{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:25:28Z","timestamp":1760243128917,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2015,10,12]],"date-time":"2015-10-12T00:00:00Z","timestamp":1444608000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, the problem of non-rigid structure estimation in trajectory space from monocular vision is investigated. Similar to the Point Trajectory Approach (PTA), based on characteristic points\u2019 trajectories described by a predefined Discrete Cosine Transform (DCT) basis, the structure matrix was also calculated by using a factorization method. To further optimize the non-rigid structure estimation from monocular vision, the rank minimization problem about structure matrix is proposed to implement the non-rigid structure estimation by introducing the basic low-rank condition. Moreover, the Accelerated Proximal Gradient (APG) algorithm is proposed to solve the rank minimization problem, and the initial structure matrix calculated by the PTA method is optimized. The APG algorithm can converge to efficient solutions quickly and lessen the reconstruction error obviously. The reconstruction results of real image sequences indicate that the proposed approach runs reliably, and effectively improves the accuracy of non-rigid structure estimation from monocular vision.<\/jats:p>","DOI":"10.3390\/s151025730","type":"journal-article","created":{"date-parts":[[2015,10,14]],"date-time":"2015-10-14T02:36:30Z","timestamp":1444790190000},"page":"25730-25745","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Non-Rigid Structure Estimation in Trajectory Space from Monocular Vision"],"prefix":"10.3390","volume":"15","author":[{"given":"Yaming","family":"Wang","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lingling","family":"Tong","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingfeng","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junbao","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,10,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF00129684","article-title":"Shape and motion from image streams under orthography: A factorization method","volume":"9","author":"Tomasi","year":"1992","journal-title":"Int. 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