{"id":"https://openalex.org/W2089666804","doi":"https://doi.org/10.1109/tip.2010.2059032","title":"Fractal Dimension of Color Fractal Images","display_name":"Fractal Dimension of Color Fractal Images","publication_year":2010,"publication_date":"2010-07-22","ids":{"openalex":"https://openalex.org/W2089666804","doi":"https://doi.org/10.1109/tip.2010.2059032","mag":"2089666804","pmid":"https://pubmed.ncbi.nlm.nih.gov/20643608"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2010.2059032","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2010.2059032","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Image Processing","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/A5023410095","display_name":"Mihai Ivanovici","orcid":"https://orcid.org/0000-0002-0803-2918"},"institutions":[{"id":"https://openalex.org/I3123573182","display_name":"Transylvania University of Bra\u0219ov","ror":"https://ror.org/01cg9ws23","country_code":"RO","type":"education","lineage":["https://openalex.org/I3123573182"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Mihai Ivanovici","raw_affiliation_strings":["Transilvania University, Bras\u00b8ov 500036, Rom\u00e2nia. Mihai.Ivanovici@gmail.com","Transilvania University,,Brasov,Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Transilvania University, Bras\u00b8ov 500036, Rom\u00e2nia. Mihai.Ivanovici@gmail.com","institution_ids":["https://openalex.org/I3123573182"]},{"raw_affiliation_string":"Transilvania University,,Brasov,Romania","institution_ids":["https://openalex.org/I3123573182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002624695","display_name":"No\u00ebl Richard","orcid":"https://orcid.org/0000-0002-6891-0540"},"institutions":[{"id":"https://openalex.org/I32881790","display_name":"Universit\u00e9 de Poitiers","ror":"https://ror.org/04xhy8q59","country_code":"FR","type":"education","lineage":["https://openalex.org/I32881790"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"No\u00ebl Richard","raw_affiliation_strings":["University of Poitiers, Poitiers, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Poitiers, Poitiers, France","institution_ids":["https://openalex.org/I32881790"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5342,"has_fulltext":false,"cited_by_count":111,"citation_normalized_percentile":{"value":0.94400712,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"20","issue":"1","first_page":"227","last_page":"235"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14339","display_name":"Image Processing and 3D Reconstruction","score":0.9822999835014343,"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/T14339","display_name":"Image Processing and 3D Reconstruction","score":0.9822999835014343,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.970300018787384,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9532999992370605,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.7407317161560059},{"id":"https://openalex.org/keywords/fractal-dimension","display_name":"Fractal dimension","score":0.6609880924224854},{"id":"https://openalex.org/keywords/fractal-analysis","display_name":"Fractal analysis","score":0.6412681341171265},{"id":"https://openalex.org/keywords/fractal-transform","display_name":"Fractal transform","score":0.6215215921401978},{"id":"https://openalex.org/keywords/fractal-dimension-on-networks","display_name":"Fractal dimension on networks","score":0.61330646276474},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6017172336578369},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6013965010643005},{"id":"https://openalex.org/keywords/grayscale","display_name":"Grayscale","score":0.5832100510597229},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5819973945617676},{"id":"https://openalex.org/keywords/fractal-compression","display_name":"Fractal compression","score":0.5687161684036255},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5210853815078735},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.45728394389152527},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45574119687080383},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.43457964062690735},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.4241946339607239},{"id":"https://openalex.org/keywords/binary-image","display_name":"Binary image","score":0.41685739159584045},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.358609676361084},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.33779269456863403},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.30077025294303894},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0782492458820343}],"concepts":[{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.7407317161560059},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.6609880924224854},{"id":"https://openalex.org/C162494671","wikidata":"https://www.wikidata.org/wiki/Q2845227","display_name":"Fractal analysis","level":4,"score":0.6412681341171265},{"id":"https://openalex.org/C144112376","wikidata":"https://www.wikidata.org/wiki/Q5477512","display_name":"Fractal transform","level":5,"score":0.6215215921401978},{"id":"https://openalex.org/C60396315","wikidata":"https://www.wikidata.org/wiki/Q5477489","display_name":"Fractal dimension on networks","level":5,"score":0.61330646276474},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6017172336578369},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6013965010643005},{"id":"https://openalex.org/C78201319","wikidata":"https://www.wikidata.org/wiki/Q685727","display_name":"Grayscale","level":3,"score":0.5832100510597229},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5819973945617676},{"id":"https://openalex.org/C109116516","wikidata":"https://www.wikidata.org/wiki/Q2872","display_name":"Fractal compression","level":5,"score":0.5687161684036255},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5210853815078735},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.45728394389152527},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45574119687080383},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.43457964062690735},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.4241946339607239},{"id":"https://openalex.org/C193828747","wikidata":"https://www.wikidata.org/wiki/Q864118","display_name":"Binary