{"id":"https://openalex.org/W2168632526","doi":"https://doi.org/10.1109/isbi.2006.1625130","title":"Shape Analysis Using the Fisher-Rao Riemannian Metric: Unifying Shape Representation and Deformation","display_name":"Shape Analysis Using the Fisher-Rao Riemannian Metric: Unifying Shape Representation and Deformation","publication_year":2006,"publication_date":"2006-05-25","ids":{"openalex":"https://openalex.org/W2168632526","doi":"https://doi.org/10.1109/isbi.2006.1625130","mag":"2168632526"},"language":"en","primary_location":{"id":"doi:10.1109/isbi.2006.1625130","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isbi.2006.1625130","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"3rd IEEE International Symposium on Biomedical Imaging: Macro to Nano, 2006.","raw_type":"proceedings-article"},"type":"conference-paper","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/A5059964562","display_name":"Adrian M. Peter","orcid":"https://orcid.org/0000-0001-8124-5648"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Peter","raw_affiliation_strings":["Department of ECE, University of Florida, Gainesville, FL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of ECE, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059870257","display_name":"Anand Rangarajan","orcid":"https://orcid.org/0000-0001-8695-8436"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Rangarajan","raw_affiliation_strings":["Department of CISE, University of Florida, Gainesville, FL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of CISE, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I33213144"],"apc_list":null,"apc_paid":null,"fwci":9.5535,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.98666667,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1164","last_page":"1167"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.955299973487854,"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/T14339","display_name":"Image Processing and 3D Reconstruction","score":0.9082000255584717,"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/geodesic","display_name":"Geodesic","score":0.9082205891609192},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.7455454468727112},{"id":"https://openalex.org/keywords/fisher-information","display_name":"Fisher information","score":0.6737268567085266},{"id":"https://openalex.org/keywords/shape-analysis","display_name":"Shape analysis (program analysis)","score":0.6591720581054688},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.6419179439544678},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6002981662750244},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5948958396911621},{"id":"https://openalex.org/keywords/fisher-information-metric","display_name":"Fisher information metric","score":0.5816115140914917},{"id":"https://openalex.org/keywords/active-shape-model","display_name":"Active shape model","score":0.4682252109050751},{"id":"https://openalex.org/keywords/statistical-manifold","display_name":"Statistical manifold","score":0.46626242995262146},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4655758738517761},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.43041738867759705},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4146685004234314},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34848666191101074},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2952626645565033},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2708795368671417},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2390810251235962},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20902341604232788},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.18406620621681213},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.16541370749473572},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.16311275959014893},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11269551515579224},{"id":"https://openalex.org/keywords/convex-metric-space","display_name":"Convex metric space","score":0.08564266562461853}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.9082205891609192},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.7455454468727112},{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.6737268567085266},{"id":"https://openalex.org/C112604564","wikidata":"https://www.wikidata.org/wiki/Q7489226","display_name":"Shape analysis (program analysis)","level":3,"score":0.6591720581054688},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6419179439544678},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6002981662750244},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5948958396911621},{"id":"https://openalex.org/C127104897","wikidata":"https://www.wikidata.org/wiki/Q5454858","display_name":"Fisher information metric","level":4,"score":0.5816115140914917},{"id":"https://openalex.org/C129641003","wikidata":"https://www.wikidata.org/wiki/Q267189","display_name":"Active shape model","level":3,"score":0.4682252109050751},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.46626242995262146},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4655758738517761},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.43041738867759705},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4146685004234314},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34848666191101074},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2952626645565033},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2708795368671417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2390810251235962},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20902341604232788},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.18406620621681213},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.16541370749473572},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.16311275959014893},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11269551515579224},{"id":"https://openalex.org/C196613150","wikidata":"https://www.wikidata.org/wiki/Q3966092","display_name":"Convex metric space","level":3,"score":0.08564266562461853},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C97686452","wikidata":"https://www.wikidata.org/wiki/Q7604153","display_name":"Static analysis","level":2,"score":0.0},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/isbi.2006.1625130","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isbi.2006.1625130","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"3rd IEEE International Symposium on Biomedical Imaging: Macro to Nano, 2006.","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.73.9222","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.73.9222","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cis.ufl.edu/~anand/pdf/Shape_matching_Riemannian.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6000000238418579}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W107085514","https://openalex.org/W646945617","https://openalex.org/W1479979375","https://openalex.org/W1573082642","https://openalex.org/W1577151846","https://openalex.org/W1680579736","https://openalex.org/W1770450209","https://openalex.org/W1992402718","https://openalex.org/W2006302620","https://openalex.org/W2078512515","https://openalex.org/W2089700743","https://openalex.org/W2101015539","https://openalex.org/W2125113735","https://openalex.org/W2128409098","https://openalex.org/W2150559991","https://openalex.org/W2165386340","https://openalex.org/W2171490473","https://openalex.org/W2529007158","https://openalex.org/W2977466517","https://openalex.org/W4248613739","https://openalex.org/W4299441806","https://openalex.org/W6670263011"],"related_works":["https://openalex.org/W4291625303","https://openalex.org/W4300760355","https://openalex.org/W2737579912","https://openalex.org/W2949438187","https://openalex.org/W2155379735","https://openalex.org/W2059474323","https://openalex.org/W1742234374","https://openalex.org/W3206765662","https://openalex.org/W2125882322","https://openalex.org/W1846472178"],"abstract_inverted_index":{"We":[0,85,112],"show":[1],"that":[2],"the":[3,29,37,41,49,53,59,62,73,104,109,128,135],"Fisher-Rao":[4,63,105],"Riemannian":[5],"metric":[6,64,106],"is":[7,22,65],"a":[8,17,26,66,91],"natural,":[9],"intrinsic":[10,78],"tool":[11],"for":[12],"computing":[13,117],"shape":[14,68,88,132],"geodesics.":[15],"When":[16],"parameterized":[18,47],"probability":[19],"density":[20,51],"function":[21],"used":[23],"to":[24,83,108],"represent":[25],"landmark-based":[27],"shape,":[28],"modes":[30],"of":[31,40,61,75],"deformation":[32,133],"are":[33,138],"automatically":[34],"established":[35],"through":[36],"Fisher":[38,118,136],"information":[39],"density.":[42],"Consequently,":[43],"given":[44],"two":[45,101],"shapes":[46,102],"by":[48,116],"same":[50],"model,":[52],"geodesic":[54,98,137],"distance":[55,69,79],"between":[56,100,120],"them":[57],"under":[58],"action":[60],"convenient":[67],"measure.":[70],"It":[71],"has":[72],"advantage":[74],"being":[76],"an":[77],"measure":[80],"and":[81,95,131],"invariant":[82],"reparameterization.":[84],"first":[86],"model":[87,94,130],"landmarks":[89],"using":[90,103],"Gaussian":[92],"mixture":[93,110,129],"then":[96],"compute":[97],"distances":[99],"corresponding":[107],"model.":[111],"illustrate":[113],"our":[114],"approach":[115,143],"geodesics":[119],"2D":[121],"corpus":[122],"callosum":[123],"shapes.":[124],"Shape":[125],"representation":[126],"via":[127,134],"hereby":[139],"unified":[140],"in":[141],"this":[142]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
