{"id":"https://openalex.org/W2090978288","doi":"https://doi.org/10.1142/s021946780600232x","title":"MTAR: A ROBUST 2D SHAPE REPRESENTATION","display_name":"MTAR: A ROBUST 2D SHAPE REPRESENTATION","publication_year":2006,"publication_date":"2006-07-01","ids":{"openalex":"https://openalex.org/W2090978288","doi":"https://doi.org/10.1142/s021946780600232x","mag":"2090978288"},"language":"en","primary_location":{"id":"doi:10.1142/s021946780600232x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021946780600232x","pdf_url":null,"source":{"id":"https://openalex.org/S60080701","display_name":"International Journal of Image and Graphics","issn_l":"0219-4678","issn":["0219-4678","1793-6756"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Image and Graphics","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/A5048698040","display_name":"Ibrahim El Rube","orcid":"https://orcid.org/0000-0001-8471-1341"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"IBRAHIM EL RUB\u00c9","raw_affiliation_strings":["Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052594698","display_name":"Naif Alajlan","orcid":"https://orcid.org/0000-0003-1846-1131"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"NAIF ALAJLAN","raw_affiliation_strings":["Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039318050","display_name":"Mohamed S. Kamel","orcid":"https://orcid.org/0000-0001-6173-8082"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"MOHAMED S. KAMEL","raw_affiliation_strings":["Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101286404","display_name":"Maher Ahmed","orcid":null},"institutions":[{"id":"https://openalex.org/I75381157","display_name":"Wilfrid Laurier University","ror":"https://ror.org/00fn7gb05","country_code":"CA","type":"education","lineage":["https://openalex.org/I75381157"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"MAHER AHMED","raw_affiliation_strings":["Physics and Computer Science Department, Wilfrid Laurier University, 75 University Avenue West, Waterloo, Ontario, Canada N2L 3C5, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Physics and Computer Science Department, Wilfrid Laurier University, 75 University Avenue West, Waterloo, Ontario, Canada N2L 3C5, Canada","institution_ids":["https://openalex.org/I75381157"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042269983","display_name":"G.H. Freeman","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"GEORGE H. FREEMAN","raw_affiliation_strings":["Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2423,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.80384691,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"06","issue":"03","first_page":"421","last_page":"443"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9997000098228455,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9997000098228455,"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/T14339","display_name":"Image Processing and 3D Reconstruction","score":0.9969000220298767,"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":0.9965999722480774,"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/maxima-and-minima","display_name":"Maxima and minima","score":0.5927830934524536},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5722755789756775},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5567549467086792},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.518226146697998},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.5056054592132568},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.49148261547088623},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47586482763290405},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.45151805877685547},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.42268916964530945},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3953288793563843},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.389028936624527},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.371357262134552},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.34100341796875},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.3281218707561493},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.3113512098789215},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25305187702178955},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16108477115631104}],"concepts":[{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.5927830934524536},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5722755789756775},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5567549467086792},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.518226146697998},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.5056054592132568},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.49148261547088623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47586482763290405},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.45151805877685547},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.42268916964530945},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3953288793563843},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.389028936624527},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.371357262134552},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.34100341796875},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.3281218707561493},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3113512098789215},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25305187702178955},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16108477115631104},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021946780600232x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021946780600232x","pdf_url":null,"source":{"id":"https://openalex.org/S60080701","display_name":"International Journal of Image and Graphics","issn_l":"0219-4678","issn":["0219-4678","1793-6756"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Image and Graphics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5199999809265137,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W109390732","https://openalex.org/W247104752","https://openalex.org/W1553171952","https://openalex.org/W1571183395","https://openalex.org/W1967914497","https://openalex.org/W1969927402","https://openalex.org/W1990954913","https://openalex.org/W2022418777","https://openalex.org/W2027393660","https://openalex.org/W2052277674","https://openalex.org/W2057175746","https://openalex.org/W2068246225","https://openalex.org/W2072738093","https://openalex.org/W2076567023","https://openalex.org/W2087135025","https://openalex.org/W2093000758","https://openalex.org/W2095358018","https://openalex.org/W2100689562","https://openalex.org/W2104053410","https://openalex.org/W2108556791","https://openalex.org/W2113713709","https://openalex.org/W2114766304","https://openalex.org/W2115755118","https://openalex.org/W2116044718","https://openalex.org/W2121013500","https://openalex.org/W2129112513","https://openalex.org/W2132204530","https://openalex.org/W2140798815","https://openalex.org/W2145425472","https://openalex.org/W2146233371","https://openalex.org/W2154039332","https://openalex.org/W2168207335","https://openalex.org/W2169937647","https://openalex.org/W2170640451","https://openalex.org/W2290144831","https://openalex.org/W2491192461","https://openalex.org/W2746698054","https://openalex.org/W3021706340","https://openalex.org/W3141443221","https://openalex.org/W4236844765","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2036778696","https://openalex.org/W2541950815","https://openalex.org/W2024152175","https://openalex.org/W1577789985","https://openalex.org/W2536727263","https://openalex.org/W2158207955","https://openalex.org/W2037328875","https://openalex.org/W1982375519","https://openalex.org/W1965790332","https://openalex.org/W2942471066"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,17,53],"new":[4],"2D":[5],"shape":[6,31,44],"Multiscale":[7],"Triangle-Area":[8],"Representation":[9],"(MTAR)":[10],"method":[11,105,128],"is":[12,37,66,88,98],"proposed.":[13],"This":[14],"representation":[15],"utilizes":[16],"simple":[18],"geometric":[19],"principle,":[20],"that":[21,121],"is,":[22],"the":[23,26,30,43,57,81,86,91,103,122,126,130],"area":[24],"of":[25],"triangles":[27],"formed":[28],"by":[29],"boundary":[32],"points.":[33],"The":[34,63,95,118],"wavelet":[35],"transform":[36],"used":[38],"for":[39,129],"smoothing":[40],"and":[41,56,73,100,111],"decomposing":[42],"boundaries":[45],"into":[46],"multiscale":[47],"levels.":[48],"At":[49],"each":[50],"scale":[51],"level,":[52],"TAR":[54],"image":[55],"corresponding":[58],"Maxima-Minima":[59],"lines":[60],"are":[61],"obtained.":[62],"resulting":[64],"MTAR":[65,87,97,124],"more":[67,74],"robust":[68],"to":[69,90,102],"noise,":[70],"less":[71],"complex,":[72],"selective":[75],"than":[76],"similar":[77],"methods":[78],"such":[79],"as":[80],"curvature":[82],"scale-space":[83],"(CSS).":[84],"Furthermore,":[85],"invariant":[89],"general":[92],"affine":[93],"transformations.":[94],"proposed":[96,123],"tested":[99],"compared":[101],"CSS":[104,127],"using":[106],"MPEG-7":[107],"CE-shape-1":[108],"part":[109],"B":[110],"Columbia":[112],"Object":[113],"Image":[114],"Library":[115],"(COIL-20)":[116],"datasets.":[117],"results":[119],"show":[120],"outperforms":[125],"conducted":[131],"tests.":[132]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"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"}