image","level":4,"score":0.41685739159584045},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.358609676361084},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.33779269456863403},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.30077025294303894},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0782492458820343},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C13481523","wikidata":"https://www.wikidata.org/wiki/Q412438","display_name":"Image compression","level":4,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003116","descriptor_name":"Color","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003116","descriptor_name":"Color","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003116","descriptor_name":"Color","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007091","descriptor_name":"Image Processing, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007091","descriptor_name":"Image Processing, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007091","descriptor_name":"Image Processing, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D008011","descriptor_name":"Lichens","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008011","descriptor_name":"Lichens","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008011","descriptor_name":"Lichens","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D010781","descriptor_name":"Photography","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010781","descriptor_name":"Photography","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010781","descriptor_name":"Photography","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011565","descriptor_name":"Psoriasis","qualifier_ui":"Q000473","qualifier_name":"pathology","is_major_topic":false},{"descriptor_ui":"D011565","descriptor_name":"Psoriasis","qualifier_ui":"Q000473","qualifier_name":"pathology","is_major_topic":false},{"descriptor_ui":"D011565","descriptor_name":"Psoriasis","qualifier_ui":"Q000473","qualifier_name":"pathology","is_major_topic":false},{"descriptor_ui":"D012044","descriptor_name":"Regression Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012044","descriptor_name":"Regression Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012044","descriptor_name":"Regression Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017709","descriptor_name":"Fractals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017709","descriptor_name":"Fractals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017709","descriptor_name":"Fractals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2010.2059032","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2010.2059032","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Image Processing","raw_type":"journal-article"},{"id":"pmid:20643608","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/20643608","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 image processing : a publication of the IEEE Signal Processing Society","raw_type":null},{"id":"pmh:oai:HAL:hal-00522174v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00522174","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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 Image Processing, 2010, 99, 10p. ⟨10.1109/TIP.2010.2059032⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W169783185","https://openalex.org/W369283474","https://openalex.org/W1493647865","https://openalex.org/W1497262258","https://openalex.org/W1648096614","https://openalex.org/W1920674727","https://openalex.org/W1968375151","https://openalex.org/W2007298029","https://openalex.org/W2024712184","https://openalex.org/W2032121576","https://openalex.org/W2039612688","https://openalex.org/W2044465660","https://openalex.org/W2048125863","https://openalex.org/W2091588795","https://openalex.org/W2093658728","https://openalex.org/W2114537326","https://openalex.org/W2126727010","https://openalex.org/W2128565996","https://openalex.org/W2134275275","https://openalex.org/W2136207315","https://openalex.org/W2137555357","https://openalex.org/W2142963076","https://openalex.org/W2154161333","https://openalex.org/W2158922575","https://openalex.org/W2161522250","https://openalex.org/W2964631455","https://openalex.org/W6606846270","https://openalex.org/W6636962537"],"related_works":["https://openalex.org/W2378555636","https://openalex.org/W1998642545","https://openalex.org/W1544850754","https://openalex.org/W2013332237","https://openalex.org/W4288450835","https://openalex.org/W2119787960","https://openalex.org/W2370240143","https://openalex.org/W2979660607","https://openalex.org/W2051989386","https://openalex.org/W1987554137"],"abstract_inverted_index":{"Fractal":[0],"dimension":[1],"is":[2,56],"a":[3,59],"very":[4],"useful":[5],"metric":[6],"for":[7,43,66,87],"the":[8,11,26,32,38,63,67,70,84,88,103],"analysis":[9],"of":[10,62,69,83,90,105],"images":[12],"with":[13,49],"self-similar":[14],"content,":[15],"such":[16],"as":[17,31],"textures.":[18],"For":[19],"its":[20],"computation":[21,68],"there":[22],"exist":[23],"several":[24],"approaches,":[25],"probabilistic":[27,64,91],"algorithm":[28,65,86],"being":[29],"accepted":[30],"most":[33],"elegant":[34],"approach.":[35],"However,":[36],"all":[37],"existing":[39,85],"methods":[40],"are":[41],"defined":[42],"1-D":[44],"signals":[45],"or":[46],"binary":[47],"images,":[48],"extension":[50,82],"to":[51,57,95],"grayscale":[52],"images.":[53,99],"Our":[54],"purpose":[55],"propose":[58,80],"color":[60,97],"version":[61],"fractal":[71,98],"dimension.":[72],"To":[73],"validate":[74],"this":[75,110],"new":[76],"approach,":[77],"we":[78,101],"also":[79],"an":[81],"generation":[89],"fractals,":[92],"in":[93],"order":[94],"obtain":[96],"Then":[100],"show":[102],"results":[104],"our":[106],"experiments":[107],"and":[108],"conclude":[109],"paper.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":6}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}