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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 趙鍵哲 | zh_TW |
| dc.contributor.advisor | Jen-Jer Jaw | en |
| dc.contributor.author | 劉又菁 | zh_TW |
| dc.contributor.author | You-Jing Liu | en |
| dc.date.accessioned | 2023-08-16T17:03:36Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-08-16 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-08-09 | - |
| dc.identifier.citation | Albertz J, Kreiling W,1975. Photogrammetric guide. Herbert Wichmann Verl, Karlsruhe, pp 58–60
Arun, K.S., Huang, T.S., Blostein, S.D.,1987. least squares fitting of two 3d point sets. IEEE Trans. PAMI, 9(5), pp. 698-700 Awange, J.L., and E.W. Grafarend, 2002. Linearized least squares and nonlinear Gauss- Jacobbi combinatorical algorithm applied to the 7 parameter datum transformation c7(3) problem. Zeitschrift fu¨rVermessungswesen127:109–116. Awange, J.L., and E.W. Grafarend,2003, Closed form solution of the overdetermined nonlinear 7 parameter datum transformatiotn. Allgemeine Vermessungsnachrichten 110:130–149 Awange, J.L., and Grafarend, E.W., 2005. Solving Algebraic Computational Problems in Geodesy and Geoinformatics, Springer, Berlin. Badekas, J.,1969.Investigations related to the establishment of a World Geodetic System, Ohio State University Department of Geodetic Science and Surveying. Report 124. Besl, P.J., McKay, N.D.,1992. Method for registration of 3-D shapes. In: Sen-sor Fusion IV: Control Paradigms and Data Structures, Vol. 1611, pp.586–606.SPIE, Bellingham,WA Bursa, M.,1962.The theory for the determination of the non-parallelism of the minor axis of the reference ellipsoid and the inertial polar axis of the earth, and the planes of the initial astronomic and geodetic meridians from observations of artificial earth satellites, Studia Geophysica et Geodetica, No. 6, pp.209-214. Deakin,R.E,2006.A Note on the Bursa-Wolf and Molodensky-Badekas Transformations. School of Mathematical and Geospatial Sciences, RMIT University: Melbourne, VIC, Australia, pp. 1–21 Fillmore, J. P.,1984. A Note on Rotation Matrices. IEEE Comp. Graph. 4,pp.30–33 Gellert, W.; Gottwald, S.; Hellwich, M.; Kästner, H.; and Künstner, H. (Eds.). VNR Concise Encyclopedia of Mathematics, 2nd ed. New York: Van Nostrand Reinhold, 1989. Golub, G. H., and Reinsch, C.,1970.Singular value decomposition and least squares solutions.Numerische Mathematik,14(5):403-420 Han, J.Y., and J.J. Jaw, 2013.Solving a similarity transformation between two reference frames using hybrid geometric control features, Journal of the Chinese Institute of Engineers, 36(3):304-313. Harris, C. W., and Kaiser, H. F.,1964. Oblique factor analytic solutions by orthogonal transformations. Psychometrika,29: 347-362. Harvey, B. R.,1986. Transformation of 3D Co-ordinates. Australian Surveyor,33, pp.105-125 Horn B.K.P,1987.Closed-form solution of absolute orientation using unit quaternions. J Optical Soc Am4:629–642 