{"id":"https://openalex.org/W2143983457","doi":"https://doi.org/10.1109/tpami.2014.2346172","title":"Skeletonization and Partitioning of Digital Images Using Discrete Morse Theory","display_name":"Skeletonization and Partitioning of Digital Images Using Discrete Morse Theory","publication_year":2014,"publication_date":"2014-08-07","ids":{"openalex":"https://openalex.org/W2143983457","doi":"https://doi.org/10.1109/tpami.2014.2346172","mag":"2143983457","pmid":"https://pubmed.ncbi.nlm.nih.gov/26353267"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2014.2346172","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2014.2346172","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":true,"oa_status":"green","oa_url":"https://openresearch-repository.anu.edu.au/bitstreams/7ea54fb5-5839-47bc-bfee-61e1adcc2407/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066088486","display_name":"Olaf Delgado\u2010Friedrichs","orcid":"https://orcid.org/0000-0001-8034-5057"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Olaf Delgado-Friedrichs","raw_affiliation_strings":["Department of Applied Mathematics, Research School of Physics and Engineering, the Australian National University, Canberra, ACT, Australia","[Department of Applied Mathematics, Research School of Physics and Engineering, the Australian National University, Canberra, ACT, Australia]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Research School of Physics and Engineering, the Australian National University, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]},{"raw_affiliation_string":"[Department of Applied Mathematics, Research School of Physics and Engineering, the Australian National University, Canberra, ACT, Australia]","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055608145","display_name":"Vanessa Robins","orcid":"https://orcid.org/0000-0001-7118-8491"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Vanessa Robins","raw_affiliation_strings":["Department of Applied Mathematics, Research School of Physics and Engineering, the Australian National University, Canberra, ACT, Australia","[Department of Applied Mathematics, Research School of Physics and Engineering, the Australian National University, Canberra, ACT, Australia]"],"raw_orcid":"https://orcid.org/0000-0001-7118-8491","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Research School of Physics and Engineering, the Australian National University, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]},{"raw_affiliation_string":"[Department of Applied Mathematics, Research School of Physics and Engineering, the Australian National University, Canberra, ACT, Australia]","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007352291","display_name":"Adrian Sheppard","orcid":"https://orcid.org/0000-0001-9792-4143"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Adrian Sheppard","raw_affiliation_strings":["Department of Applied Mathematics, Research School of Physics and Engineering, the Australian National University, Canberra, ACT, Australia","[Department of Applied Mathematics, Research School of Physics and Engineering, the Australian National University, Canberra, ACT, Australia]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Research School of Physics and Engineering, the Australian National University, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]},{"raw_affiliation_string":"[Department of Applied Mathematics, Research School of Physics and Engineering, the Australian National University, Canberra, ACT, Australia]","institution_ids":["https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I118347636"],"apc_list":null,"apc_paid":null,"fwci":5.3607,"has_fulltext":true,"cited_by_count":98,"citation_normalized_percentile":{"value":0.96147904,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"37","issue":"3","first_page":"654","last_page":"666"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12859","display_name":"Cell Image Analysis Techniques","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/1304","display_name":"Biophysics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9930999875068665,"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/discrete-morse-theory","display_name":"Discrete Morse theory","score":0.8833416700363159},{"id":"https://openalex.org/keywords/skeletonization","display_name":"Skeletonization","score":0.6759676933288574},{"id":"https://openalex.org/keywords/morse-theory","display_name":"Morse theory","score":0.6737564206123352},{"id":"https://openalex.org/keywords/persistent-homology","display_name":"Persistent homology","score":0.523294985294342},{"id":"https://openalex.org/keywords/digital-topology","display_name":"Digital topology","score":0.5148400664329529},{"id":"https://openalex.org/keywords/medial-axis","display_name":"Medial