{"id":"https://openalex.org/W2134560790","doi":"https://doi.org/10.1109/tpami.2003.1177156","title":"A linear time algorithm for computing exact Euclidean distance transforms of binary images in arbitrary dimensions","display_name":"A linear time algorithm for computing exact Euclidean distance transforms of binary images in arbitrary dimensions","publication_year":2003,"publication_date":"2003-02-01","ids":{"openalex":"https://openalex.org/W2134560790","doi":"https://doi.org/10.1109/tpami.2003.1177156","mag":"2134560790"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2003.1177156","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2003.1177156","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"],"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/A5108427167","display_name":"Calvin R. Maurer","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"C.R. Maurer","raw_affiliation_strings":["Department of Neurosurgery, University of Stanford, Stanford, CA, USA","Dept. of Neurosurg., Stanford Univ., CA, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Neurosurgery, University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Dept. of Neurosurg., Stanford Univ., CA, USA#TAB#","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057129472","display_name":"Rensheng Qi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rensheng Qi","raw_affiliation_strings":["Imaging Diagnostic Systems, Inc., Plantation, FL, USA","[Imaging Diagnostic Systems, Inc., Plantation, FL, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Imaging Diagnostic Systems, Inc., Plantation, FL, USA","institution_ids":[]},{"raw_affiliation_string":"[Imaging Diagnostic Systems, Inc., Plantation, FL, USA]","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103238611","display_name":"Vijay Raghavan","orcid":"https://orcid.org/0000-0002-2286-7719"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"V. Raghavan","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, Vanderbilt University, Nashville, TN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, Vanderbilt University, Nashville, TN, USA","institution_ids":["https://openalex.org/I200719446"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108427167"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":11.8556,"has_fulltext":false,"cited_by_count":911,"citation_normalized_percentile":{"value":0.98969738,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"25","issue":"2","first_page":"265","last_page":"270"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":1.0,"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/T12923","display_name":"Digital Image Processing Techniques","score":1.0,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9995999932289124,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9987000226974487,"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/voronoi-diagram","display_name":"Voronoi diagram","score":0.7111363410949707},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6019423007965088},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5681240558624268},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.5028695464134216},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4928038418292999},{"id":"https://openalex.org/keywords/voxel","display_name":"Voxel","score":0.4813866913318634},{"id":"https://openalex.org/keywords/weighted-voronoi-diagram","display_name":"Weighted Voronoi diagram","score":0.48022064566612244},{"id":"https://openalex.org/keywords/binary-image","display_name":"Binary image","score":0.472801148891449},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.46929293870925903},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.46324220299720764},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.42958056926727295},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37345442175865173},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.3311402499675751},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.31382542848587036},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2731668949127197},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.26500171422958374},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10815468430519104}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.7111363410949707},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6019423007965088},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5681240558624268},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5028695464134216},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4928038418292999},{"id":"https://openalex.org/C54170458","wikidata":"https://www.wikidata.org/wiki/Q663554","display_name":"Voxel","level":2,"score":0.4813866913318634},{"id":"https://openalex.org/C20468658","wikidata":"https://www.wikidata.org/wiki/Q17130624","display_name":"Weighted Voronoi diagram","level":3,"score":0.48022064566612244},{"id":"https://openalex.org/C193828747","wikidata":"https://www.wikidata.org/wiki/Q864118","display_name":"Binary image","level":4,"score":0.472801148891449},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.46929293870925903},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.46324220299720764},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.42958056926727295},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37345442175865173},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.3311402499675751},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.31382542848587036},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2731668949127197},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26500171422958374},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10815468430519104},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2003.1177156","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2003.1177156","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":"pmh:oai:CiteSeerX.psu:10.1.1.507.6791","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.507.6791","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eecs.vanderbilt.edu/courses/cs359/other_links/papers/maurer_DT_2003.