基于约束总体最小二乘的单应性矩阵求解方法

A Method for Solving Homography Matrix Based on Constrained Total Least Squares

在多视图几何中,单应性矩阵的求解常采用RANSAC(随机采样一致性算法)与总体最小二乘相结合的方法。RANSAC算法的主要作用是滤除特征点对中的误匹配点,当前已有多种基于RANSAC的改进算法能较好地实现这一目标。用总体最小二乘法求解正确匹配点(内点)所构建的方程组,在噪声较小时能求解准确,但在内点普遍具有较大噪声时,总体最小二乘法已不能满足求解精度的需要。从内点像素坐标上含有高斯噪声这一基本假设出发,考虑到噪声矩阵列之间的相关关系,重新推导了求解单应性矩阵的方程形式,将其构造为约束总体最小二乘问题,并优化求解。在合成数据和真实图像上与其他几种常用的最小二乘法作对比实验,结果表明,约束总体最小二乘法在精度上优于传统的总体最小二乘法,以及线性方程组求解中常用的普通最小二乘法和数据最小二乘法。

RANSAC(Random Sample Consensus)and Total Least Squares are used to solve homography matrix in multi-view geometry.The main function of RANSAC algorithm is to filter out the false matching points in the feature point pairs.At present,there are many improved algorithms based on RANSAC that can achieve this goal better.When the noise is low,the system of equations constructed by the Total Least Square method solving the correct matching points(interior points)can be solved accurately,but when the interior points generally have large noise,the Total Least Square method cannot meet the needs of solving accuracy.Based on the assumption that the interior pixel coordinates contain Gaussian noise and the correlation between the noise matrix columns,the equation form of solving the homography matrix is rederived,which is constructed as a Constrained Total Least Squares problem which is solved and optimized.Compared with several other commonly used least squares methods on synthetic data and real images,the Constrained Total Least Squares method is superior to the traditional Total Least Squares method in accuracy,as well as the Ordinary Least Squares method and the Data Least Squares method commonly used in solving linear equations.