{"id":"https://openalex.org/W1965575981","doi":"https://doi.org/10.1137/s0036139997318032","title":"Generic Structure of Two-Dimensional Images Under Gaussian Blurring","display_name":"Generic Structure of Two-Dimensional Images Under Gaussian Blurring","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1965575981","doi":"https://doi.org/10.1137/s0036139997318032","mag":"1965575981"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139997318032","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139997318032","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","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/A5048285002","display_name":"James Damon","orcid":"https://orcid.org/0000-0002-8511-2604"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"James Damon","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5048285002"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5482,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.92531298,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"59","issue":"1","first_page":"97","last_page":"138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9980999827384949,"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":0.9980999827384949,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9840999841690063,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9815999865531921,"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/transversality","display_name":"Transversality","score":0.8122261762619019},{"id":"https://openalex.org/keywords/grayscale","display_name":"Grayscale","score":0.6315872073173523},{"id":"https://openalex.org/keywords/ridge","display_name":"Ridge","score":0.622268557548523},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.50553297996521},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5039405226707458},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.4905371069908142},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46363183856010437},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.46280306577682495},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.43460237979888916},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.430225670337677},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42597201466560364},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4150771498680115},{"id":"https://openalex.org/keywords/scale-space","display_name":"Scale space","score":0.4109949767589569},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3794563114643097},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3266499638557434},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.2699311077594757},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.25841224193573},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09241878986358643}],"concepts":[{"id":"https://openalex.org/C24167531","wikidata":"https://www.wikidata.org/wiki/Q2300767","display_name":"Transversality","level":2,"score":0.8122261762619019},{"id":"https://openalex.org/C78201319","wikidata":"https://www.wikidata.org/wiki/Q685727","display_name":"Grayscale","level":3,"score":0.6315872073173523},{"id":"https://openalex.org/C32277403","wikidata":"https://www.wikidata.org/wiki/Q740445","display_name":"Ridge","level":2,"score":0.622268557548523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.50553297996521},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5039405226707458},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.4905371069908142},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46363183856010437},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.46280306577682495},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.43460237979888916},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.430225670337677},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42597201466560364},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4150771498680115},{"id":"https://openalex.org/C99102927","wikidata":"https://www.wikidata.org/wiki/Q3058184","display_name":"Scale space","level":4,"score":0.4109949767589569},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3794563114643097},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3266499638557434},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.2699311077594757},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25841224193573},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09241878986358643},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139997318032","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139997318032","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W4499174","https://openalex.org/W10117285","https://openalex.org/W62783252","https://openalex.org/W954361660","https://openalex.org/W1487459268","https://openalex.org/W1543268313","https://openalex.org/W1563062848","https://openalex.org/W1570039896","https://openalex.org/W1603966462","https://openalex.org/W1964806616","https://openalex.org/W1976166337","https://openalex.org/W1983558856","https://openalex.org/W2020845919","https://openalex.org/W2022735534","https://openalex.org/W2062024414","https://openalex.org/W2075085615","https://openalex.org/W2077246452","https://openalex.org/W2077931785","https://openalex.org/W2083673120","https://openalex.org/W2085020989","https://openalex.org/W2091715895","https://openalex.org/W2120959665","https://openalex.org/W2145023731","https://openalex.org/W2146052399","https://openalex.org/W2150134853","https://openalex.org/W2314460146","https://openalex.org/W2316271461","https://openalex.org/W2400999500","https://openalex.org/W2573472341","https://openalex.org/W3198617015","https://openalex.org/W4237267517","https://openalex.org/W4238332724","https://openalex.org/W4244389630","https://openalex.org/W4255272544","https://openalex.org/W4319068731"],"related_works":["https://openalex.org/W2045665826","https://openalex.org/W155037358","https://openalex.org/W4240610494","https://openalex.org/W2980627813","https://openalex.org/W3006004107","https://openalex.org/W2615244697","https://openalex.org/W1548318403","https://openalex.org/W2068498411","https://openalex.org/W2750926009","https://openalex.org/W2146817246"],"abstract_inverted_index":{"For":[0],"medical":[1],"imaging":[2],"problems,":[3],"computer":[4],"scientists":[5],"Pizer":[6],"and":[7,56],"Eberly":[8],"introduced":[9],"the":[10,13,19,29,51,62,83,98,136,157,160,177],"\"core\"":[11],"as":[12,28,76],"analogue":[14],"for":[15,25,58,67,110,117,121],"grayscale":[16],"images":[17,27,70],"of":[18,31,54,69,132,159,168,176],"medial":[20,122],"axis.":[21],"It":[22],"is":[23],"defined":[24,35],"two-dimensional":[26,59],"\"ridge\"":[30],"a":[32,73,87,115,130],"\"medial":[33],"function\"":[34],"on":[36],"(2+1)-dimensional":[37],"scale":[38,169],"space.":[39],"In":[40],"this":[41],"paper,":[42],"we":[43,148],"extend":[44],"methods":[45],"from":[46],"singularity":[47],"theory":[48],"to":[49,135,142],"analyze":[50],"generic":[52,63],"properties":[53,95,104,145],"ridges":[55],"cores":[57],"images,":[60],"including":[61],"transitions":[64],"which":[65,93],"occur":[66],"sequences":[68],"varying":[71],"with":[72],"parameter":[74],"such":[75],"time.":[77],"We":[78,113],"do":[79],"so":[80],"by":[81,97,125,128],"placing":[82],"ridge":[84],"construction":[85],"into":[86],"larger":[88],"\"relative":[89],"critical":[90],"set":[91],"structure,\"":[92],"captures":[94],"undetected":[96],"disjoint":[99],"ridge/core":[100],"segments.":[101],"The":[102,139],"genericity":[103,152],"are":[105],"established":[106],"using":[107,129],"transversality":[108,119,154],"conditions":[109,120,155],"associated":[111],"mappings.":[112],"introduce":[114],"method":[116,140],"establishing":[118,151],"functions":[123],"obtained":[124],"Gaussian":[126],"blurring":[127],"basis":[131],"local":[133],"solutions":[134],"heat":[137],"equation.":[138],"applies":[141],"many":[143],"other":[144],"besides":[146],"those":[147],"consider.":[149],"Furthermore,":[150],"via":[153],"implies":[156],"stability":[158],"full":[161],"structure":[162],"in":[163],"any":[164],"compact":[165],"viewing":[166],"area":[167],"space":[170],"under":[171],"sufficiently":[172],"small":[173],"L2":[174],"perturbations":[175],"image":[178],"intensity":[179],"function.":[180]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
