{"id":"https://openalex.org/W1800203173","doi":"https://doi.org/10.1109/tip.2016.2541924","title":"Image Segmentation With Eigenfunctions of an Anisotropic Diffusion Operator","display_name":"Image Segmentation With Eigenfunctions of an Anisotropic Diffusion Operator","publication_year":2016,"publication_date":"2016-03-14","ids":{"openalex":"https://openalex.org/W1800203173","doi":"https://doi.org/10.1109/tip.2016.2541924","mag":"1800203173","pmid":"https://pubmed.ncbi.nlm.nih.gov/26992021"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2016.2541924","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2016.2541924","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1404.0723","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jingyue Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I146416000","display_name":"University of Kansas","ror":"https://ror.org/001tmjg57","country_code":"US","type":"education","lineage":["https://openalex.org/I146416000"]},{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN","US"],"is_corresponding":true,"raw_author_name":"Jingyue Wang","raw_affiliation_strings":["College of Mathematics and Computer Science, Fuzhou University, Fuzhou, China","Department of Mathematics, The University of Kansas, Lawrence, KS, USA"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Computer Science, Fuzhou University, Fuzhou, China","institution_ids":["https://openalex.org/I80947539"]},{"raw_affiliation_string":"Department of Mathematics, The University of Kansas, Lawrence, KS, USA","institution_ids":["https://openalex.org/I146416000"]}]},{"author_position":"last","author":{"id":null,"display_name":"Weizhang Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I146416000","display_name":"University of Kansas","ror":"https://ror.org/001tmjg57","country_code":"US","type":"education","lineage":["https://openalex.org/I146416000"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weizhang Huang","raw_affiliation_strings":["Department of Mathematics, The University of Kansas, Lawrence, KS, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Kansas, Lawrence, KS, USA","institution_ids":["https://openalex.org/I146416000"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I146416000","https://openalex.org/I80947539"],"apc_list":null,"apc_paid":null,"fwci":0.8473,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.79455814,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"25","issue":"5","first_page":"2155","last_page":"2167"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.886900007724762,"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":0.886900007724762,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.02250000089406967,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.010900000110268593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.597000002861023},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.586899995803833},{"id":"https://openalex.org/keywords/anisotropic-diffusion","display_name":"Anisotropic diffusion","score":0.5838000178337097},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.47870001196861267},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4742000102996826},{"id":"https://openalex.org/keywords/image-segmentation","display_name":"Image segmentation","score":0.4542999863624573},{"id":"https://openalex.org/keywords/edge-detection","display_name":"Edge detection","score":0.40450000762939453},{"id":"https://openalex.org/keywords/spectral-clustering","display_name":"Spectral clustering","score":0.40299999713897705},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3499000072479248}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.609000027179718},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.597000002861023},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.586899995803833},{"id":"https://openalex.org/C203504353","wikidata":"https://www.wikidata.org/wiki/Q4765461","display_name":"Anisotropic diffusion","level":3,"score":0.5838000178337097},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47870001196861267},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4742000102996826},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46219998598098755},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.4542999863624573},{"id":"https://openalex.org/C193536780","wikidata":"https://www.wikidata.org/wiki/Q1513153","display_name":"Edge detection","level":4,"score":0.40450000762939453},{"id":"https://openalex.org/C105611402","wikidata":"https://www.wikidata.org/wiki/Q2976589","display_name":"Spectral clustering","level":3,"score":0.40299999713897705},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3788999915122986},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35600000619888306},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.33489999175071716},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.3303000032901764},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3206000030040741},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3199999928474426},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.31220000982284546},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3068000078201294},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.2994000017642975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2897999882698059},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.2840999960899353},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C55128770","wikidata":"https://www.wikidata.org/wiki/Q5275440","display_name":"Diffusion