Distortion correction method of a zoom lens based on the vanishing point geometric constraint

Abstract

In order to solve the problem that the distortion parameter of the zoom lens varies with focal length changes, a correction method for a zoom lens based on the minimum fitting error of a vanishing point geometric constraint is proposed. In light of a calibrated image with parallel line clusters without knowing the metric, the method can quickly correct the distortion of zoom lens in full focal length by the regression fitting of parameters. Firstly, based on the radial distortion division model, the functional relationship between the vanishing point and the radial distortion coefficient is established according to the geometric constraint of the vanishing point, and the first-order radial distortion coefficient of the camera is estimated by the Levenberg–Marquardt algorithm. And then, in terms of the principle of the deviation error minimization, the least squares can be used to fit the equation of straight line of the corrected points to optimize the center-of-distortion. Finally, the variation of distortion parameters with focal length is analyzed, the distortion parameter corresponding table between distortion parameters and focal length and the empirical formula of fitting are established. The results show that the root mean square error corrected by the fitting empirical formulas and the least squares support vector regression parameter corresponding table method for three different focal lengths are 1.16 pixels and 0.83 pixels, respectively. Moreover, those two ways are about 13% and 19% faster than Zhang’s method, respectively. By mapping this method to FPGA, the application effect of photographic UAV, security monitoring and other equipment requiring rapid response can be greatly improved.