[1]孙海迅,罗健欣,潘志松,等.基于约束总体最小二乘的单应性矩阵求解方法[J].计算机技术与发展,2022,32(12):50-56.[doi:10. 3969 / j. issn. 1673-629X. 2022. 12. 008]
　SUN Hai-xun,LUO Jian-xin,PAN Zhi-song,et al.A Method for Solving Homography Matrix Based on Constrained Total Least Squares[J].,2022,32(12):50-56.[doi:10. 3969 / j. issn. 1673-629X. 2022. 12. 008]
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基于约束总体最小二乘的单应性矩阵求解方法()
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《计算机技术与发展》[ISSN:1006-6977/CN:61-1281/TN]

卷:
32
期数:
2022年12期
页码:
50-56
栏目:
媒体计算
出版日期:
2022-12-10

文章信息/Info

Title:
A Method for Solving Homography Matrix Based on Constrained Total Least Squares
文章编号:
1673-629X(2022)12-0050-07
作者:
孙海迅; 罗健欣; 潘志松; 张艳艳; 郑义桀
陆军工程大学 指挥控制工程学院,江苏 南京 210001
Author(s):
SUN Hai-xun; LUO Jian-xin; PAN Zhi-song; ZHANG Yan-yan; ZHENG Yi-jie
School of Command and Control Engineering,Army Engineering University of PLA,Nanjing 210001,China
关键词:
约束总体最小二乘; 单应性矩阵; 三维重建; 随机抽样一致性算法; 多视图几何
Keywords:
Constrained Total Least Squares;  homography matrix;  three - dimensional reconstruction;  random sample consensus( RANSAC) ; multi-view geometry
分类号:
TP391. 41
DOI:
10. 3969 / j. issn. 1673-629X. 2022. 12. 008
摘要:
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。
Abstract:
RANSAC ( Random Sample Consensus ) and Total Least Squares are used to solve homography matrix in multi - viewgeometry. The main function of RANSAC algorithm is to filter out the false matching points in the feature point pairs. At present,thereare many improved algorithms based on RANSAC that can achieve this goal better. When the noise is low,the system of equations con鄄structed by the Total Least Square method solving the correct matching points ( interior points) can be solved accurately,but when theinterior points generally have large noise, the Total Least Square method cannot meet the needs of solving accuracy. Based on theassumption that the interior pixel coordinates contain Gaussian noise and the correlation between the noise matrix columns,the equationform of solving the homography matrix is rederived,which is constructed as a Constrained Total Least Squares problem which is solvedand optimized. Compared with several other commonly used least squares methods on synthetic data and real images,the ConstrainedTotal Least Squares method is superior to the traditional Total Least Squares method in accuracy,as well as the Ordinary Least Squaresmethod and the Data Least Squares method commonly used in solving linear equations.
更新日期/Last Update: 2022-12-10