","https://openalex.org/W2146545007","https://openalex.org/W2156764761","https://openalex.org/W2158167845","https://openalex.org/W2406977418","https://openalex.org/W2776491914","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W3029645440","https://openalex.org/W2992981188","https://openalex.org/W1965921897","https://openalex.org/W1970222673","https://openalex.org/W2963942766","https://openalex.org/W2312233215","https://openalex.org/W2286032140","https://openalex.org/W2157358125","https://openalex.org/W2135558784","https://openalex.org/W2130257210","https://openalex.org/W2112130807","https://openalex.org/W2090808267","https://openalex.org/W2078708982","https://openalex.org/W2061575214","https://openalex.org/W2051820877","https://openalex.org/W2038607477","https://openalex.org/W2037316890","https://openalex.org/W1986775347","https://openalex.org/W1976987057","https://openalex.org/W1758403314"],"abstract_inverted_index":{"In":[0],"the":[1,71,82,85,94,108,144],"present":[2],"work,":[3],"a":[4,64,68,103,128,157,178,190],"novel":[5],"computational":[6],"framework":[7,49,193],"for":[8,67,81],"variational":[9,72,192],"non-rigid":[10],"image":[11],"registration":[12],"is":[13,18,50,87,171,187],"discussed.":[14],"The":[15,52,75],"fundamental":[16],"aim":[17],"to":[19,23,39,102,121],"provide":[20],"an":[21,90,166],"alternative":[22],"approximate":[24],"approaches":[25],"based":[26,135,194,205],"on":[27,107,136,148,195,206],"successive":[28],"convolution,":[29],"which":[30,57,170],"have":[31],"gained":[32],"great":[33],"popularity":[34],"in":[35,116,124,162,165],"recent":[36],"years,":[37],"due":[38],"their":[40],"linear":[41],"complexity":[42],"and":[43,119,199,212],"ease":[44],"of":[45,61,70,84,133,180,202],"implementation.":[46],"An":[47],"optimise-then-discretise":[48],"considered.":[51,185],"corresponding":[53],"Euler-Lagrange":[54],"equations":[55],"(ELEs),":[56],"arise":[58],"from":[59],"calculus":[60],"variation,":[62],"constitute":[63],"necessary":[65],"condition":[66],"minimiser":[69],"optimisation":[73],"problem.":[74],"conventional,":[76],"semi-implicit":[77],"(SI)":[78],"time":[79,111,140,151],"integration":[80],"solution":[83],"ELEs":[86],"replaced":[88,155],"by":[89,156],"explicit":[91,98,138],"approach":[92],"rendering":[93],"implementation":[95],"straightforward.":[96],"Since":[97],"methods":[99,134,183],"are":[100,115,184],"subject":[101],"restrictive":[104],"stability":[105,146,159],"requirement":[106,147],"maximal":[109],"admissible":[110],"step":[112,152],"size,":[113],"they":[114],"general":[117],"inefficient":[118],"prone":[120],"get":[122],"stuck":[123],"local":[125],"minima.":[126],"As":[127,177],"remedy,":[129],"we":[130],"take":[131],"advantage":[132],"cyclic":[137],"numerical":[139,203],"integration.":[141],"With":[142],"this":[143],"strong":[145],"each":[149],"individual":[150],"can":[153],"be":[154],"relaxed":[158],"requirement.":[160],"This":[161],"turn":[163],"results":[164],"unconditionally":[167],"stable":[168],"method,":[169],"as":[172,174],"efficient":[173],"SI":[175,182],"approaches.":[176],"basis":[179],"comparison,":[181],"Generalisability":[186],"demonstrated":[188],"within":[189],"generic":[191],"quadratic":[196],"regularisation.":[197],"Qualitative":[198],"quantitative":[200],"analysis":[201],"experiments":[204],"synthetic":[207],"test":[208],"data":[209],"demonstrates":[210],"accuracy":[211],"efficiency.":[213]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
