三維物體的姿態估測在電腦視覺於機器人的應用上，擔任著重要的位置。本文結合模板追蹤方法與PnP演算法完成三維物體的姿態估測方法。所使用的方法是先透過擷取並匹配物體與參考影像的特徵點，並將特徵點經過單應性矩陣轉換出物體與影像的相對關係。再利用模板追蹤方法進行追蹤。最後再將追蹤的結果利用事先建立好的模型進行點匹配，並利用PnP方法將物體的三維姿態估測出來。在實驗中進行旋轉與平移的實驗。在平移實驗上有良好的結果。在旋轉實驗上，在正負20度旋轉都有不錯的結果，此外估測出來的角度相對不穩定。

3D object pose estimation plays a crucial role in computer and robotic vision. In this thesis, a novel model-based object pose estimation algorithm is proposed by integrating template matching and PnP pose estimation methods to deal with this issue efficiently. The proposed method firstly extracts and matches keypoints of the scene image and the object reference image. Using the matched keypoints, a 2D mapping between the reference image and the observed object can be formulated by a homography matrix, which is used as an initial setting for a template-based tracking algorithm. Based on the visual tracking result, the corresponding points between image keypoints and control points of the CAD model of the object can be determined efficiently. Finally, the 3D pose of the object with respect to the camera is estimated by adopting the PnP algorithm based on the corresponding points between 2D image keypoints and 3D model control points. The experimental results validate the estimation accuracy and real-time performance of the proposed model-based object pose estimation algorithm.

III 
 
目錄 
中文摘要 ........................................................................................................ I 
Abstract ........................................................................................................... II     
目錄 ................................................................................................................ III 
圖目錄 ........................................................................................................... VII 
表目錄 .......................................................................................................... VIII 
第一章  序論 ..................................................................................................... 1 
1.1  研究背景 ........................................................................................... 1 
1.2  研究動機與目的 ............................................................................... 2 
1.3  論文架構 ........................................................................................... 3 
第二章  相關研究 ............................................................................................. 4 
2.1  角度表示方法 ................................................................................... 4 
2.1.1  尤拉角表示法 ............................................................................... 4 
2.1.2  四元數表示法 ............................................................................... 5 
2.1.3  羅德里格旋轉矩陣表示法 ........................................................... 5  
IV 
 
第三章  物體辨識與追蹤相關演算法 ............................................................. 8 
3.1  物體辨識 ........................................................................................... 8 
3.1.1  SIFT 演算法 .................................................................................. 9 
3.1.1.1  尺度空間極值偵測 ......................................................... 10 
3.1.1.2  關鍵點定位 ..................................................................... 10 
3.1.1.3  定位分配 ......................................................................... 10 
3.1.1.4  關鍵點描述 ..................................................................... 10 
3.2  模板匹配追蹤 ................................................................................. 11 
3.2.1  離線學習 ..................................................................................... 11 
3.2.1.1  物體與參考影像的學習資料建置 ................................. 12 
3.2.1.2  超平面轉換 ..................................................................... 13 
3.2.1.3  追蹤模型的建置 ............................................................. 14 
3.2.2  追蹤初始化 ................................................................................. 14 
3.2.2.1  離群點移除演算法 ......................................................... 15 
3.2.2.2  單應性矩陣初始化 ......................................................... 15 
3.2.3  線上追蹤 ..................................................................................... 17 
3.2.3.1  模板追蹤 ......................................................................... 17  
V 
 
第四章  物體姿態估測相關演算法 ............................................................... 19 
4.1  相機內部參數估測 ......................................................................... 20 
4.2  姿態估測演算法 ............................................................................. 23 
4.2.1  EPnP 演算法 ............................................................................... 23 
4.2.2  本論文使用的 PnP 演算法 ........................................................ 25 
第五章  實驗結果與分析 ............................................................................ 28 
5.1  軟硬體介紹 ..................................................................................... 28 
5.2  物體姿態估測實驗 ......................................................................... 30 
5.2.1  平移實驗 ..................................................................................... 32 
5.2.1.1  X 軸平移 ......................................................................... 32 
5.2.1.2  Y 軸平移 ......................................................................... 33 
5.2.1.3  Z 軸平移 ......................................................................... 33 
5.2.1.4  平移實驗結果 ................................................................. 33 
5.3  旋轉實驗 ......................................................................................... 34 
5.3.1.1  X 軸旋轉 ......................................................................... 34 
5.3.1.2  Y 軸旋轉 ......................................................................... 35 
5.3.1.3  Z 軸旋轉 ......................................................................... 35  
VI 
 
