三维重建中的算法研究

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	三维重建中的算法研究
	张明
	2016-05-31
学位类型	工学博士
英文摘要	摄像机标定是三维重建中的基本问题。自标定方法的灵活性使得它是摄像机标定中的重要研究方向。其中，基于分层重建方法和基于绝对对偶二次曲面方法是较为成熟和广泛应用的自标定方法。然而，这两种方法对图像噪声较为敏感且计算复杂性较高。图像中直线特征相对于点特征更为鲁棒，因此直线重建也是三维重建中的重要研究方向。本文讨论如何提高自标定算法的精度和直线三角化算法的精度，主要工作概括如下： 1. 基于 Cayley 变换的摄像机自标定算法。在摄像机内参数固定的假设下，基于无穷远 Cayley 变换（ICT），提出了无穷远平面法向量的新约束方程。然后基于这些新约束和 ICT 的射影表示，提出了两种自标定算法，分别是分层 Cayley 算法和整体 Cayley 算法。这两种算法相比传统算法具有更高的标定精度。 2. 基于绝对对偶二次曲面（ADQ）的线性自标定算法。对于内参数变化的情形，提出了一种线性自标定算法。首先通过分析 ADQ 射影表达中关于内参数和无穷远平面法向量的高次项之间的关系，将 ADQ 的二次约束方程变换为多变量的线性方程，然后通过求解线性方程组实现了自标定。所提出的算法不仅提高计算精度，也极大地降低了计算复杂性。 3. 直线三角化算法和三维直线的距离度量。首先，提出了一种新的线性直线三角化算法。然后，利用拉格朗日乘子法，提出了两种基于代数误差最小化的优化算法和一种基于几何误差最小化的迭代算法。为了更准确评估三角化方法中直线估计的 3D 误差，提出了两种新的三维直线空间中的距离度量。 4. 基本矩阵估计的快速鲁棒算法。首先采用具有几何意义的重投影误差准则，评估基本矩阵的估计。然后通过分析外点的概率分布，基于概率统计理论提出了新的外点检测策略。所提出的算法不仅能得到鲁棒和精确的估计，而且减少了计算时间。 ; Camera calibration is a fundamental problem in 3D reconstruction. Due to the flexibility of self-calibration, it is an important research topic in camera calibration. Stratified reconstruction and Absolute Dual Quadric based self-calibration methods are two mature and widely used self-calibration techniques in computer vision. However, these methods are of high sensitivity to image noise and of high computation complexity. Line feature is more robust than point feature; therefore line reconstruction is also an important research topic in 3D reconstruction. This thesis discusses how to increase the accuracy of camera self-calibration algorithms and line reconstruction algorithms. The main work is summarized as follows: 1. Cayley transform based camera self-calibration algorithm. Under the assumption of constant camera intrinsic parameters, new constraints on the normal vector of infinite plane are proposed based on Infinite Cayley Transformation (ICT). Then, a stratified Cayley algorithm and a total Cayley algorithm are proposed based on the new constraints and the projective expression of ICT. Both the two algorithms have higher calibration accuracy than classic algorithms. 2. Absolute Dual Quadric (ADQ) based linear self-calibration algorithm. For the situation of varying camera intrinsic parameters, a linear self-calibration algorithm is proposed. Through analyzing the relationship of high order terms between camera intrinsic parameters and normal vector of infinite plane in the projective expression of ADQ, the quadratic constraints on ADQ are transformed to multi-variable linear equations. Then by solving the linear equation groups, camera self-calibration is fulfilled. The proposed algorithm increases the calibration accuracy and decreases the computation time. 3. Line triangulation and metric of 3D lines. First of all, a new linear line triangulation algorithm is proposed. Then, using the Lagrange multiplier method, two algebraic error minimization based optimal algorithms and a geometric error minimization based iterative algorithm are proposed. In addition, to more accurately assess the 3D estimation error in line triangulation methods, two new metrics in 3D line space are proposed. 4. Fast and robust algorithm for fundamental matrix estimation. First of all, re-projection error which has specific geometric meaning is adopted to assess the estimation of fundamental matrix. Then through analyzing the probabilistic distribution of outliers, a new strategy for outlier detection is obtained based on the probability and statistics theory. The algorithm has more accurate and robust estimation as well as less computation time.
关键词	Cayley 变换摄像机自标定分层重建直线三角化基本矩阵估计
语种	中文
文献类型	学位论文
条目标识符	http://ir.ia.ac.cn/handle/173211/11665
专题	毕业生_博士学位论文
作者单位	中国科学院自动化研究所模式识别实验室
第一作者单位	中国科学院自动化研究所
推荐引用方式 GB/T 7714	张明. 三维重建中的算法研究[D]. 北京. 中国科学院大学,2016.

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文件名称/大小	文献类型	版本类型	开放类型	使用许可
毕业论文 201118014628070（4697KB）	学位论文		限制开放	CC BY-NC-SA