{"id":"https://openalex.org/W2293773261","doi":"https://doi.org/10.1109/icip.2003.1246609","title":"Combinatorial pyramids","display_name":"Combinatorial pyramids","publication_year":2004,"publication_date":"2004-06-03","ids":{"openalex":"https://openalex.org/W2293773261","doi":"https://doi.org/10.1109/icip.2003.1246609","mag":"2293773261"},"language":"en","primary_location":{"id":"doi:10.1109/icip.2003.1246609","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2003.1246609","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429)","raw_type":"proceedings-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/A5067287623","display_name":"Luc Brun","orcid":"https://orcid.org/0000-0002-1658-0527"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"L. Brun","raw_affiliation_strings":["LERI, I.U.T. de Reims, Reims, France"],"affiliations":[{"raw_affiliation_string":"LERI, I.U.T. de Reims, Reims, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081777844","display_name":"Walter G. Kropatsch","orcid":"https://orcid.org/0000-0003-4915-4118"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"W. Kropatsch","raw_affiliation_strings":["Institute for Computer-aided Automation, Vienna Univ. of Technology, Austria"],"affiliations":[{"raw_affiliation_string":"Institute for Computer-aided Automation, Vienna Univ. of Technology, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5067287623"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.207,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.89209555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"3","issue":null,"first_page":"II","last_page":"33"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9980999827384949,"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":0.9919999837875366,"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/pyramid","display_name":"Pyramid (geometry)","score":0.6610532999038696},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6162398457527161},{"id":"https://openalex.org/keywords/decimation","display_name":"Decimation","score":0.5250434875488281},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.4934927225112915},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.4700671136379242},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4682197570800781},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4676389694213867},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4332291781902313},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42922770977020264},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22935786843299866},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.14577224850654602},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11744242906570435}],"concepts":[{"id":"https://openalex.org/C142575187","wikidata":"https://www.wikidata.org/wiki/Q3358290","display_name":"Pyramid (geometry)","level":2,"score":0.6610532999038696},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6162398457527161},{"id":"https://openalex.org/C173642442","wikidata":"https://www.wikidata.org/wiki/Q1253346","display_name":"Decimation","level":3,"score":0.5250434875488281},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.4934927225112915},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.4700671136379242},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4682197570800781},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4676389694213867},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4332291781902313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42922770977020264},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22935786843299866},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.14577224850654602},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11744242906570435},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/icip.2003.1246609","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2003.1246609","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.714.4551","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.714.4551","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://brunl01.users.greyc.fr/ARTICLES/icip2003.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":4,"referenced_works":["https://openalex.org/W2073899708","https://openalex.org/W2114748206","https://openalex.org/W3130044242","https://openalex.org/W6836982560"],"related_works":["https://openalex.org/W1550871964","https://openalex.org/W2372020181","https://openalex.org/W2156531654","https://openalex.org/W4378714697","https://openalex.org/W1581723585","https://openalex.org/W2294330161","https://openalex.org/W2804553224","https://openalex.org/W2253069048","https://openalex.org/W140709781","https://openalex.org/W2940472653"],"abstract_inverted_index":{"An":[0],"irregular":[1],"pyramid":[2,77,84,116],"consists":[3],"of":[4,7,26,29,74,98,101,114,125],"a":[5,27,32,51,75,96],"stack":[6],"successively":[8],"reduced":[9,111],"graphs.":[10],"Each":[11],"smaller":[12],"graph":[13,53],"is":[14,106],"deduced":[15],"from":[16,117],"the":[17,21,24,44,59,65,82,86,93,99,115,123,126,130],"preceding":[18],"one":[19],"by":[20,129],"contraction":[22],"or":[23],"removal":[25],"set":[28],"edges.":[30],"Using":[31],"fixed":[33],"decimation":[34],"ratio":[35],"we":[36],"need":[37],"approximately":[38],"O(log(image":[39],"size))":[40],"graphs":[41],"to":[42,55,80,108,121],"encode":[43],"whole":[45,83],"pyramid.":[46],"A":[47],"combinatorial":[48,76,112,131],"map":[49,113],"encodes":[50],"planar":[52],"thanks":[54],"two":[56],"permutations":[57],"encoding":[58,73,105],"edges":[60],"and":[61,90,120],"their":[62],"orientation":[63],"around":[64],"vertices.":[66],"We":[67],"present":[68],"in":[69,85],"this":[70],"article":[71],"an":[72],"which":[78],"allows":[79],"fold":[81],"base":[87,119],"level":[88],"layer":[89],"provides":[91],"at":[92],"same":[94],"time":[95],"measure":[97],"relevance":[100],"every":[102],"pixel.":[103],"This":[104],"used":[107],"retrieve":[109],"any":[110],"its":[118],"compute":[122],"borders":[124],"partition":[127],"encoded":[128],"maps.":[132]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
