{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:29:59Z","timestamp":1760146199135,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,18]],"date-time":"2024-10-18T00:00:00Z","timestamp":1729209600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>The comment disputes some of the inferences in the paper \u201cHelmert Transformation Problem. From Euler Angles Method to Quaternion Algebra\u201d, published in this journal. The key points in the dissent are the following: (1) The number of unknown parameters in the reverse transformation problem using dual quaternions. (2) The reliability of both data and the results. (3) There should be no differences between Euler angles and quaternion methods. Our response is summarized as follows: (1) The problem can be solved using either eight or nine unknown parameters. (2) All the data and results are real. (3) There should be differences between methods because of different calculations.<\/jats:p>","DOI":"10.3390\/ijgi13100366","type":"journal-article","created":{"date-parts":[[2024,10,18]],"date-time":"2024-10-18T05:03:49Z","timestamp":1729227829000},"page":"366","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Reply to Bekta\u015f, S. Comment on \u201cIoannidou, S.; Pantazis, G. Helmert Transformation Problem. From Euler Angles Method to Quaternion Algebra. ISPRS Int. J. Geo-Inf. 2020, 9, 494\u201d"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9993-9146","authenticated-orcid":false,"given":"George","family":"Pantazis","sequence":"first","affiliation":[{"name":"School of Rural, Surveying and Geoinformatics Engineering, National Technical University of Athens, 15780 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1356-1934","authenticated-orcid":false,"given":"Stefania","family":"Ioannidou","sequence":"additional","affiliation":[{"name":"School of Rural, Surveying and Geoinformatics Engineering, National Technical University of Athens, 15780 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,18]]},"reference":[{"key":"#cr-split#-ref_1.1","unstructured":"Bekta\u015f, S. (2024). 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Dual Quaternions, Iowa State University."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1186\/s40623-018-0792-x","article-title":"A dual quaternion algorithm of the Helmert transformation problem","volume":"70","author":"Zeng","year":"2018","journal-title":"Earth Planets Space"},{"key":"ref_6","first-page":"225","article-title":"Application of dual quaternions algorithm for geodetic datum transformation","volume":"4","author":"Jitka","year":"2011","journal-title":"J. Appl. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1007\/s12517-022-10457-z","article-title":"A new algorithm for 3D similarity transformation with dual quaternion","volume":"15","author":"Bektas","year":"2022","journal-title":"Arab. J. Geosci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.isprsjprs.2014.04.013","article-title":"A dual quaternion-based, closed-form pairwise registration algorithm for point clouds","volume":"94","author":"Wang","year":"2014","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_9","unstructured":"G\u00fcuna\u015fti, G. (2016). Quaternions Algebra, Their Applications in Rotations and Beyond Quaternions, School of Computer Science, Physics and Mathematics, Faculty of Science and Engineering, Linnaeus University."},{"key":"ref_10","first-page":"35","article-title":"Quaternion and Its Application in Rotation Using Sets of Regions","volume":"1","author":"Perumal","year":"2011","journal-title":"Int. J. Eng. Technol. Innov."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kuipers, J. (2000). Quaternions and Rotation Sequences, Coral Press.","DOI":"10.1515\/9780691211701"},{"key":"ref_12","unstructured":"Slabaugh, G.G. (2024, June 20). Computing Euler Angles from a Rotation Matrix, Technical Report City University, London, Retrieved on August. Available online: https:\/\/eecs.qmul.ac.uk\/~gslabaugh\/publications\/euler.pdf."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/13\/10\/366\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:15:40Z","timestamp":1760112940000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/13\/10\/366"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,18]]},"references-count":13,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["ijgi13100366"],"URL":"https:\/\/doi.org\/10.3390\/ijgi13100366","relation":{},"ISSN":["2220-9964"],"issn-type":[{"type":"electronic","value":"2220-9964"}],"subject":[],"published":{"date-parts":[[2024,10,18]]}}}