Vol.14, No.3 ©2003 Journal of Software 软 件 学 报 1000-9825/2003/14(03)0703 由矩形确定摄像机内参数与位置的线性方法 ∗ 吴福朝, 王光辉 + , 胡占义 (中国科学院 自研究所 模式识别国家重点实验室,京 100080) A Linear Approach for Determining Intrinsic Parameters and Pose of Cameras from Rectangles WU Fu-Chao, WANG Guang-Hui + , HU Zhan-Yi (National Laboratory of Pattern Recognition, Institute of Automation, The Chinese Academy of Sciences, Beijing 100080, China) + Corresponding author: Phn: 86-10-62542946, E-mail: ghwang@nlpr.ia.ac.cn http://nlpr-web.ia.ac.cn/english/rv Received 2001-11-30; Accepted 2002-02-27 Wu FC, Wang GH, Hu ZY. A linear approach for determining intrinsic parameters and pose of cameras from rectangles. Journal of Software, 2003,14(3):703~712. Abstract: In this paper, a linear approach is proposed to determine the camera’s intrinsic parameters as well as its pose. At first, the images of the two circular points are derived from the images of two unparallel coplanar rectangles in space, then some linear constraints on the intrinsic parameters are established via the obtained images of the circular points. In addition, the necessary and sufficient condition of the constraint system for a unique solution is also provided. Having obtained intrinsic parameters, the camera’s pose can be computed from the homography between the image plane and the space plane. Besides, a linear approach is also presented to retrieve the metric information (i.e., the Euclidean one up to a scale) of the rectangles by means of the Laguerre theorem. The main advantage of these approaches lie in that neither the metric information of the rectangles nor the correspondences between images are required, and the involved algorithms are all linear. Extensive simulations and experimental results with real images show that these proposed approaches are both accurate and robust. Key words: camera calibration; camera’s pose; circular point; rectangle; 3D reconstruction 摘 要: 提出种求解摄像机内参数及确定摄像机位置的线性方法. 首先通过空间平面上个非平行矩形 的图像来计算圆环点的图像, 进而由圆环点对摄像机内参数的约束方程标定摄像机内参数, 并给出此约束方 程具有惟解的充条件. 摄像机方位是通过计算图像与空间平面间的单矩阵来确定的. 外, 还给出在相 差个比子的情况下, 由拉盖尔定恢复矩形欧氏度信息的线性方法. 该方法的特点在于, 无知道矩形 的任何几何信息,不涉及图像匹配问题, 而且所有计算方法均是线性的. 大的模拟和真实图像实结果表明, 所给出的方法具有求解精度高、棒性强的优点. ∗ Supported by the National Natural Science Foundation of China under Grant Nos.60075004, 60033010, 69975021 (国家自然科学 基金); the National Grand Fundamental Research 973 Program of China under Grant No.G1998030502 (国家重点基础研究发展规划 (973)) 第一作者简介: 吴福朝(1957－),男,安徽安庆人,教授,博士生导师,主要研究领域为计算机视觉,人工智能.