5.3.1.4  旋轉實驗結果 ................................................................. 36 
第六章  結論與未來展望 ............................................................................... 39 
參考文獻 ......................................................................................................... 40 
附錄一-X 軸平移實驗圖 ............................................................................... 42 
附錄二-Y 軸平移實驗圖 ............................................................................... 44 
附錄三-Z 軸平移實驗圖 ................................................................................ 45 
附錄四-X 軸旋轉實驗圖 ............................................................................... 46 
附錄五-Y 軸旋轉實驗圖 ............................................................................... 49 
附錄六-Z 軸旋轉實驗圖 ................................................................................ 52 

圖目錄 
圖 2. 1  羅德里格旋轉矩陣示意圖 .............................................................. 6 
圖 3. 1  物體姿態估測流程圖 ...................................................................... 8 
圖 3. 2 物體辨識流程圖 ............................................................................... 9 
圖 3. 3  超平面近似法的模板追蹤流程圖 ................................................ 11 
圖 3. 4 超平面轉換示意圖 ......................................................................... 13 
圖 4. 1  物體姿態估測流程圖 .................................................................... 19 
圖 4. 2  二維平面圖 .................................................................................... 20 
圖 4. 3 PnP 方法虛擬碼 ............................................................................. 27 
圖 5. 1 Microsoft    Lifecam cinema HD  攝影機 ...................................... 29 
圖 5. 2 Pan-Tilt Unit-D46 控制平台 .......................................................... 30 
圖 5. 3 參考影像:中間為第一參考影像，左邊為第二參考影像，右邊
為第三參考影像 ................................................................................. 31 

表目錄 
表 5. 1 電腦規格 ......................................................................................... 29 
表 5. 2 使用軟體 ......................................................................................... 29 
表 5. 3 各階段所花費時間表 ..................................................................... 31 
表 5. 4 X 軸平移數據 ................................................................................. 32 
表 5. 5 Y 軸平移數據 ................................................................................. 33 
表 5. 6 Z 軸平移數據 ................................................................................. 33 
表 5. 7 X 軸、Y 軸、Z 軸之平移誤差 ..................................................... 34 
表 5. 8 X 軸旋轉數據 ................................................................................. 35 
表 5. 9 Y 軸旋轉數據 ................................................................................. 36 
表 5. 10 Z 軸旋轉數據 ............................................................................... 37 
表 5. 11 X 軸、Y 軸、Z 軸之旋轉誤差 .................................................... 38

[1] 	Amazon, "Amazon Picking Challenge," 2016. Available: http://amazonpickingchallenge.org/details.shtml.
[2] 	Changhyun Choi and Henrik I. Christensen, “Real-time 3D Model-based Tracking Using Edge and Keypoint Features for Robotic Manipulation,” International Conference on Robotics and Automation Anchorage Convention District IEEE, pp. 4048-4055, 2010. 
[3] 	Chi-Yi Tsai ,Wei-Yi Wang, Chi-Hung Huang, and Bo-Ren Shih, "CAD Model-based 3D Object Pose Estimation using an Edge-Based," Proceedings of the 3rd IIAE International Conference on Intelligent Systems and Image Processing 2015 , 2015. 
[4] 	Samuel Dambreville, Romeil Sandhu, Anthony Yezzi, and Allen Tannenbaum, "Robust 3D Pose Estimation and Efficient 2D Region-Based Segmentation from a 3D Shape Prior," In Proc. 10th European Conference on Computer Vision, 2008. 
[5] 	Gimbal Lock, . Available: https://en.wikipedia.org/wiki/Gimbal_lock.
[6] 	D. G. Lowe, "Distinctive image features from scale-invariant," International Journal of Computer Vision, Vols. 60,No. 2, pp. 91-110, 2004. 
[7] 	F.Jurie, M.Dhome, Hyperplane Approximation for Template Matching, vol. 24, 2002., pp. 996-1000.
[8] 	M. A. F. &. R. C.Bolles, "Random Sampling Consensus: a Paradigm for Model Ftting with Application to Image Analysis and Automated Cartography," Communications of the ACM, vol. 24, pp. 381-395, June 1981. 
[9] 	] P. Sturm & S. Maybank, "On Plane-Based Camera Calibration: A General Algorithm, Singularities, Applications," Proceedings of the IEEE Conference on Computer vision and Pattern Recognitions, pp. 432-437, 1990. 
[10] 	Vincent Lepetit • Francesc Moreno-Noguer • Pascal Fua, "EPnP: An Accurate O(n) Solution to the PnP Problem," Int J Comput Vision, vol. 81, pp. 155-166, 2009.