Most computer vision applications, such as structure from motion and camera pose estimation, rely on the assumption of linear pinhole camera models. However, the pinhole assumption is invalid for most commercially available cameras, and distortion correction for digital cameras is necessary. Methods for distortion parameter estimation can be classified into three major categories: point correspondence-based methods, multi-view auto-calibration, and line-based methods. Point correspondence-based methods estimate the distortion parameters by using a known pattern such as a chessboard, and they are highly reliable and accurate in distortion parameter estimation. However, these methods have high requirements for working conditions. Multi-view auto-calibration aims to extract camera parameters automatically from a sequence of arbitrary natural images without any special pattern. The main limitation of the method is that it requires multiple images under camera motion, and it is inappropriate for fixed cameras and online distortion parameter estimation. In contrast to the point correspondence and auto-calibration methods, line-based methods estimate distortion parameters by using distorted straight lines from a single image or a small number of images and can achieve robust distortion parameter estimation. However, line-based methods require at least three or more distorted straight lines to estimate the distortion parameters. In our research, we find that two distorted straight lines can provide the constraints of distortion parameters, and the ranges of the distortion parameters can be determined via these constraints. Based on the above conditions, we present a novel method for distortion parameter estimation via two distorted straight lines, and experimental results demonstrate that the proposed method is robust and efficient in distortion parameter estimation and can be widely applied.

According to the property that the straight lines in three-dimensional (3D) space projected to the two-dimensional (2D) image plane do not change, an estimation method of lens distortion parameters based on two lines is presented in this study. Firstly, two distorted edges, which correspond to two straight lines, are used to derive the equation satisfied by the distortion parameters, and the ranges of the distortion parameters are determined using the size of the real image. Then an optimization objective function, which contains the distortion parameters, is constructed according to the fact that there are deviations between ideal straight lines and distorted straight lines, and the optimal distortion parameters are obtained using the enumerating-search method. The simulation and real experiments show that although the proposed method only uses two lines, it can accurately and effectively estimate the distortion parameters, which has obvious advantages compared with the mainstream methods.

The simulated grid images and real images are used to test the proposed method, and the following results can be obtained:

1) The proposed method is extremely accurate in distortion parameter estimation (Table 1 and Table 2), and it is applicable for correcting pincushion and barrel distortions (Fig. 3).

2) In order to ensure the reliability and accuracy of distortion parameter estimation, two distorted straight lines, which are far from the image center, should be selected to estimate the distortion parameters (Fig. 4 and Fig. 5).

3) The proposed method is robust with respect to varying noise levels from 0.1 to 1 pixel for simulated images, and it is better than the mainstream methods (Fig. 6).

4) The proposed method is accurate enough for correcting real distorted images (Fig. 7).

We propose a novel method based on two distorted straight lines to estimate the distortion parameters. This method works on a single image and does not require a special calibration pattern. Experimental results show that the proposed method is robust and accurate in distortion parameter estimation compared with the mainstream methods, and it is extremely useful in many applications such as self-driving and self-parking.