基于共面点直接线性变换的摄像机畸变校正

Camera Lens Distortion Correction Based on Coplanar Point Direct Liner Transformation

直接线性变换(DLT)是基于理想的透视变换模型,通过求解线性方程组得到二维(2D)图像坐标与三维(3D)世界坐标的映射关系矩阵,该方法具有求解简单、速度快等优点,但没有考虑透镜畸变的影响。为了达到既求解简单又能校正畸变的目的,在采用共面点线性求解的基础上充分考虑透镜畸变的影响,在根据摄像机的信息确定参数初值后,通过最小二乘优化算法修正变换矩阵及畸变系数,得到了最佳参数值,并采用不同位置分布的数据点对,验证了该方法标定的畸变系数具有相对独立性。最后,利用求得的畸变系数对摄像机获得的方格图像进行校正,校正后图像的变形有了明显的改善,证明了本方法的有效性。

The direct linear transformation （DLT） based on the ideal perspective transformation model can obtain the mapping matrix between the two-dimensional （2D） image coordinates and the three-dimensional （3D） coordinates by solving the linear equations. The method is simple and fast, but it does not take the effect of lens distortion into consideration. In order to correct the distortion in an easy way, this paper takes full account of the lens distortion on the basis of coplanar point linear solution. After initial parameters determined according to the camera information, transformation matrix and distortion coefficient are modified continuously by least-squares method to obtain the optimal parameters, and use data points pair of different location distribution to verify that the distortion coefficient calibrated by the method is relative independence. Finally, square image obtained by the camera was selected and corrected using the distortion coefficient gained by the above-mentioned method. The results have improved significantly and verified the validity of the method.