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As such, it is necessary to adjust the designed scheme to accommodate these discrepancies. Specifically, the adjustment of the designed scheme involves a rigorous process of repeatedly selecting and verifying the feasibility of the proposed modifications using point-cloud data obtained from the tunnel. However, this process can be considerably time-consuming due to the large-scale and potentially redundant nature of the point-cloud data. This paper proposes a mathematical model for point-cloud data acquired in measuring a mined tunnel, which may deviate from the originally designed one. The modeling, which mainly includes determining its normal plane, and building the equation of tunnel point-cloud data, is to quickly extract several key locations in the tunnel surface for modifying the original design in order to achieve a minimum error between the modified design and the mined tunnel. In comparison with the conventional processing of extracting several key locations directly from point-cloud data, our model shows a significant promotion of extraction efficiency under an acceptable error bound. The model is tested in a real tunnel point-cloud data and the testing results confirm the increase of fitting accuracy and the decrease of computational load.<\/jats:p>","DOI":"10.1007\/s44244-023-00011-5","type":"journal-article","created":{"date-parts":[[2023,12,4]],"date-time":"2023-12-04T00:02:02Z","timestamp":1701648122000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A mathematical model for efficient extraction of key locations from point-cloud data in track area"],"prefix":"10.1007","volume":"1","author":[{"given":"Shuyue","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaolv","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Lu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xizhao","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,12,4]]},"reference":[{"issue":"6","key":"11_CR1","doi-asserted-by":"publisher","first-page":"1363","DOI":"10.1007\/s11709-019-0561-3","volume":"13","author":"R Chen","year":"2019","unstructured":"Chen R, Zhang P, Wu H, Wang Z, Zhong Z (2019) Prediction of shield tunneling-induced ground settlement using machine learning techniques. 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