A three-step camera calibration method

Abstract

Camera calibration is a crucial problem for many industrial applications that incorporate visual sensing. In this paper, we compute the intrinsic and extrinsic calibration parameters in three steps. In the first step, the calibration parameters are approximated using the linear least-squares method. In the second step, we develop two alternative formulations to obtain an optimal rotation matrix from the calibration parameters computed in the first step. Further optimization of translational and perspective transformations is then performed based on the optimized rotation matrix. In the third step, a nonlinear optimization is performed to handle lens distortion. The solution of the nonlinear system not only minimizes the perspective transformation relations between the image points and the corresponding world coordinates, but also satisfies the orthonormality constraints on the rotational transformation. To assess the performance of our proposed method, the Euclidean norm of the error matrix between the calculated and the original 4/spl times/4 homogeneous transformation matrices is used as a basis for comparison with existing methods. Simulation results from applying the method show significant improvements both before and after the nonlinear optimization step.