map","level":4,"score":0.2784000039100647},{"id":"https://openalex.org/C112353826","wikidata":"https://www.wikidata.org/wiki/Q127313","display_name":"Active contour model","level":4,"score":0.2775999903678894},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.25780001282691956},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2016.2541924","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2016.2541924","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},{"id":"pmid:26992021","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26992021","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null},{"id":"pmh:oai:arXiv.org:1404.0723","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1404.0723","pdf_url":"https://arxiv.org/pdf/1404.0723","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1404.0723","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1404.0723","pdf_url":"https://arxiv.org/pdf/1404.0723","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W118271839","https://openalex.org/W1549562450","https://openalex.org/W1780366808","https://openalex.org/W1866611211","https://openalex.org/W1963559994","https://openalex.org/W1984032850","https://openalex.org/W2000082576","https://openalex.org/W2000594943","https://openalex.org/W2001002651","https://openalex.org/W2005005412","https://openalex.org/W2016081265","https://openalex.org/W2035984669","https://openalex.org/W2061214064","https://openalex.org/W2075136389","https://openalex.org/W2097323414","https://openalex.org/W2103975664","https://openalex.org/W2104404402","https://openalex.org/W2114253824","https://openalex.org/W2116609734","https://openalex.org/W2117684310","https://openalex.org/W2119823327","https://openalex.org/W2120398992","https://openalex.org/W2121927366","https://openalex.org/W2121947440","https://openalex.org/W2125637308","https://openalex.org/W2125654406","https://openalex.org/W2132603077","https://openalex.org/W2132914434","https://openalex.org/W2137137397","https://openalex.org/W2143496291","https://openalex.org/W2146052399","https://openalex.org/W2150134853","https://openalex.org/W2157129549","https://openalex.org/W2952125423","https://openalex.org/W3011612142","https://openalex.org/W4248635988","https://openalex.org/W6604258192","https://openalex.org/W6608197349","https://openalex.org/W6675685020"],"related_works":[],"abstract_inverted_index":{"We":[0],"propose":[1],"the":[2,20,26,29,39,46,54,69,92,151,174,191],"eigenvalue":[3,84,94],"problem":[4,85],"of":[5,28,38,45,74,190],"an":[6,163],"anisotropic":[7,164],"diffusion":[8,14],"operator":[9],"for":[10,50,71,122,149],"image":[11,31,78],"segmentation.":[12],"The":[13,23,83,105,127],"matrix":[15],"is":[16,48,86,131,147,168,171],"defined":[17],"based":[18,157],"on":[19,158,182],"input":[21,30,40,52],"image.":[22,41],"eigenfunctions":[24,57,183],"and":[25,80,111,118,198],"projection":[27],"in":[32,142,150,195],"some":[33],"eigenspace":[34],"capture":[35],"key":[36],"features":[37,189],"An":[42],"important":[43],"property":[44],"model":[47,130,192],"that":[49,143,173],"many":[51],"images,":[53],"first":[55],"few":[56],"are":[58,193,201],"close":[59],"to":[60,88,91],"being":[61],"piecewise":[62],"constant,":[63],"which":[64],"makes":[65],"them":[66],"useful":[67],"as":[68,77,138],"basis":[70],"a":[72,108,159],"variety":[73],"applications,":[75],"such":[76,137],"segmentation":[79,125],"edge":[81],"detection.":[82],"shown":[87,172],"be":[89],"related":[90],"algebraic":[93],"problems":[95],"resulting":[96],"from":[97,134],"several":[98],"commonly":[99],"used":[100],"discrete":[101,123],"spectral":[102,124],"clustering":[103],"models.":[104],"relation":[106],"provides":[107],"better":[109],"understanding":[110],"helps":[112],"developing":[113],"more":[114,179],"efficient":[115],"numerical":[116,120,155,175,196],"implementation":[117,156],"rigorous":[119],"analysis":[121],"methods.":[126],"new":[128],"continuous":[129],"also":[132],"different":[133],"energy-minimization":[135],"methods":[136],"active":[139],"contour":[140],"models":[141],"no":[144],"initial":[145],"guess":[146],"required":[148],"current":[152],"model.":[153],"A":[154],"finite-element":[160],"method":[161],"with":[162],"mesh":[165],"adaptation":[166],"strategy":[167],"presented.":[169],"It":[170],"scheme":[176],"gives":[177],"much":[178],"accurate":[180],"results":[181],"than":[184],"uniform":[185],"meshes.":[186],"Several":[187],"interesting":[188],"examined":[194],"examples,":[197],"possible":[199],"applications":[200],"discussed.":[202]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}