{"id":"https://openalex.org/W1973628819","doi":"https://doi.org/10.1137/s0036139902403901","title":"A Second Order Shape Optimization Approach for Image Segmentation","display_name":"A Second Order Shape Optimization Approach for Image Segmentation","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1973628819","doi":"https://doi.org/10.1137/s0036139902403901","mag":"1973628819"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139902403901","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139902403901","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":true,"oa_status":"green","oa_url":"https://unipub.uni-graz.at/obvugroa/content/titleinfo/3782650/full.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062202097","display_name":"Michael Hinterm\u00fcller","orcid":"https://orcid.org/0000-0001-9471-2479"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Michael Hinterm\u00fcller","raw_affiliation_strings":["Special Research Center on Optimization and Control, Institute of Mathematics, University of Graz, Heinrichstrasse 36, A-8010 Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Special Research Center on Optimization and Control, Institute of Mathematics, University of Graz, Heinrichstrasse 36, A-8010 Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064913797","display_name":"Wolfgang Ring","orcid":null},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Wolfgang Ring","raw_affiliation_strings":["Special Research Center on Optimization and Control, Institute of Mathematics, University of Graz, Heinrichstrasse 36, A-8010 Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Special Research Center on Optimization and Control, Institute of Mathematics, University of Graz, Heinrichstrasse 36, A-8010 Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I15766117"],"apc_list":null,"apc_paid":null,"fwci":6.7593,"has_fulltext":true,"cited_by_count":120,"citation_normalized_percentile":{"value":0.96835637,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"64","issue":"2","first_page":"442","last_page":"467"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9810000061988831,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9735000133514404,"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/active-contour-model","display_name":"Active contour model","score":0.8037170171737671},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.5504041910171509},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5406225919723511},{"id":"https://openalex.org/keywords/segmentation","display_name":"Segmentation","score":0.5117113590240479},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5004720687866211},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.4964058995246887},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4437185823917389},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.4311046600341797},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4276614189147949},{"id":"https://openalex.org/keywords/image-segmentation","display_name":"Image segmentation","score":0.4146747589111328},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3725121021270752},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34024280309677124},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.27421319484710693},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.18254560232162476},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07622015476226807}],"concepts":[{"id":"https://openalex.org/C112353826","wikidata":"https://www.wikidata.org/wiki/Q127313","display_name":"Active contour model","level":4,"score":0.8037170171737671},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.5504041910171509},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5406225919723511},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.5117113590240479},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5004720687866211},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.4964058995246887},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4437185823917389},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.4311046600341797},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4276614189147949},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.4146747589111328},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3725121021270752},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34024280309677124},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27421319484710693},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18254560232162476},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07622015476226807},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0036139902403901","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139902403901","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"},{"id":"pmh:oai:unipub.uni-graz.at:3782650","is_oa":true,"landing_page_url":"https://unipub.uni-graz.at/doi/10.1137/S0036139902403901","pdf_url":"https://unipub.uni-graz.at/obvugroa/content/titleinfo/3782650/full.pdf","source":{"id":"https://openalex.org/S4306400359","display_name":"Unipub UB Graz (Universit\u00e4t Graz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I15766117","host_organization_name":"University of Graz","host_organization_lineage":["https://openalex.org/I15766117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:bibcyt.ucla.edu.ve:T070300013542/4","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300013542/4&Nombrebd=Bciucla","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"pmh:oai:figshare.com:article/23370467","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/A_second_order_shape_optimization_approach_for_image_segmentation/23370467","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:unipub.uni-graz.at:3782650","is_oa":true,"landing_page_url":"https://unipub.uni-graz.at/doi/10.1137/S0036139902403901","pdf_url":"https://unipub.uni-graz.at/obvugroa/content/titleinfo/3782650/full.pdf","source":{"id":"https://openalex.org/S4306400359","display_name":"Unipub UB Graz (Universit\u00e4t Graz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I15766117","host_organization_name":"University of Graz","host_organization_lineage":["https://openalex.org/I15766117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1973628819.pdf","grobid_xml":"https://content.openalex.org/works/W1973628819.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W50490584","https://openalex.org/W151368118","https://openalex.org/W1483079458","https://openalex.org/W1516415680","https://openalex.org/W1977946246","https://openalex.org/W1999244633","https://openalex.org/W2009967126","https://openalex.org/W2026356722","https://openalex.org/W2034976587","https://openalex.org/W2037677143","https://openalex.org/W2044562173","https://openalex.org/W2050427737","https://openalex.org/W2054113582","https://openalex.org/W2056528953","https://openalex.org/W2058981386","https://openalex.org/W2062396579","https://openalex.org/W2082052570","https://openalex.org/W2089503490","https://openalex.org/W2096201928","https://openalex.org/W2097924771","https://openalex.org/W2104095591","https://openalex.org/W2116040950","https://openalex.org/W2116737017","https://openalex.org/W2144133758","https://openalex.org/W2146052399","https://openalex.org/W2149184914","https://openalex.org/W2151783599","https://openalex.org/W2151810041","https://openalex.org/W2161237731","https://openalex.org/W2208153982","https://openalex.org/W2998023265","https://openalex.org/W3211330693","https://openalex.org/W4293183906","https://openalex.org/W4293775970","https://openalex.org/W4302436815"],"related_works":["https://openalex.org/W2387003628","https://openalex.org/W123102278","https://openalex.org/W2081609930","https://openalex.org/W2365596436","https://openalex.org/W1522196789","https://openalex.org/W4210537690","https://openalex.org/W2885157826","https://openalex.org/W1979702773","https://openalex.org/W2159463658","https://openalex.org/W2051067977"],"abstract_inverted_index":{"The":[0,39,64],"problem":[1,74],"of":[2,4],"segmentation":[3,29],"a":[5],"given":[6],"image":[7,28],"using":[8],"the":[9,60,76,87],"active":[10,24,78],"contour":[11,25,79],"technique":[12],"is":[13,37,46,68],"considered.":[14],"An":[15],"abstract":[16],"calculus":[17],"to":[18,48,54],"find":[19],"appropriate":[20],"speed":[21,40,50,66],"functions":[22,51],"for":[23,59],"models":[26],"in":[27,80],"or":[30,56],"related":[31],"problems":[32],"based":[33],"on":[34,75],"variational":[35],"principles":[36],"presented.":[38,95],"method":[41,90,93],"from":[42],"shape":[43],"sensitivity":[44],"analysis":[45],"used":[47],"derive":[49],"which":[52],"correspond":[53],"gradient":[55,89],"Newton-type":[57,65],"directions":[58],"underlying":[61],"optimization":[62],"problem.":[63],"function":[67],"found":[69],"by":[70],"solving":[71],"an":[72],"elliptic":[73],"current":[77],"every":[81],"time":[82],"step.":[83],"Numerical":[84],"experiments":[85],"comparing":[86],"classical":[88],"with":[91],"Newton's":[92],"are":[94]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}