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研究生： 黃柏豪
Po-Hao Huang
論文名稱： 長程影像串列包含資訊遮蔽情形中，以分解為基礎，強固的三維重建方法
Robust Long-Term Factorization-based SfM with Occlusions
指導教授： 賴尚宏
Shang-Hong Lai
口試委員:
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 資訊工程學系
Computer Science
論文出版年： 2004
畢業學年度： 92
語文別： 中文
論文頁數： 79
中文關鍵詞： 三維重建 、相機校正 、遮蔽 、消失 、錯誤對應 、基本矩陣 、長程 、強固 、分解
外文關鍵詞： Structure from Motion, Self-Calibration, Occclude, Missing, Outliers, Fundamental Matrix, Long-term, Robust, Factorization
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    • 從影像中重建物體的三維模型，在電腦視覺領域裡一直是一個很有趣且很有挑戰性的問題。從運動求得結構(Structure from motion)是其中一種從影像中重建物體三維結構的方法。在這篇論文中，我們提出了一個強固的長程影像三維重建方法，同時這個方法也克服了對應點找尋錯誤或是被遮蔽的問題。
    針對對應點被遮蔽(Occluded or Missing)的問題，這種問題特別容易發生在長程影像中，我們提出了一個新的方法來處理因為這些消失的資料而產生的問題。藉由把長程影像分割成很多的區段影像列，憑藉每個區段影像彼此有覆蓋兩張影像以上的條件，將看得到的對應點資訊擴散分布到那些消失的點資訊，進而猜得那些消失的點原本應該存在的位置。而那些被猜測出來的點正如同真正的影像對應點加上某種程度的高斯雜訊(Gaussian Noise)。沒有使用任何校正(registration)的方法，這個方法很直接且在實際應用上運作的相當良好。
    針對對應點找尋錯誤(Outliers)的問題，我們提出了將RANSAC理論套用到Projective Factorization的方法上。加上一些修改，我們在一次的取樣中，可以拿到更多的inliers，藉此減少最大的取樣次數。最後，藉著最小化(minimize)那些看得到而且被認為是inlier點的投影誤差，我們提出一個改良的方法去修正我們求得的模型，進而得到更符合所有資料的模型。
    實驗結果分別呈現在模擬以及真實的資料，以驗證我們方法的強固性。

    3D modeling from images is an interesting and challenging problem in computer vision. Structure from motion (SfM) is a method that reconstruct 3D model from images. In this thesis, we propose a robust long-term SfM algorithm to reconstruct 3D models. This method overcomes the problems due to tracking errors and occlusion.
    For the problem of occlusions, especially occurs in the long-term sequence, we propose a new scheme for dealing with the missing data. Base on the idea of dividing image sequence into overlapped sub-sequences and then propagating points from the visible ones to the occluded ones. Those putative points are treated as the actual image points with some level of Gaussian Noise. Without any registration methods, this approach is straight-forward and works well in practice.
    To achieve robustness against outliers, we propose a robust SfM algorithm by applying the adaptive RANSAC technique on the projective factorization method. With slightly modifying the adaptive RANSAC algorithm, we obtain more inliers in one sample, thus reducing the maximal sampling times. Furthermore, to minimize the re-projection errors of the visible points considered as inliers, we propose a refinement algorithm to refine the model.
    Experimental results on both synthetic and real data show the robustness of the proposed algorithm.

    Contents i List of Figures iii List of Algorithms v List of Tables vi Chapter 1 Introduction 1 1.1 Methods for 3D Modeling 1 1.2 Structure from Motion 2 1.3 Projective Factorization Method 4 1.4 Challenges of SfM 5 1.5 Our Approach 6 1.6 Organization of this thesis 9 Chapter 2 Related Works 10 2.1 Camera Model and Two View Geometry 10 2.1.1 Camera Model 10 2.1.2 Projection Matrix 13 2.1.3 Triangulation Method 14 2.1.4 Fundamental Matrix 15 2.1.5 Normalization Method 17 2.2 Projective Factorization 19 2.2.1 Factorization Method 20 2.2.2 Projective Depth Recovery Method 21 2.3 Self-Calibration 24 2.3.1 Canonical Expression 24 2.3.2 Assumptions and Constraints for Self-Calibration 26 2.3.3 From General Expression to the Canonical One 27 2.4 Robust Estimators 28 2.4.1 Determine the maximal sampling times N 30 2.4.2 Adaptive RANSAC algorithm 32 2.5 Multiple View Consistency 33 2.5.1 Sequential Updates 33 2.5.2 Batch Update 35 Chapter 3 Robust SfM Methods 38 3.1 Multiple-View Projective Reconstruction 40 3.1.1 Iterative Projective Factorization Method 40 3.1.2 Initialization of Projective Depth 41 3.2 Projective SfM with Occlusions 42 3.3 Projective SfM with Outliers 44 3.3.1 Estimating Fundamental Matrix by adaptive RANSAC method 45 3.3.2 Estimating Projective SfM by adaptive RANSAC method 46 3.3.3 Weighted Linear Equation for obtaining X with outliers 48 3.3.4 Refine the Structure and Motion using All Inliers 49 3.4 Long-term SfM with Outliers and Occlusions 50 3.4.1 Image Sequence Division 51 3.4.2. Applying Robust Estimator on each Sub-sequence 51 3.4.3. Point Propagation to the Whole Sequence 52 3.5 Upgrade form Projective to Metric Frame 54 Chapter 4 Experimental Results 56 4.1 Synthetic Data 56 4.1.1 Tolerance of Missing Data with Noise 56 4.1.2 Tolerance of Outliers with Noise 60 4.1.3 The Result of Long-term SfM 63 4.14 The Result of Different Amount of Views as Sub-sequences 64 4.1.5 Comparison with the Results without Using the Robust Estimator 67 4.2 Real Data 70 Chapter 5 Conclusion 75 References 77

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