IEEE Trans Pattern Anal Mach Intell. 2011 Dec;33(12):2410-22. doi: 10.1109/TPAMI.2011.86. Epub 2011 May 12.
Simultaneous estimation of radial distortion, epipolar geometry, and relative camera pose can be formulated as a minimal problem and solved from a minimal number of image points. Finding the solution to this problem leads to solving a system of algebraic equations. In this paper, we provide two different solutions to the problem of estimating radial distortion and epipolar geometry from eight point correspondences in two images. Unlike previous algorithms which were able to solve the problem from nine correspondences only, we enforce the determinant of the fundamental matrix be zero. This leads to a system of eight quadratic and one cubic equation in nine variables. We first simplify this system by eliminating six of these variables and then solve the system by two alternative techniques. The first one is based on the Gröbner basis method and the second one on the polynomial eigenvalue computation. We demonstrate that our solutions are efficient, robust, and practical by experiments on synthetic and real data.
径向畸变、极线几何和相对相机姿态的同时估计可以被公式化为一个最小化问题，并从最少数量的图像点中求解。找到这个问题的解会导致求解一个代数方程组。在本文中，我们提供了两种不同的方法来从两幅图像中的八个点对应关系中估计径向畸变和极线几何。与之前只能从九个对应关系中解决问题的算法不同，我们强制基本矩阵的行列式为零。这导致了一个包含九个变量的八个二次方程和一个三次方程的系统。我们首先通过消去其中的六个变量来简化这个系统，然后通过两种替代技术来求解这个系统。第一种方法基于 Grobner 基方法，第二种方法基于多项式特征值计算。我们通过对合成数据和真实数据的实验证明了我们的解决方案是高效、鲁棒和实用的。
