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Therefore, it can deal with noisy data which clutters the orientation of the points. The method performs well in cases of ambiguous orientation, e.g., if two folds of a surface lie near each other, and other cases of complex geometry in which methods based upon local plane fitting may fail. Although defined by a global minimization problem, the method is effectively local, and it provides a second order approximation to smooth surfaces. Hence allowing good surface approximation without using any explicit or implicit approximation space. Furthermore, we show that LOP is highly robust to noise and outliers and demonstrate its effectiveness by applying it to raw scanned data of complex shapes.<\/jats:p>","DOI":"10.1145\/1276377.1276405","type":"journal-article","created":{"date-parts":[[2007,9,14]],"date-time":"2007-09-14T13:44:55Z","timestamp":1189777495000},"page":"22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":346,"title":["Parameterization-free projection for geometry reconstruction"],"prefix":"10.1145","volume":"26","author":[{"given":"Yaron","family":"Lipman","sequence":"first","affiliation":[{"name":"Tel-Aviv University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Cohen-Or","sequence":"additional","affiliation":[{"name":"Tel-Aviv University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Levin","sequence":"additional","affiliation":[{"name":"Academic College of Tel-Aviv Yaffo"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hillel","family":"Tal-Ezer","sequence":"additional","affiliation":[{"name":"Academic College of Tel-Aviv Yaffo"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2007,7,29]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"VIS '01: Proceedings of the conference on Visualization '01","author":"Alexa M.","unstructured":"Alexa , M. , Behr , J. , Cohen-Or , D. , Fleishman , S. , Levin , D. , and Silva , C. T . 2001. Point set surfaces . In VIS '01: Proceedings of the conference on Visualization '01 , 21--28. Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., and Silva, C. T. 2001. Point set surfaces. In VIS '01: Proceedings of the conference on Visualization '01, 21--28."},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015713"},{"key":"e_1_2_2_3_1","doi-asserted-by":"crossref","unstructured":"Amenta N. Bern M. and Kamvysselis M. 1998. A new voronoi-based surface reconstruction algorithm. ACM Press New York NY USA 415--421. Amenta N. Bern M. and Kamvysselis M. 1998. A new voronoi-based surface reconstruction algorithm. ACM Press New York NY USA 415--421.","DOI":"10.1145\/280814.280947"},{"key":"e_1_2_2_4_1","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1111\/j.2517-6161.1983.tb01226.x","article-title":"Statistical uses of the spatial median","volume":"45","author":"Brown B. M.","year":"1983","unstructured":"Brown , B. M. 1983 . 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