Horn B.K.P, Hilden H.M, Negahdaripour S,1988.Closed-form solution of absolute orientation using orthonormal matrices. J Opt Soc Am 5:1127–1135 Kutoglu, H. S., Mekik, C., and Alcin, H,2002. A Comparison of Two Well Known Models for 7-Parameter Transformation. The Australian Surveyor, 47(1), pp. 24–30 Molodensky, M.S., Eremeev, V.F. and Yurkina, M.I., 1962. Methods for the Study of the External Gravitational Field and Figure of the Earth, Israeli Programme for the Translation of Scientific Publications, Jerusalem. Okwuashi, O.,and Eyoh, A,2012.3D coordinate transformation using total least squares. Academic Research International, 3(1):2223-9553. Reit, B. G.,1998.The 7-parameter transformation to a horizontal geodetic datum. Survey Review, 34(268): 400-404 Shen, Y.Z., Chen, Y.and Zheng, D.H.,2006. A quaternion-based geodetic datum transformation algorithm. Journal of Geodesy, 80,pp. 233-239. Shepperd, S. W.,1978.Quaternion from Rotation Matrix.Journal of Guidance and Control Wolf,H.,1963.Geometric connection and re-orientation of three-dimensional triangulation nets, Bulletin Geodesique, No. 68, pp. 165-169. Z´avoti, J., 2012.A simple proof of the solutions of the Helmert- and the overdetermined nonlinear 7-parameter datum transformation. Acta Geodaetica et Geophysica, 47(4):453–464. Za´voti , J.,2013. New treatment of the solution of 2D and 3D non-linear similarity (Helmert) transformations.Publ Geomat 16:7–16 Z´avoti, J., and Kalmár, J.,2015. A comparison of different solutions of the Bursa–Wolf model and of the 3D, 7-parameter datum transformation. Acta Geodaetica et Geophysica, 51(2):245–256. Zinßer, T., Schmidt, J., and Niemann, H.,2005. Point Set Registration with Integrated Scale Estimation. In International Conference on Pattern Recognition and Image Processing (PRIP 2005),pp.116-119 莊子毅，趙鍵哲，2016。光達點雲幾何特徵萃取及匹配，航測及遙測學刊，20(2):109-128。 | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/89083 | - |
| dc.description.abstract | 三維空間相似轉換是測量應用常見任務，空間資料的收集常藉由不同手法及儀器設備，在各自定義坐標系下進行測量，相同之空間幾何的測量成果必須藉由坐標系的旋轉、平移及尺度縮放整合或轉換至同一坐標系統下。尺度因子影響幾何長度、面積及體積等之度量，三維空間相似轉換模式下的尺度因子可聯合或獨立於其它參數進行解算。而當僅解算尺度因子，其解算程序相對簡易，可採不同模式。尺度因子參數求定之後，對依序解旋轉及平移參數並簡化整個三維空間相似轉換參數計算是十分有幫助的。
基於點坐標的觀測量，本課題針對尺度因子之單獨求解進行探討，並從文獻中收集幾種常用的尺度因子計算方式，詳細檢視方法原理、計算公式以及影響因子，並以定性及定量方式比較及分析方法特性，釐清異同點，供作實務應用尺度因子解算任務之參考。 | zh_TW |
| dc.description.abstract | 3D Spatial Similarity Transformation is a common task in geomatics . The collection of spatial data is often performed using various methods and instruments, in respective coordinate systems, to integrate or transform measurements of the same spatial geometry into a unified coordinate system, rotations, translations, and scaling are required. The scale factor of the 3D Spatial Similarity Transformation affects geometric lengths, areas, volumes, and other measurements. The scale factor of the 3D Spatial Similarity Transformation can be solved either jointly with or separately from other parameters.
