{"id":"https://openalex.org/W2804647158","doi":"https://doi.org/10.1109/tpami.2018.2839733","title":"Piecewise Flat Embedding for Image Segmentation","display_name":"Piecewise Flat Embedding for Image Segmentation","publication_year":2018,"publication_date":"2018-05-23","ids":{"openalex":"https://openalex.org/W2804647158","doi":"https://doi.org/10.1109/tpami.2018.2839733","mag":"2804647158","pmid":"https://pubmed.ncbi.nlm.nih.gov/29994301"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2018.2839733","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2018.2839733","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5003019748","display_name":"Chaowei Fang","orcid":"https://orcid.org/0000-0001-8805-9792"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Chaowei Fang","raw_affiliation_strings":["Department of Computer Science, The University of Hong Kong, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, The University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101460914","display_name":"Zicheng Liao","orcid":"https://orcid.org/0000-0002-2008-9239"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zicheng Liao","raw_affiliation_strings":["College of Computer Science, Zhejiang University, Hangzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-2008-9239","affiliations":[{"raw_affiliation_string":"College of Computer Science, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108557359","display_name":"Yizhou Yu","orcid":"https://orcid.org/0000-0002-0470-5548"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Yizhou Yu","raw_affiliation_strings":["Department of Computer Science, The University of Hong Kong, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, The University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003019748"],"corresponding_institution_ids":["https://openalex.org/I889458895"],"apc_list":null,"apc_paid":null,"fwci":2.497,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.88461239,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"41","issue":"6","first_page":"1470","last_page":"1485"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9969000220298767,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9944000244140625,"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/embedding","display_name":"Embedding","score":0.6948068141937256},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5316598415374756},{"id":"https://openalex.org/keywords/segmentation","display_name":"Segmentation","score":0.5154955983161926},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.475144624710083},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4662797451019287},{"id":"https://openalex.org/keywords/image-segmentation","display_name":"Image segmentation","score":0.4570063352584839},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.45121434330940247},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42450961470603943},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33686602115631104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06348031759262085}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6948068141937256},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5316598415374756},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.5154955983161926},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.475144624710083},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4662797451019287},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.4570063352584839},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.45121434330940247},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42450961470603943},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33686602115631104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06348031759262085}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2018.2839733","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2018.2839733","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:29994301","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29994301","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 pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8089497224","display_name":null,"funder_award_id":"61602406","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":74,"referenced_works":["https://openalex.org/W79315950","https://openalex.org/W100944330","https://openalex.org/W117482296","https://openalex.org/W1528789833","https://openalex.org/W1543963486","https://openalex.org/W1587669286","https://openalex.org/W1597739853","https://openalex.org/W1918250297","https://openalex.org/W1961988472","https://openalex.org/W1976047850","https://openalex.org/W1993962865","https://openalex.org/W1997149618","https://openalex.org/W1999478155","https://openalex.org/W2001141328","https://openalex.org/W2009685382","https://openalex.org/W2015207482","https://openalex.org/W2033468335","https://openalex.org/W2040072996","https://openalex.org/W2042948547","https://openalex.org/W2053186076","https://openalex.org/W2053608531","https://openalex.org/W2060945009","https://openalex.org/W2062797058","https://openalex.org/W2067191022","https://openalex.org/W2080794127","https://openalex.org/W2080920426","https://openalex.org/W2084809122","https://openalex.org/W2086374833","https://openalex.org/W2089024363","https://openalex.org/W2097308346","https://openalex.org/W2097323414","https://openalex.org/W2101309634","https://openalex.org/W2103559027","https://openalex.org/W2107861471","https://openalex.org/W2108119513","https://openalex.org/W2108565035","https://openalex.org/W2110158442","https://openalex.org/W2116046277","https://openalex.org/W2118331541","https://openalex.org/W2119823327","https://openalex.org/W2119883478","https://openalex.org/W2121947440","https://openalex.org/W2125215748","https://openalex.org/W2125455772","https://openalex.org/W2125531986","https://openalex.org/W2128356031","https://openalex.org/W2141376824","https://openalex.org/W2141957843","https://openalex.org/W2142058898","https://openalex.org/W2155754954","https://openalex.org/W2157444450","https://openalex.org/W2157872906","https://openalex.org/W2160398355","https://openalex.org/W2161675672","https://openalex.org/W2164847484","https://openalex.org/W2168804568","https://openalex.org/W2187089797","https://openalex.org/W2198626657","https://openalex.org/W2323866876","https://openalex.org/W2405933695","https://openalex.org/W2417254599","https://openalex.org/W2536208356","https://openalex.org/W2574253917","https://openalex.org/W2962803021","https://openalex.org/W6604134081","https://openalex.org/W6604736770","https://openalex.org/W6631412525","https://openalex.org/W6632620505","https://openalex.org/W6683161245","https://openalex.org/W6683194942","https://openalex.org/W6684113476","https://openalex.org/W6696310042","https://openalex.org/W6701196506","https://openalex.org/W6713590816"],"related_works":["https://openalex.org/W2081900870","https://openalex.org/W2183306018","https://openalex.org/W2549990292","https://openalex.org/W2345479200","https://openalex.org/W2385263368","https://openalex.org/W2951819827","https://openalex.org/W2849310602","https://openalex.org/W2419146053","https://openalex.org/W2347422947","https://openalex.org/W1522196789"],"abstract_inverted_index":{"We":[0,77,117],"introduce":[1],"a":[2,29,82,103],"new":[3],"multi-dimensional":[4],"nonlinear":[5],"embedding-Piecewise":[6],"Flat":[7],"Embedding":[8],"(PFE)-for":[9],"image":[10,32,60,70,141],"segmentation.":[11],"Based":[12],"on":[13,108,146,152,156],"the":[14,85,127],"theory":[15],"of":[16,84],"sparse":[17,35,39,98],"signal":[18],"recovery,":[19],"piecewise":[20,30,45,114],"flat":[21,46,115],"embedding":[22,47,80,88,175],"with":[23,34,62,89],"diverse":[24],"channels":[25],"attempts":[26],"to":[27,96,111,125],"recover":[28],"constant":[31],"representation":[33,61],"region":[36,64],"boundaries":[37],"and":[38,57,148,166],"cluster":[40],"value":[41],"scattering.":[42],"The":[43],"resultant":[44],"exhibits":[48],"interesting":[49],"properties":[50],"such":[51],"as":[52,81],"suppressing":[53],"slowly":[54],"varying":[55],"signals,":[56],"offers":[58],"an":[59,90],"higher":[63],"identifiability":[65],"which":[66],"is":[67],"desirable":[68],"for":[69],"segmentation":[71,142,144,150,171],"or":[72],"high-level":[73],"semantic":[74],"analysis":[75],"tasks.":[76],"formulate":[78],"our":[79,174],"variant":[83],"Laplacian":[86],"Eigenmap":[87],"$L_{1,p}":[91],"(0<p\\leq":[92],"1)$L1,p(0<p\u22641)":[93],"regularization":[94],"term":[95],"promote":[97],"solutions.":[99],"First,":[100],"we":[101,135],"devise":[102],"two-stage":[104],"numerical":[105],"algorithm":[106,121],"based":[107,145,151],"Bregman":[109],"iterations":[110],"compute":[112],"$L_{1,1}$L1,1-regularized":[113],"embeddings.":[116],"further":[118],"generalize":[119],"this":[120],"through":[122],"iterative":[123],"reweighting":[124],"solve":[126],"general":[128],"$L_{1,p}$L1,p-regularized":[129],"problem.":[130],"To":[131],"demonstrate":[132],"its":[133],"efficacy,":[134],"integrate":[136],"PFE":[137],"into":[138],"two":[139],"existing":[140],"frameworks,":[143],"clustering":[147],"hierarchical":[149],"contour":[153],"detection.":[154],"Experiments":[155],"four":[157],"major":[158],"benchmark":[159],"datasets,":[160],"BSDS500,":[161],"MSRC,":[162],"Stanford":[163],"Background":[164],"Dataset,":[165],"PASCAL":[167],"Context,":[168],"show":[169],"that":[170],"algorithms":[172],"incorporating":[173],"achieve":[176],"significantly":[177],"improved":[178],"results.":[179]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
