一种立体像对极线矫正的新方法

A new rectification algorithm of epipolar lines on stereo-image pair

提出一种无相机标定的立体像对矫正算法,该算法只需要图像对间的匹配点信息.首先,寻找一个投影矩阵H′将右图的对极点e′映射到无穷远点,此时该图上的对极线被映射为平行于x轴的直线;然后,基于矫正后立体像对的对应极线相同的原理,推导出应用在左图上的矫正矩阵H;最后,根据得到的投影矩阵H和H′重新采样对应的图像,达到最终的矫正目的.尤其对摄像机对的角度进行分析,摄像机主轴夹角越小,对极点则离图像平面越远,矫正效果也越好.通过两种无需计算基本矩阵的非线性最优化矫正方法进行实验对比,实验结果表明,该算法实现简单、矫正速度快、并且有效地消除了垂直误差.

Propose a rectification algorithm base on a pair of stereo images without calibration of camer- as. This method only needs the matching points of image pair,and has three steps. First, find a projec- tion matrix H＇ which transform the epipole in right image to infinite point, and the epipolar lines of this image become parallel to the x axis. Then, base on the fact that corresponding epipolar lines in rectified image are identical, the corresponding projection matrix H is followed to rectify the left image. At last, each image is re-sampled with the projection matrix H and H＇ to achieve image rectification. Further- more, by studying the relative position of cameras, the authors find that, the smaller the angle of princi- pal axes of camera pairs is, the farer the distance between epipole and image plane is, and the better the rectification result is. According to the comparison with two typical rectification methods that use funda- mental matrix with nonlinear optimization theory, this algorithm is rapid to rectify, and effectively elim- inate the vertical errors.