A Tighter Relaxation for the Relative Pose Problem Between Cameras
A Tighter Relaxation for the Relative Pose Problem Between Cameras
复制标题
相机间相对位姿问题的更严格松弛
DOI：
10.1007/s10851-022-01085-z
复制
发表时间：
2022
影响因子：
2
通讯作者：
J. Gonzalez
中科院分区：
文献类型：
--
作者：
Mercedes Garcia;Jesus Briales;J. Gonzalez
This paper tackles the resolution of the Relative Pose problem with optimality guarantees by stating it as an optimization problem over the set of essential matrices that minimizes the squared epipolar error. We relax this non-convex problem with its Shor’s relaxation, a convex program that can be solved by off-the-shelf tools. We follow the empirical observation that redundant but independent constraints tighten the relaxation. For that, we leverage equivalent definitions of the set of essential matrices based on the translation vectors between the cameras. Overconstrained characterizations of the set of essential matrices are derived by the combination of these definitions. Through extensive experiments on synthetic and real data, our proposal is empirically proved to remain tight and to require only 7 milliseconds to be solved even for the overconstrained formulations, finding the optimal solution under a wide variety of configurations, including highly noisy data and outliers. The solver cannot certify the solution only in very extreme cases,e.g.noise \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$100~{\texttt {pix}} $$\end{document} and number of pair-wise correspondences under 15. The proposal is thus faster than other overconstrained formulations while being faster than the minimal ones, making it suitable for real-world applications that require optimality certification.
This paper tackles the resolution of the Relative Pose problem with optimality guarantees by stating it as an optimization problem over the set of essential matrices that minimizes the squared epipolar error. We relax this non-convex problem with its Shor’s relaxation, a convex program that can be solved by off-the-shelf tools. We follow the empirical observation that redundant but independent constraints tighten the relaxation. For that, we leverage equivalent definitions of the set of essential matrices based on the translation vectors between the cameras. Overconstrained characterizations of the set of essential matrices are derived by the combination of these definitions. Through extensive experiments on synthetic and real data, our proposal is empirically proved to remain tight and to require only 7 milliseconds to be solved even for the overconstrained formulations, finding the optimal solution under a wide variety of configurations, including highly noisy data and outliers. The solver cannot certify the solution only in very extreme cases,e.g.noise \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$100~{\texttt {pix}} $$\end{document} and number of pair-wise correspondences under 15. The proposal is thus faster than other overconstrained formulations while being faster than the minimal ones, making it suitable for real-world applications that require optimality certification.
DOI：
10.1007/978-1-4614-0769-0_24
发表时间：
2012
期刊：
--
影响因子：
--
作者：
M. Yamashita;K. Fujisawa;Mituhiro Fukuda;Kazuhiro Kobayashi;K. Nakata;Maho Nakata
通讯作者：
M. Yamashita;K. Fujisawa;Mituhiro Fukuda;Kazuhiro Kobayashi;K. Nakata;Maho Nakata
DOI：
10.1007/11744023_32
发表时间：
2006-01-01
期刊：
COMPUTER VISION - ECCV 2006 , PT 1, PROCEEDINGS
影响因子：
--
作者：
Bay, Herbert;Tuytelaars, Tinne;Van Gool, Luc
通讯作者：
Van Gool, Luc