本研究旨在基於近景攝影測量(close-range photogrammetry)發展非接觸性之振動位移量測技術，由兩不同角度拍攝同一目標物之影像，便可利用影像對(image pair)間之相對方位(relative orientation)關係解算相對空間點座標。所用之解算方式是基於射影幾何之共面式(coplanarity condition)搭配共線式(collinearity condition)，其中，共面式以線性方程可快速求解空間點初始值，而有利於動態影像連續分析，且計算過程僅需要使用相機內方位參數，而後續共線式之解算則可以將誤差最小化。首先，根據共面式搭配共線式之原理，以Python程式語言建置一共軛影像處理程式，用以解算兩圖像之共軛點於空間之座標；接著，將程式實際應用於靜態尺寸測量及動態振動位移分析，分別以實際案例進行驗證，包括以消費級相機拍攝一建築物並進行靜態分析，以及利用工業級攝影機於振動台試驗過程中高速連續拍攝試體並進行動態分析；前者用以確認基於共面式搭配共線式解算空間點座標的可行性及設置編碼標之需求，後者則是振動位移量測之實際應用，藉由與其他可信之量測儀器所得結果間的相關性，來評估本研究所發展方法之精度，並歸納實務應用上的限制。根據測試結果可知，應用本方法時編碼標採非平面配置之解算精度遠高於採平面配置，於靜態分析中在量測距離約3.5 m、編碼標點間距約20 cm左右之平均相對誤差約0.45%；動態分析中在距離試體約13.5 m、可拍攝到之試體長寬約 3 m (W) × 4.5 m (H)，當試體振動位移振幅約100 mm以上時與參考量測值之相關係數可達0.95以上，振動位移振幅達200 mm以上時相關係數更達0.99以上，驗證本方法適用於公分級振動位移之量測，如振動台地震模擬試驗之結構反應。

This study aimed to obtain the spatial coordinates of the conjugate points of image pair using the concept of relative orientation in close-range photogrammetry. The algorithm which defines the optical constraint between image space and object space used in was based on the coplanarity condition of projective geometry accompanied with the collinearity condition. According this algorithm, the Python programming language was adopted to develop an application program named Conjugate Image Processing Program. This program can process a specific image pair for static measurement of dimensions as well as a continuous sequence of image pairs for dynamic measurement of vibration. In the static application, the accuracy of measurement at different configurations of targets for detection as the conjugate points was discussed, whereas in the dynamic application the correlation between the measured vibration displacement by Conjugate Image Processing Program and that by other reliable methods was examined. Results showed that a non-planar configuration of targets led to better accuracy than a planar one, and the proposed program was verified to be capable of centimeter-level vibration measurement, such as the structural response in large-scale shaking table tests.

1. Bracewell, R. Pentagram Notation for Cross Correlation. The Fourier Transform and Its Applications. New York: McGraw-Hill, pp. 46 and 243.1965.
2. Britannica, T. Editors of Encyclopaedia, Jean-Victor Poncelet. Encyclopedia Britannica. https://www.britannica.com/biography/Jean-Victor-Poncelet.2021.
3. Chien, J. Beginner’s guide to fundamental matrix, essential matrix and camera motion recovery. 2016.
4. Handayani, H. Space intersection by collinearity. Geoid, 5(2), 105-109. doi:10.12962/j24423998.v5i2.7339. 2010.
5. Longuet-Higgins, H.C. A computer algorithm for reconstructing a scene from two projections. Nature, no. 291, vol. 5828. 1981.
6. Mohr, R., & Triggs, B. Projective geometry for image analysis. XVIIIth International Symposium on Photogrammetry & Remote Sensing (ISPRS ’96), Jul, Vienna, Austria. Inria-00548361. 1996.
7. Mikhail, M., Bethel, S., and McGlone, J.C. Introduction to modern photogrammetry. ISBN: 0-471-30924-9, Ch. 4, Ch. 5, Ch. 9.2001.
8. Rodgers, J. L., & Nicewander, W. A. Thirteen Ways to Look at the Correlation Coefficient. The American Statistician, 42(1), 59–66. https://doi.org/10.2307/2685263.1988.
9. Smith, D. E. History of Modern Mathematics. Lit2Go Edition.1906.
10. Steel, R. G. D., & Torrie, J. H. Principles and Procedures of Statistics with Special Reference to the Biological Sciences. McGraw Hill. 246-247.1960.
11. Walford, A. One Part in 300,000. Precision and accuracy discussion. EOS Inc., 2006.
12. Yung-Yen Ko, Jen-Yu Han and Jun-Yun Cho. Application of close-range photogrammetry for post-failure Reconnaissance of a Retaining Wall. NCREE Newsletter, vol. 10, 1. 2015.
13. 康明昌，古希臘幾何三大問題，數學傳播，中央研究院數學研究所發行，第八卷第二期，1984。
14. 鄭傑文，射影幾何於攝影量測之應用，國立臺灣大學碩士論文，2007。
15. 賴建邑，以影像技術進行結構物相對幾何變遷偵測，國立臺灣大學土木工程學研究所碩士論文，2013。
16. 盧煉元、胡宣德、林子堯、林柏樺，減震技術於離岸風力發電支撐結構之應用研究，結構工程期刊、第三十一卷、第一期、第 99-130 頁、表3，2016。
17. 林照捷，以解算連續像對相對方位參數之單眼視覺里程計，航測及遙測學刊、第二十四卷、第2期，2019。
18. 鄭崑硯，土壤液化對地下維生管線影響之振動台試驗研究—建築物近端管線，國立成功大學碩士論文，2022。