{"id":"https://openalex.org/W2057286960","doi":"https://doi.org/10.1145/1644015.1644035","title":"Computing rank-convolutions with a mask","display_name":"Computing rank-convolutions with a mask","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W2057286960","doi":"https://doi.org/10.1145/1644015.1644035","mag":"2057286960"},"language":"en","primary_location":{"id":"doi:10.1145/1644015.1644035","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1644015.1644035","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","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/A5014978503","display_name":"L\u00e1szl\u00f3 Babai","orcid":"https://orcid.org/0000-0002-2058-685X"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L\u00e1szl\u00f3 Babai","raw_affiliation_strings":["University of Chicago, Chicago, IL"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Chicago, Chicago, IL","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023765219","display_name":"Pedro F. Felzenszwalb","orcid":null},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pedro F. Felzenszwalb","raw_affiliation_strings":["University of Chicago, Chicago, IL"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Chicago, Chicago, IL","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I40347166"],"apc_list":null,"apc_paid":null,"fwci":1.2932,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.81784819,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"6","issue":"1","first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9987999796867371,"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":0.9987999796867371,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9986000061035156,"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":0.9961000084877014,"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/rank","display_name":"Rank (graph theory)","score":0.7368341088294983},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.7292215824127197},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5794073939323425},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5654264688491821},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.5573319792747498},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5187947154045105},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.5163065791130066},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.488489031791687},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4745693504810333},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4715205430984497},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.4188682436943054},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3524191975593567},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2903839349746704},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21713417768478394},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.13725656270980835},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.11348190903663635},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09312915802001953}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7368341088294983},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.7292215824127197},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5794073939323425},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5654264688491821},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.5573319792747498},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5187947154045105},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.5163065791130066},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.488489031791687},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4745693504810333},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4715205430984497},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.4188682436943054},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3524191975593567},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2903839349746704},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21713417768478394},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.13725656270980835},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.11348190903663635},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09312915802001953},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1644015.1644035","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1644015.1644035","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.156.2005","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.2005","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uchicago.edu/~laci/papers/conv.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.231.3921","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.231.3921","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.brown.edu/%7Epff/papers/bf.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.79.4056","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.79.4056","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.cs.uchicago.edu/~pff/papers/bf.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1501400124","https://openalex.org/W1518641734","https://openalex.org/W1982209249","https://openalex.org/W1996641400","https://openalex.org/W1997906726","https://openalex.org/W2016871180","https://openalex.org/W2030536784","https://openalex.org/W2034760775","https://openalex.org/W2055257826","https://openalex.org/W2057830245","https://openalex.org/W2093626764","https://openalex.org/W2097382431","https://openalex.org/W2100020153","https://openalex.org/W2102182691","https://openalex.org/W2104947808","https://openalex.org/W2113656553","https://openalex.org/W2123119012","https://openalex.org/W2144977619","https://openalex.org/W2147810058","https://openalex.org/W2153419872","https://openalex.org/W2164741953","https://openalex.org/W2165949176","https://openalex.org/W2273959428","https://openalex.org/W4230982142"],"related_works":["https://openalex.org/W2058965144","https://openalex.org/W2164382479","https://openalex.org/W2146343568","https://openalex.org/W98480971","https://openalex.org/W2150291671","https://openalex.org/W2013643406","https://openalex.org/W2027972911","https://openalex.org/W2157978810","https://openalex.org/W3157543420","https://openalex.org/W4205555276"],"abstract_inverted_index":{"Rank-convolutions":[0,29],"have":[1],"important":[2],"applications":[3],"in":[4,64,104,116],"a":[5,18,21,49,114,127],"variety":[6],"of":[7,33,48,54,61],"areas":[8],"such":[9],"as":[10,20],"signal":[11],"processing":[12],"and":[13,27],"computer":[14],"vision.":[15],"We":[16,39,106],"define":[17],"mask":[19,60],"function":[22,50],"taking":[23],"only":[24],"values":[25],"zero":[26],"infinity.":[28],"with":[30,57],"masks":[31],"are":[32],"special":[34],"interest":[35],"to":[36,42,77,101,113,131],"image":[37,117],"processing.":[38,118],"show":[40,126],"how":[41],"compute":[43],"the":[44,78,89],"rank-":[45],"k":[46],"convolution":[47],"over":[51],"an":[52,58,108],"interval":[53],"length":[55,62],"n":[56,67],"arbitrary":[59],"m":[63,69,71],"O":[65,91],"(":[66,92],"\u221a":[68],"log":[70],")":[72,94],"time.":[73],"The":[74],"result":[75],"generalizes":[76],"d":[79],"-dimensional":[80],"case.":[81],"Previously":[82],"no":[83],"algorithm":[84,99],"performing":[85],"significantly":[86],"better":[87],"than":[88],"brute-force":[90],"nm":[93],"bound":[95],"was":[96],"known.":[97],"Our":[98],"seems":[100],"perform":[102],"well":[103],"practice.":[105],"describe":[107],"implementation,":[109],"illustrating":[110],"its":[111],"application":[112],"problem":[115],"Already":[119],"on":[120],"relatively":[121],"small":[122],"images,":[123],"our":[124],"experiments":[125],"signficant":[128],"speedup":[129],"compared":[130],"brute":[132],"force.":[133]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}