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摄像机一维标定的加权线性算法研究
Alternative TitleStudy on the Weighted Linear Algorithms for Camera Calibration with 1D Objects
史坤峰
Subtype工学博士
Thesis Advisor吴福朝
2014-05-17
Degree Grantor中国科学院大学
Place of Conferral中国科学院自动化研究所
Degree Discipline模式识别与智能系统
Keyword摄像机标定 一维物体 加权线性算法 一阶误差分析 Camera Calibration 1d Objects Weighted Linear Algorithm First-order Error Analysis
Abstract摄像机标定是计算机视觉中的基本问题之一,它是三维重建、机器人导航、虚拟现实等视觉应用的必要步骤。在基于参考物的标定方法中,一维物体因制作简单以及不发生自遮挡的优点而被广泛使用。本文讨论如何利用加权技术进一步提高基于一维物体的摄像机标定的精度,主要贡献能被概括如下: 1.加权线性算法的一阶误差分析。根据一阶误差传播理论,发现简单加权线性算法的一阶误差项不受权重的一阶误差项影响,进而得到一阶误差项的简单形式。然后将此结论应用到最优加权线性算法,发现最优加权算法与迭代最优加权算法有相同的一阶误差项,因此最优加权线性算法在保证一阶精度的前提下极大地降低了计算量。这些结论是加权线性算法设计和分析的理论基础。 2.基于一维物体的单摄像机标定的加权线性算法。为了提高现有线性标定算法的精度,提出了两个加权线性算法。首先,为一维物体标记点的相对深度给出了一个相似不变的估计量,使用该估计量标准差的倒数作为绝对二次曲线的像的约束方程的权重,得到简单加权线性算法;然后,对相对深度约束方程和绝对二次曲线的像的约束方程都进行最优加权,得到最优加权线性算法。这两个算法都是相似不变的,并且最优加权线性算法与捆绑调整算法有相当的标定精度。 3.基于线段的多摄像机标定和欧氏提升的加权线性算法。首先,通过对基于线段长度的非线性标定方程进行线性化,得到一个比现有线性算法有更高精度、更鲁棒的线性算法;然后,基于一阶误差分析对这个新线性算法进行简单加权和最优加权,得到两个更高精度的加权线性算法;最后,根据线段长度约束给出了一个加权非线性算法,进一步提高了加权线性算法的精度。
Other AbstractCamera calibration is one of the fundamental problems in computer vision, which is necessary to many applications of computer vision such as 3D reconstruction, mobile robot navigation, and virtual reality. Among the camera calibration methods based on reference objects, camera calibration with 1D objects is used widely because 1D objects have the advantage that they are easy to manufacture and immune to self-occlusion. This thesis investigates how to use weighted algorithms to further improve the accuracy of camera calibration with 1D objects, and the main contributions include: 1. The first-order error terms of weighted linear algorithms are analyzed. Based on the first-order error propagation theory, we find out that the first-order error term of the simply weighted linear algorithm is not influenced by the first-order error terms of the weights, and then obtain a compact expression for its first-order error term. Next, we apply this conclusion to the optimally weighted linear algorithm, and find out that it has the same first-order error term as the iteratively and optimally weighted linear algorithm, which shows that the optimally weighted linear algorithm can reduce the computational load dramatically while ensuring the same first-order accuracy. These conclusions are the theoretical bases of the designing and analysing of weighted linear algorithms. 2. To further improve the accuracies of the existing linear algorithms for single camera calibration with 1D objects, two weighted linear algorithms are proposed. First, a similarity-invariant estimator for the relative depths of the moving endpoints is introduced, and the reciprocal of the standard deviation of the estimator in each pose is used as the weight of the corresponding constraint on the image of the absolute conic (IAC), resulting in a simply weighted linear algorithm. Then, the constraint equations on the relative depths and the IAC are both optimally weighted, resulting an optimally weighted linear algorithm. These two weighted linear algorithms are both similarity-invariant, and the optimally weighted linear algorithm achieves comparable accuracy to the bundle adjustment algorithm. 3. Two weighted linear algorithms for multi-camera calibration and Euclidean upgrading with segments are proposed. First, the nonlinear calibration equations derived from the knowledge of segment lengths are linearized, resulting a new linear algorithm which achieves higher accuracy and robustness than the...
shelfnumXWLW1983
Other Identifier201018014628054
Language中文
Document Type学位论文
Identifierhttp://ir.ia.ac.cn/handle/173211/6579
Collection毕业生_博士学位论文
Recommended Citation
GB/T 7714
史坤峰. 摄像机一维标定的加权线性算法研究[D]. 中国科学院自动化研究所. 中国科学院大学,2014.
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