{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T14:55:17Z","timestamp":1761058517887},"reference-count":31,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Image Grap."],"published-print":{"date-parts":[[2006,7]]},"abstract":"<jats:p> In this paper, a new 2D shape Multiscale Triangle-Area Representation (MTAR) method is proposed. This representation utilizes a simple geometric principle, that is, the area of the triangles formed by the shape boundary points. The wavelet transform is used for smoothing and decomposing the shape boundaries into multiscale levels. At each scale level, a TAR image and the corresponding Maxima-Minima lines are obtained. The resulting MTAR is more robust to noise, less complex, and more selective than similar methods such as the curvature scale-space (CSS). Furthermore, the MTAR is invariant to the general affine transformations. The proposed MTAR is tested and compared to the CSS method using MPEG-7 CE-shape-1 part B and Columbia Object Image Library (COIL-20) datasets. The results show that the proposed MTAR outperforms the CSS method for the conducted tests. <\/jats:p>","DOI":"10.1142\/s021946780600232x","type":"journal-article","created":{"date-parts":[[2006,8,1]],"date-time":"2006-08-01T17:00:26Z","timestamp":1154451626000},"page":"421-443","source":"Crossref","is-referenced-by-count":6,"title":["MTAR: A ROBUST 2D SHAPE REPRESENTATION"],"prefix":"10.1142","volume":"06","author":[{"given":"IBRAHIM","family":"EL RUB\u00c9","sequence":"first","affiliation":[{"name":"Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1, Canada"}]},{"given":"NAIF","family":"ALAJLAN","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1, Canada"}]},{"given":"MOHAMED S.","family":"KAMEL","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1, Canada"}]},{"given":"MAHER","family":"AHMED","sequence":"additional","affiliation":[{"name":"Physics and Computer Science Department, Wilfrid Laurier University, 75 University Avenue West, Waterloo, Ontario, Canada N2L 3C5, Canada"}]},{"given":"GEORGE H.","family":"FREEMAN","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1, Canada"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1109\/83.892449"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s005300050147"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1109\/34.771318"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2005.21"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1109\/34.993558"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1109\/83.481671"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2002.1033216"},{"key":"rf9","volume-title":"Shape Analysis and Classification, Theory and Practice","author":"Costa L.","year":"2001"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218001401000873"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1177\/003754979606600303"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1109\/34.368168"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1109\/34.954605"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2004.1262333"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/B978-012466606-1\/50004-0"},{"key":"rf17","author":"Mandal M.","journal-title":"Journal of Electronic Imaging"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1109\/34.391387"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-0343-7"},{"key":"rf20","first-page":"34","volume":"8","author":"Mokhtarian F.","journal-title":"IEEE Trans. PAMI"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1109\/34.149591"},{"key":"rf22","volume-title":"Geometric Transformations","author":"Mortenson M.","year":"1995"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2002.1046166"},{"key":"rf25","volume-title":"Digital Image Processing","author":"Pratt W. K.","year":"1991"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2004.1273924"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1016\/S0031-3203(98)00137-X"},{"key":"rf30","volume-title":"Image Processing Analysis and Machine Vision","author":"Sonka M.","year":"1999"},{"key":"rf31","doi-asserted-by":"publisher","DOI":"10.1109\/34.608294"},{"key":"rf32","doi-asserted-by":"publisher","DOI":"10.1142\/S021800140100109X"},{"key":"rf33","doi-asserted-by":"publisher","DOI":"10.1109\/34.722612"},{"key":"rf34","doi-asserted-by":"publisher","DOI":"10.1109\/83.799886"},{"key":"rf35","doi-asserted-by":"publisher","DOI":"10.1016\/S0923-5965(02)00084-X"},{"key":"rf36","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2003.07.008"}],"container-title":["International Journal of Image and Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021946780600232X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:26:39Z","timestamp":1565187999000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021946780600232X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7]]},"references-count":31,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,7]]}},"alternative-id":["10.1142\/S021946780600232X"],"URL":"https:\/\/doi.org\/10.1142\/s021946780600232x","relation":{},"ISSN":["0219-4678","1793-6756"],"issn-type":[{"value":"0219-4678","type":"print"},{"value":"1793-6756","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,7]]}}}