Closed-Form Solution of Principal Line for Camera Calibration Based on Orthogonal Vanishing Points

Vanishing point is an important geometric element in sports video. In this paper, a new calibration algorithm is proposed by using the algebraic and geometric properties of vanishing points, which resolves the three main problems of the traditional camera calibration technology based on vanishing points: (1) calibrating camera with varied focal length; (2) screening out outliers from a set of images; (3) estimation of distortion coefficients. The principal line passes through the principal point, and the algebraic relationship between it and the vanishing points is deduced. Using the geometry feature of the principal line, problems (1) and (2) can be easily solved. The linear relationship between the point and the line is used to estimate the distortion coefficient under the condition of obtaining the principal point. Simulation and real experiments show the validity and robustness of the proposed algorithm, and satisfactory results can be obtained by solving the above three problems.