axis","score":0.5104166865348816},{"id":"https://openalex.org/keywords/tree-traversal","display_name":"Tree traversal","score":0.46542876958847046},{"id":"https://openalex.org/keywords/grayscale","display_name":"Grayscale","score":0.45344454050064087},{"id":"https://openalex.org/keywords/morse-code","display_name":"Morse code","score":0.4327843189239502},{"id":"https://openalex.org/keywords/voxel","display_name":"Voxel","score":0.42778584361076355},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42204374074935913},{"id":"https://openalex.org/keywords/pixel","display_name":"Pixel","score":0.41886845231056213},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.407571941614151},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.39711683988571167},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3681718409061432},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.21201768517494202},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1791750192642212},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.1444239318370819}],"concepts":[{"id":"https://openalex.org/C170315498","wikidata":"https://www.wikidata.org/wiki/Q5282039","display_name":"Discrete Morse theory","level":3,"score":0.8833416700363159},{"id":"https://openalex.org/C23951316","wikidata":"https://www.wikidata.org/wiki/Q1984140","display_name":"Skeletonization","level":2,"score":0.6759676933288574},{"id":"https://openalex.org/C156730297","wikidata":"https://www.wikidata.org/wiki/Q2296951","display_name":"Morse theory","level":2,"score":0.6737564206123352},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.523294985294342},{"id":"https://openalex.org/C557022819","wikidata":"https://www.wikidata.org/wiki/Q5276205","display_name":"Digital topology","level":5,"score":0.5148400664329529},{"id":"https://openalex.org/C185877587","wikidata":"https://www.wikidata.org/wiki/Q1757407","display_name":"Medial axis","level":2,"score":0.5104166865348816},{"id":"https://openalex.org/C140745168","wikidata":"https://www.wikidata.org/wiki/Q1210082","display_name":"Tree traversal","level":2,"score":0.46542876958847046},{"id":"https://openalex.org/C78201319","wikidata":"https://www.wikidata.org/wiki/Q685727","display_name":"Grayscale","level":3,"score":0.45344454050064087},{"id":"https://openalex.org/C140031139","wikidata":"https://www.wikidata.org/wiki/Q79897","display_name":"Morse code","level":2,"score":0.4327843189239502},{"id":"https://openalex.org/C54170458","wikidata":"https://www.wikidata.org/wiki/Q663554","display_name":"Voxel","level":2,"score":0.42778584361076355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42204374074935913},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.41886845231056213},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.407571941614151},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39711683988571167},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3681718409061432},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.21201768517494202},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1791750192642212},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.1444239318370819},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C143913944","wikidata":"https://www.wikidata.org/wiki/Q5421952","display_name":"Extension topology","level":4,"score":0.0},{"id":"https://openalex.org/C129089157","wikidata":"https://www.wikidata.org/wiki/Q621550","display_name":"General topology","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tpami.2014.2346172","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2014.2346172","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:26353267","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26353267","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},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/12873","is_oa":true,"landing_page_url":"http://hdl.handle.net/1885/12873","pdf_url":"https://openresearch-repository.anu.edu.au/bitstreams/7ea54fb5-5839-47bc-bfee-61e1adcc2407/download","source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"Journal article"}],"best_oa_location":{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/12873","is_oa":true,"landing_page_url":"http://hdl.handle.net/1885/12873","pdf_url":"https://openresearch-repository.anu.edu.au/bitstreams/7ea54fb5-5839-47bc-bfee-61e1adcc2407/download","source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"Journal article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6600000262260437,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G1344137850","display_name":null,"funder_award_id":"DP110102888","funder_id":"https://openalex.org/F4320338275","funder_display_name":"Division of Arctic Sciences"}],"funders":[{"id":"https://openalex.org/F4320338275","display_name":"Division of Arctic Sciences","ror":"https://ror.org/02trddg58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2143983457.pdf","grobid_xml":"https://content.openalex.org/works/W2143983457.