近年來空間定位在各個領域都被廣泛的應用，本研究想藉由單一數位相機所擷取之影像進行空間定位以滿足普及化的需求。本篇論文主要研究目標為，在目標物尺寸已知時，透過單一數位相機對目標物攝影的單張影像進行空間定位。透過目標物尺寸與在影像中位置，可對不同物平面法向量算出不同物距，若物平面方程式為ax + by + z = z0，則令非線性函數含有三參數，分別為a; b; z0，其值為物距平方總和，當正確的參數帶入時，函數值為0。為了解非線性方程式，在擷取定位用影像前，必須先用其他影像計算相機內部參數以進行校正。解非線性方程式疊代所採用的數值法分別為梯度下降法及牛頓法，在不同條件下比較兩種算法之間的準確度和所需的疊代次數。根據實驗結果，具有較好收斂穩定性的梯度下降法將是主要的疊代方法。

In recent years, spatial positioning has been widely used in various fields.
This study intends to spatially locate images captured by a digital camera to meet the needs of popularization. The main research object of this paper is that when the size of the target is known, we would like to locate the target through a single image captured by a digital camera. Through the size of the object and the position in the image of the object, different object distances can be calculated for different object plane normal vectors. If the object plane equation is ax + by + z = z0, then let the nonlinear function contains three parameters, respectively a; b; z0, which is the total sum of squares of the object distances. When the correct parameters are brought in, the function value will be 0. In order to solve the nonlinear function, the camera’s internal parameters must be calculated with other image for correction before capturing the image for positioning. The numerical methods used are gradient method and Newton method, the accuracy between the two algorithms and the number of iterations required are compared under different conditions.
According to the experimental results, the gradient descent method with better convergence stability will be the main iterative method.

[1] Dhond,U. and Aggarwal,J.(1989), Structure from stereo-a review,IEEE Transactions on Systems,Man,and Cybernetics V19(6),pp.1498–1510.
[2] Schastein,D. and Szeliski,R.(2002), A taxonomy and evaluation of dense two-frame stereo correspondence algorithm, International Journal of Computer Vision,47,pp.7–42.
[3] Kolb,A.,Barth,E.,Koch,R.,Larsen,R.(2010), Time-of-Flight Cameras in Computer Graphics,Computer Graphics Forum, V29(1),pp.141–159.
[4] Geng,J.(2011), Structured-light 3D surface imaging:a tutorial,Advances in Optics and Photonics,V3(2),pp.128–160.
[5] 呂建德(2009)，「以結構光為基礎的3D 立體物件自動掃描系統研究」，中華大學資訊工程學系碩士論文。
[6] Song,J.,Park,Y.(2014), Image Features Comparison-Based Position Estimation Method Using a Camera Sensor,World Academy of Science,Engineering and Technology International Journal of Mechanical and Mechatronics Engineering,V8(9)
[7] Fukunaga,K.(1990), Introduction to Statistical Pattern Recognition(2nded),San Diego：Academic Press Professional
[8] Bradski,G. and Kaehler,A.(2012), Learning OpenCV:Computer Vision with the OpenCV Library(1sted),Sebastopol,California：O’Reilly Media