关键词: 相机标定, 交比不变, 比例因子, 线性解析

Abstract: Aiming at the pinhole perspective projection model of radial distortion, a simple and fast camera calibration algorithm is proposed. This algorithm separates the internal and external parameters of the camera and the distortion parameters of the camera model on the premise that the image center point coincides with the center of the CCD or CMOS sensor, so that the camera calibration can be further linearly performed, which avoids errors caused by nonlinear optimization, reduces the algorithm complexity, appropriately improves the calibration accuracy, and saves the calculation time. Firstly, the lens distortion coefficient is calibrated according to the principle of cross-ratio invariance of perspective projection. Then, according to the rotation transformation relationship and translation transformation relationship, the internal and external parameters of the camera are solved linearly by making full use of the radial distortion constraint, the orthogonality of the rotation transformation and the unique properties of the rotation matrix. Finally, experiments show that, compared with the Tsai’s camera plane calibration algorithm, this algorithm  saves about 35% in calibration time and improves accuracy by at least 15%.

Key words: camera calibration, constant cross ratio, scale factor, linear analysis