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An Efficient Hidden Variable Approach to Minimal-Case Camera Motion Estimation

机译:一种有效的隐式变量最小摄像机运动估计方法

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摘要

In this paper, we present an efficient new approach for solving two-view minimal-case problems in camera motion estimation, most notably the so-called five-point relative orientation problem and the six-point focal-length problem. Our approach is based on the hidden variable technique used in solving multivariate polynomial systems. The resulting algorithm is conceptually simple, which involves a relaxation which replaces monomials in all but one of the variables to reduce the problem to the solution of sets of linear equations, as well as solving a polynomial eigenvalue problem (polyeig). To efficiently find the polynomial eigenvalues, we make novel use of several numeric techniques, which include quotient-free Gaussian elimination, Levinson-Durbin iteration, and also a dedicated root-polishing procedure. We have tested the approach on different minimal cases and extensions, with satisfactory results obtained. Both the executables and source codes of the proposed algorithms are made freely downloadable.
机译:在本文中,我们提出了一种有效的新方法来解决相机运动估计中的两视图最小情况问题,最著名的是所谓的五点相对取向问题和六点焦距问题。我们的方法基于用于求解多元多项式系统的隐藏变量技术。所得的算法在概念上很简单,其中涉及一种松弛,该松弛可替换除一个变量之外的所有变量中的单项式,以将问题简化为一组线性方程组的求解,以及求解多项式特征值问题(polyeig)。为了有效地找到多项式特征值,我们新颖地使用了多种数值技术,其中包括无商高斯消元,Levinson-Durbin迭代以及专用的根抛光程序。我们已经在不同的最小案例和扩展上测试了该方法,并获得了令人满意的结果。所提出算法的可执行文件和源代码均可免费下载。

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