Lens distortion

which is a fundamental problem in photogrammetry and computer vision

has serious effects on the three-dimensional reconstruction and on the geometric image measurements. In this paper

an automatic correction of weak radial distortions based on vanishing points from a single image is presented. In order to reduce the effects caused by the nonlinear model included in the distortion center

the distortion center is further optimized after the radial distortion is estimated. A nonlinear model of vanishing points and radial distortion

which can be estimated by the Levenberg-Marquardt (LM) algorithms

is established based on the geometric constraint of vanishing points;then

the distortion center and radial distortion is optimized by an iterative method based on a suitable quality measurement. At last

the presented method is tested and verified. The radial distortions using different data are all effectively corrected. Compared with the traditional methods based on non-metric distortion correction

the results of camera calibration after correction are significantly improved. The results of our experiments indicate that the approach can effectively correct radial lens distortion

while effectively overcome the instability of the traditional methods based on non-metric distortion correction.