Accurate Camera Calibration and Correction Using Rigidity and Radial Alignment Constraints

In this paper, we develop a novel method for camera calibration and correction. The novel method first employs a rigidity constraint from the rigid rotation matrix and the radial alignment constraint from the pin-hole camera model to estimate both camera intrinsic and extrinsic parameters with a closed-form solution without considering the camera distortion. Then the well-known Levernburg-Marquardt (LM) algorithm is employed to optimize the parameters of interest in two steps: the first step optimizes the first order radial distortion coefficient and the z component of the camera position using a partial image formation model, and the second step optimizes all the parameters of interest using a complete image formation model: 4 intrinsic, 7 extrinsic and 4 distortion parameters. The LM algorithm is initialised either as the parameters estimated so far or as zero. The optimization is achieved through minimising the sum of the squared differences between the distorted projected 3D world control points and their given corresponding distorted image points. The distorted points are finally corrected using again the LM algorithm initialized by the distorted image points themselves, minimizing the squared difference between the distorted corrected point and the given distorted image point. The experimental results based on both synthetic data and real images show that the proposed algorithm produces promising camera calibration and correction results. Index Terms−3D imaging; camera calibration, distortion, and correction