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However, most existing methods estimated the parameters via 3D-2D correspondences based on the 2D alignment, which is cumbersome, time-consuming, theoretically complex, and results in insufficient robustness. To alleviate this issue, in this paper, we propose an efficient and simple calibration method based on the principle of directly calculating the projection transformation between virtual space and the real world via 3D-3D alignment. The proposed method merely needs to record the motion trajectory of the cube-marker in the real and virtual world, and then calculate the transformation matrix between the virtual space and the real world by aligning the two trajectories in the observed view. There are two advantages associated with the proposed method. First, the operation is simple. Theoretically, the user only needs to perform four alignment operations for calibration without changing the rotation variation. Second, the trajectory can be easily distributed throughout the entire observation view, resulting in more robust calibration results. To validate the effectiveness of the proposed method, we conducted extensive experiments on our self-built optical see-through head-mounted display (OST-HMD) device. The experimental results show that the proposed method can achieve better calibration results than other calibration methods.<\/jats:p>","DOI":"10.1007\/s11042-024-18252-6","type":"journal-article","created":{"date-parts":[[2024,2,3]],"date-time":"2024-02-03T04:58:46Z","timestamp":1706936326000},"page":"71925-71950","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Trajectory-based alignment for optical see-through HMD calibration"],"prefix":"10.1007","volume":"83","author":[{"given":"Lingling","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaohua","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6314-5600","authenticated-orcid":false,"given":"Wei","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongchen","family":"Shi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Xie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ye","family":"Yan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erwei","family":"Yin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,2,3]]},"reference":[{"issue":"3","key":"18252_CR1","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1017\/S1460396913000277","volume":"13","author":"F Cosentino","year":"2014","unstructured":"Cosentino F, John NW, Vaarkamp J (2014) An overview of augmented and virtual reality applications in radiotherapy and future developments enabled by modern tablet devices. 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