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W23044499","https://openalex.org/W1828517481","https://openalex.org/W1964563867","https://openalex.org/W1966219816","https://openalex.org/W1967005434","https://openalex.org/W1967132687","https://openalex.org/W1968547043","https://openalex.org/W1973965874","https://openalex.org/W1996342882","https://openalex.org/W2000374918","https://openalex.org/W2004125362","https://openalex.org/W2005314985","https://openalex.org/W2007301572","https://openalex.org/W2008608905","https://openalex.org/W2011723506","https://openalex.org/W2012219217","https://openalex.org/W2029778733","https://openalex.org/W2035814473","https://openalex.org/W2036141792","https://openalex.org/W2039180386","https://openalex.org/W2039759479","https://openalex.org/W2046647050","https://openalex.org/W2047250593","https://openalex.org/W2051603011","https://openalex.org/W2057886711","https://openalex.org/W2069537876","https://openalex.org/W2078059979","https://openalex.org/W2078978762","https://openalex.org/W2081135354","https://openalex.org/W2088797232","https://openalex.org/W2090698554","https://openalex.org/W2094518347","https://openalex.org/W2095450675","https://openalex.org/W2113612687","https://openalex.org/W2117136603","https://openalex.org/W2119014534","https://openalex.org/W2130538955","https://openalex.org/W2136815994","https://openalex.org/W2143693180","https://openalex.org/W2144819133","https://openalex.org/W2147236542","https://openalex.org/W2148107243","https://openalex.org/W2151297710","https://openalex.org/W2151622247","https://openalex.org/W2158240273","https://openalex.org/W2164102350","https://openalex.org/W2167862746","https://openalex.org/W2212899008","https://openalex.org/W2248001717","https://openalex.org/W2296301307","https://openalex.org/W2511410159","https://openalex.org/W2911302472","https://openalex.org/W4234792997","https://openalex.org/W6681881021"],"related_works":["https://openalex.org/W3201352909","https://openalex.org/W2110413734","https://openalex.org/W1518796918","https://openalex.org/W1492333335","https://openalex.org/W2383087774","https://openalex.org/W2039506401","https://openalex.org/W1588722399","https://openalex.org/W2358048887","https://openalex.org/W2042999093","https://openalex.org/W2739428663"],"abstract_inverted_index":{"A":[0,151,171],"sequential":[1],"algorithm":[2,117,156,176],"is":[3,31,68,92,125,134,149,163],"presented":[4],"for":[5,44,48,165],"computing":[6,45],"the":[7,22,46,56,66,72,75,81,88,97,100,146,155,158,175],"exact":[8],"Euclidean":[9,160],"distance":[10,53],"transform":[11],"(DT)":[12],"of":[13,25,52,74,87,120,154,174],"a":[14,49],"k-dimensional":[15],"binary":[16],"image":[17],"in":[18,21,99,142,178],"time":[19,108,144,147,180],"linear":[20,107],"total":[23],"number":[24],"voxels":[26,83],"N.":[27],"The":[28,104,116],"algorithm,":[29],"which":[30,162],"based":[32],"on":[33],"dimensionality":[34],"reduction":[35],"and":[36,59,106,113,128,132],"partial":[37],"Voronoi":[38,76],"diagram":[39,77],"construction,":[40],"can":[41],"be":[42,119],"used":[43],"DT":[47,67,98],"wide":[50],"class":[51],"functions,":[54],"including":[55],"L/sub":[57],"p/":[58],"chamfer":[60],"metrics.":[61],"At":[62],"each":[63,85],"dimension":[64],"level,":[65],"computed":[69],"by":[70,95],"constructing":[71],"intersection":[73],"whose":[78],"sites":[79],"are":[80,110],"feature":[82],"with":[84,167,181],"row":[86],"image.":[89],"This":[90],"construction":[91],"performed":[93],"efficiently":[94],"using":[96],"next":[101],"lower":[102],"dimension.":[103],"correctness":[105],"complexity":[109],"demonstrated":[111],"analytically":[112],"verified":[114],"experimentally.":[115],"may":[118],"practical":[121],"value":[122],"since":[123],"it":[124,133,140],"relatively":[126,135],"simple":[127,152],"easy":[129],"to":[130],"implement":[131],"fast":[136],"(not":[137],"only":[138],"does":[139],"run":[141],"O(N)":[143],"but":[145],"constant":[148],"small).":[150],"modification":[153],"computes":[157],"weighted":[159],"DT,":[161],"useful":[164],"images":[166],"anisotropic":[168],"voxel":[169],"dimensions.":[170],"parallel":[172],"version":[173],"runs":[177],"O(N/p)":[179],"p":[182],"processors.":[183]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":28},{"year":2024,"cited_by_count":35},{"year":2023,"cited_by_count":52},{"year":2022,"cited_by_count":54},{"year":2021,"cited_by_count":61},{"year":2020,"cited_by_count":74},{"year":2019,"cited_by_count":70},{"year":2018,"cited_by_count":60},{"year":2017,"cited_by_count":74},{"year":2016,"cited_by_count":42},{"year":2015,"cited_by_count":47},{"year":2014,"cited_by_count":47},{"year":2013,"cited_by_count":45},{"year":2012,"cited_by_count":46}],"updated_date":"2026-05-09T13:55:54.758798","created_date":"2025-10-10T00:00:00"}