Determine Calibration Parameters with Satisfied Constraints for Coplanar Camera Calibration

Coplanar camera calibration is the process of determining a set of calibration parameters that describe the mapping between 2D control points and 2D image coordinates. However, the optimal solution for coplanar calibration can be obtained by solving a set of constrained optimization problem. This paper presents a technique to determine the calibration parameters for coplanar calibration, where a set of orthogonality constraints is fully satisfied. The solving of camera calibration consists of two steps. The first step is an estimating of calibration parameters using a closed form solution based on distortion free. In the second step, the parameters estimated in first step are iteratively improved by nonlinear optimization method, where the objective function is enforced to satisfy the constraints during optimization process. The computing of parameters is directly performed on computer image array by assuming that scale factor is equal to 1. Consequently, the image center can be simultaneously computed with the other parameters. The proposed technique is tested with a synthetic image that known distortion. The result shows that the proposed technique gives sufficient accuracy.