{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T14:52:50Z","timestamp":1773154370910,"version":"3.50.1"},"reference-count":53,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,21]],"date-time":"2022-05-21T00:00:00Z","timestamp":1653091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004329","name":"Slovene Research Agency","doi-asserted-by":"publisher","award":["N2-0181"],"award-info":[{"award-number":["N2-0181"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Slovene Research Agency","doi-asserted-by":"publisher","award":["P2-0041"],"award-info":[{"award-number":["P2-0041"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Slovene Research Agency","doi-asserted-by":"publisher","award":["21-08009K"],"award-info":[{"award-number":["21-08009K"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001824","name":"Czech Science Foundation","doi-asserted-by":"publisher","award":["N2-0181"],"award-info":[{"award-number":["N2-0181"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001824","name":"Czech Science Foundation","doi-asserted-by":"publisher","award":["P2-0041"],"award-info":[{"award-number":["P2-0041"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001824","name":"Czech Science Foundation","doi-asserted-by":"publisher","award":["21-08009K"],"award-info":[{"award-number":["21-08009K"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A new algorithm is presented for detecting the global reflection symmetry of geometric objects. The algorithm works for 2D and 3D objects which may be open or closed and may or may not contain holes. The algorithm accepts a point cloud obtained by sampling the object\u2019s surface at the input. The points are inserted into a uniform grid and so-called boundary cells are identified. The centroid of the boundary cells is determined, and a testing symmetry axis\/plane is set through it. In this way, the boundary cells are split into two parts and they are faced with the symmetry estimation function. If the function estimates the symmetric case, the boundary cells are further split until a given threshold is reached or a non-symmetric result is obtained. The new testing axis\/plane is then derived and tested by rotation around the centroid. This paper introduces three techniques to accelerate the computation. Competitive results were obtained when the algorithm was compared against the state of the art.<\/jats:p>","DOI":"10.3390\/sym14051060","type":"journal-article","created":{"date-parts":[[2022,5,21]],"date-time":"2022-05-21T09:18:08Z","timestamp":1653124688000},"page":"1060","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Hierarchical Universal Algorithm for Geometric Objects\u2019 Reflection Symmetry Detection"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4372-5020","authenticated-orcid":false,"given":"Borut","family":"\u017dalik","sequence":"first","affiliation":[{"name":"Faculty of Electrical Engineering and Computer Science, University of Maribor, Koro\u0161ka Cesta 46, SI-2000 Maribor, Slovenia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4468-0290","authenticated-orcid":false,"given":"Damjan","family":"Strnad","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Computer Science, University of Maribor, Koro\u0161ka Cesta 46, SI-2000 Maribor, Slovenia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6210-0889","authenticated-orcid":false,"given":"\u0160tefan","family":"Kohek","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Computer Science, University of Maribor, Koro\u0161ka Cesta 46, SI-2000 Maribor, Slovenia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4556-2771","authenticated-orcid":false,"given":"Ivana","family":"Kolingerov\u00e1","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, University of West Bohemia, Technick\u00e1 8, 306 14 Plze\u0148, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1559-9776","authenticated-orcid":false,"given":"Andrej","family":"Nerat","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Computer Science, University of Maribor, Koro\u0161ka Cesta 46, SI-2000 Maribor, Slovenia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9517-1157","authenticated-orcid":false,"given":"Niko","family":"Luka\u010d","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Computer Science, University of Maribor, Koro\u0161ka Cesta 46, SI-2000 Maribor, Slovenia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0701-9201","authenticated-orcid":false,"given":"David","family":"Podgorelec","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering and Computer Science, University of Maribor, Koro\u0161ka Cesta 46, SI-2000 Maribor, Slovenia"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1017\/S1062798705000736","article-title":"Symmetry and Asymmetry in Aesthetics and the Arts","volume":"13","author":"McManus","year":"2005","journal-title":"Eur. 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