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W116833144","https://openalex.org/W124643305","https://openalex.org/W151895561","https://openalex.org/W181053014","https://openalex.org/W1503771062","https://openalex.org/W1526753291","https://openalex.org/W1552904969","https://openalex.org/W1558576290","https://openalex.org/W1586704216","https://openalex.org/W1831954423","https://openalex.org/W1977010014","https://openalex.org/W1979249881","https://openalex.org/W1983948426","https://openalex.org/W1991977354","https://openalex.org/W2002165972","https://openalex.org/W2005989959","https://openalex.org/W2009859144","https://openalex.org/W2010792042","https://openalex.org/W2012140862","https://openalex.org/W2026316104","https://openalex.org/W2029833645","https://openalex.org/W2038021960","https://openalex.org/W2053798192","https://openalex.org/W2064020260","https://openalex.org/W2067946238","https://openalex.org/W2068014716","https://openalex.org/W2081133342","https://openalex.org/W2086860590","https://openalex.org/W2091006082","https://openalex.org/W2101570837","https://openalex.org/W2104284394","https://openalex.org/W2111169612","https://openalex.org/W2124338751","https://openalex.org/W2130212173","https://openalex.org/W2132131517","https://openalex.org/W2142345929","https://openalex.org/W2143931888","https://openalex.org/W2146019744","https://openalex.org/W2150049246","https://openalex.org/W2159329531","https://openalex.org/W2160639462","https://openalex.org/W2167962735","https://openalex.org/W2346033130","https://openalex.org/W2499066376","https://openalex.org/W2793167574","https://openalex.org/W3013741643","https://openalex.org/W3037671387","https://openalex.org/W3106485825","https://openalex.org/W3122470830","https://openalex.org/W3140579943","https://openalex.org/W4206264541","https://openalex.org/W4247832325","https://openalex.org/W4251431888","https://openalex.org/W4308689907","https://openalex.org/W6606194389","https://openalex.org/W6775610265","https://openalex.org/W6807835113","https://openalex.org/W6846734499","https://openalex.org/W7038205764"],"related_works":["https://openalex.org/W1970932056","https://openalex.org/W1984855521","https://openalex.org/W2051997380","https://openalex.org/W4402387632","https://openalex.org/W2011808502","https://openalex.org/W4285761029","https://openalex.org/W3204405814","https://openalex.org/W1561739522","https://openalex.org/W2072362562","https://openalex.org/W2001655492"],"abstract_inverted_index":{"We":[0,21,119],"show":[1],"how":[2],"discrete":[3,47,133],"Morse":[4,94],"theory":[5,95],"provides":[6],"a":[7,23,27,31,46,73,138],"rigorous":[8],"and":[9,15,75,83,96,123],"unifying":[10],"foundation":[11],"for":[12,108,148,151,180],"defining":[13],"skeletons":[14,124],"partitions":[16],"of":[17,72,77,105,128,165,175],"grayscale":[18,24],"digital":[19],"images.":[20],"model":[22],"image":[25],"as":[26],"cubical":[28],"complex":[29],"with":[30,87],"real-valued":[32],"function":[33,42],"defined":[34],"on":[35],"its":[36],"vertices":[37],"(the":[38,69],"voxel":[39],"values).":[40],"This":[41],"is":[43,113,156],"extended":[44],"to":[45,100,115],"gradient":[48,134],"vector":[49,135,153],"field":[50,136,154],"using":[51,80,137],"the":[52,63,78,81,102,111,116,121,132],"algorithm":[53],"presented":[54],"in":[55,131],"Robins,":[56],"Wood,":[57],"Sheppard":[58],"TPAMI":[59],"33:1646":[60],"(2011).":[61],"In":[62],"current":[64],"paper":[65],"we":[66],"define":[67],"basins":[68,122],"building":[70],"blocks":[71],"partition)":[74],"segments":[76],"skeleton":[79,112],"stable":[82],"unstable":[84],"sets":[85],"associated":[86],"critical":[88,129],"cells.":[89],"The":[90],"natural":[91],"connection":[92],"between":[93],"homology":[97],"allows":[98],"us":[99],"prove":[101],"topological":[103,173],"validity":[104],"these":[106],"constructions;":[107],"example,":[109],"that":[110],"homotopic":[114],"initial":[117],"object.":[118],"simplify":[120],"via":[125],"Morse-theoretic":[126],"cancellation":[127],"cells":[130],"strategy":[139],"informed":[140],"by":[141],"persistent":[142],"homology.":[143],"Simple":[144],"working":[145],"Python":[146],"code":[147],"our":[149],"algorithms":[150],"efficient":[152],"traversal":[155],"included.":[157],"Example":[158],"data":[159],"are":[160,178],"taken":[161],"from":[162],"micro-CT":[163],"images":[164],"porous":[166],"materials,":[167],"an":[168],"application":[169],"area":[170],"where":[171],"accurate":[172],"models":[174],"pore":[176],"connectivity":[177],"vital":[179],"fluid-flow":[181],"modelling.":[182]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":22},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3}],"updated_date":"2026-07-14T08:27:34.040176","created_date":"2025-10-10T00:00:00"}
