Plane-Based Resection for Metric Affine Cameras
Plane-Based Resection for Metric Affine Cameras
复制标题
公制仿射相机的基于平面的切除
DOI：
10.1007/s10851-018-0794-0
复制
发表时间：
2018
影响因子：
2
通讯作者：
T. Collins
中科院分区：
文献类型：
--
作者：
A. Bartoli;T. Collins
研究了从至少三个非共线点对应中切除度量仿射摄像机模型的问题。一个直接的应用是平面姿态估计。我们认为三个最流行的度量仿射相机，即paraprospective，弱透视和正交相机。对于每个模型，我们给出了一个代数过程，找到最佳的解决方案，其中最佳的，我们的意思是全球最小的重投影误差下的欧几里德范数。我们的代数程序涵盖了最小的情况下，三个点和多余的情况下，超过三个点。他们总是返回两个解决方案，因为在一般情况下，该问题在三个相机的旋转和平移上具有双向模糊性。的paraprospective和弱透视相机的规模，然而，恢复独特。正字法的情况下是最复杂的，并没有得到解决的分析在文献中。我们表征其内在的复杂性表明，它减少到寻找根的不可约和不可解的根六次多项式。以前的算法paraprospective和弱透视的情况下有奇点，而相反，我们的代数程序没有。
We study the problem of resecting the metric affine camera models from at least three non-colinear point correspondences. A direct application is plane pose estimation. We consider the three most popular metric affine cameras, namely the paraperspective, weak-perspective and orthographic cameras. For each model, we give an algebraic procedure which finds the optimal solution, where by optimal we mean the global minimizer of the reprojection error under the Euclidean norm. Our algebraic procedures cover both the minimal case of three points and the redundant cases of more than three points. They always return two solutions, as the problem has a two-way ambiguity on the rotation and translation for the three cameras in the general case. The scale of the paraperspective and weak-perspective cameras is, however, recovered uniquely. The orthographic case is the most involved and has not been solved analytically in the literature. We characterize its intrinsic complexity by showing that it reduces to finding the roots of an irreducible and non-solvable by radicals sextic polynomial. The previous algorithms for the paraperspective and weak-perspective cases have singularities, while, in contrast, our algebraic procedures do not.