Torr P H S, Fitzgibbon A W
School of Mathematics and Computing, Oxford Brookes University, Wheatley, Oxford OX33 1HX, UK.
IEEE Trans Pattern Anal Mach Intell. 2004 May;26(5):648-50. doi: 10.1109/tpami.2004.1273967.
This paper describes an extension of Bookstein's and Sampson's methods, for fitting conics, to the determination of epipolar geometry, both in the calibrated case, where the Essential matrix E is to be determined or in the uncalibrated case, where we seek the fundamental matrix F. We desire that the fitting of the relation be invariant to Euclidean transformations of the image, and show that there is only one suitable normalization of the coefficients and that this normalization gives rise to a quadratic form allowing eigenvector methods to be used to find E or F, or an arbitrary homography H. The resulting method has the advantage that it exhibits the improved stability of previous methods for estimating the epipolar geometry, such as the preconditioning method of Hartley, while also being invariant to equiform transformations.
本文描述了将Bookstein和Sampson用于拟合圆锥曲线的方法扩展到极线几何的确定，包括校准情况下确定本质矩阵E，以及未校准情况下寻找基础矩阵F。我们希望关系的拟合对于图像的欧几里得变换是不变的，并表明系数只有一种合适的归一化方式，且这种归一化会产生一个二次型，允许使用特征向量方法来找到E或F，或任意单应性矩阵H。所得方法的优点是，它展现出了如Hartley的预处理方法等先前估计极线几何方法所具有的更高稳定性，同时对于等形变换也是不变的。