When solely solving for the scale factor, the computation process is relatively simple and can be done using different approaches. Once the scale factor is determined, simplifying the computation of the entire 3D Spatial Similarity Transformation parameters and benefit for sequentially solving for rotation and translation parameters. This study focuses on the individual solution of the scale factor based on point coordinates. Various commonly used methods for scale factor calculation are collected from the literature. The principles, formulas, and influential factors of these methods are examined in detail. A qualitative and quantitative comparison and analysis of the characteristics of these methods are conducted to clarify their similarities and differences, providing a reference for practical applications of scale factor solving tasks. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-08-16T17:03:36Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-08-16T17:03:36Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 口試委員會審定書 Ⅰ
誌謝 Ⅱ 中文摘要 Ⅲ 英文摘要 Ⅳ 第一章 緒論 1 1.1前言 1 1.2研究動機與目的 1 1.3研究流程及論文架構 2 第二章 文獻回顧 4 2.1三維空間相似轉換 4 2.2共軛長度的種類 6 2.3不同場景下的尺度估計 6 2.4 旋轉矩陣的影響 7 2.5三維空間相似轉換尺度因子解算的變通公式 8 2.5.1 轉換參數非迭代解法 8 2.5.2以質心坐標系作為轉換基準之尺度解算 11 2.6尺度因子不同解算方法介紹 13 2.6.1 尺度因子解算方法(共軛長度總和比值) 14 2.6.2尺度因子解算方法(含旋轉矩陣/共軛長度平方總和比值開根號) 14 2.6.3尺度因子解算方法(源於共軛長度改正數) 16 2.7 小結 16 第三章 研究方法 18 3.1 尺度因子解算方法型態變通 18 3.1.1尺度因子解算方法推導來源改正數對稱式 20 3.1.2 尺度因子解算方法 4_1、4_2 22 3.1.3 尺度因子不同解算方法特性分析 22 3.1.4 尺度因子解算方法異同比較 26 3.2 以最小二乘法證明以質心坐標系作為轉換基準較佳 27 3.3以廣義平差模式分析尺度因子解算方法 30 3.3.1以廣義平差模式分析尺度因子解算方法(等權) 34 3.3.2尺度因子解算方法1 35 3.3.3尺度因子解算方法2_1、2_2 35 3.3.4尺度因子解算方法3 37 3.3.5尺度因子解算方法4_1、4_2 38 3.4平差模式 39 3.4.1 廣義平差模式 39 3.4.2 使用誤差傳播方式推導精度 43 3.5共軛長度之方差 49 3.5.1以共軛長度推導尺度因子之方差 50 3.5.2各段共軛長度之權重影響因子 55 3.6精度評估方式 57 第四章 實驗及分析 58 4.1試驗設計說明 59 4.2轉換前後皆未授予誤差之試驗 64 4.3考量尺度縮放及授予轉換前後誤差約略相等之試驗 65 4.4考量尺度縮放及授予轉換前誤差較大之試驗 71 4.5考量尺度縮放及授予轉換後誤差較大之試驗 77 4.6點位數量不同但長度總和約略相同之試驗 83 4.7綜合試驗分析 92 第五章 結論與建議 102 5.1結論 102 5.2建議 104 參考文獻 105 附錄一 108 附錄二 113 | - |
| dc.language.iso | zh_TW | - |
| dc.subject | 影響因子 | zh_TW |
| dc.subject | 尺度因子 | zh_TW |
| dc.subject | 平差模式 | zh_TW |
| dc.subject | 誤差傳播 | zh_TW |
| dc.subject | 理論精度 | zh_TW |
| dc.subject | 相對精度 | zh_TW |
| dc.subject | Relative accuracy | en |
| dc.subject | Scale factor | en |
| dc.subject | Influential factors | en |
| dc.subject | Theoretical accuracy | en |
| dc.subject | Adjustment mode | en |
| dc.subject | Error propagation | en |
| dc.title | 基於點坐標之三維空間相似轉換尺度因子解算分析 | zh_TW |
| dc.title | Solution Analysis of Scale Factor in 3D Spatial Similarity Transformation Based on Point Coordinates | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 徐百輝;邱式鴻 | zh_TW |
| dc.contributor.oralexamcommittee | Pai-Hui Hsu;Shih-Hung Chiu | en |
| dc.subject.keyword | 尺度因子,平差模式,誤差傳播,理論精度,相對精度,影響因子, | zh_TW |
| dc.subject.keyword | Scale factor,Adjustment mode,Error propagation,Theoretical accuracy,Relative accuracy,Influential factors, | en |
| dc.relation.page | 114 | - |
| dc.identifier.doi | 10.6342/NTU202302548 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2023-08-11 | - |
| dc.contributor.author-college | 工學院 | - |
| dc.contributor.author-dept | 土木工程學系 | - |
| dc.date.embargo-lift | 2028-08-09 | - |
| 顯示於系所單位： | 土木工程學系 | |
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