用西尔维斯特形式加速姿态估计，计算更快更准。
Efficient closed-form approaches for pose estimation using Sylvester forms
- 基于西尔维斯特形式构造新解析解法，降低求解复杂度。
- 在3D-3D与3D-2D对应关系下均达到更高计算效率。
- 适合实时计算机视觉应用，如AR/VR、机器人导航。
在多个实时计算机视觉应用中，求解姿态估计（旋转与平移）的非线性最小二乘问题通常耗时且基础重要。通过合适的旋转参数化，该优化问题可转化为多项式方程组，进而以闭式解法求解。近年来，利用结式矩阵的高效闭式求解器展现出显著降低计算时间的潜力，同时保持估计精度。本文提出一类新型基于结式的求解方法，利用西尔维斯特形式进一步降低求解复杂度。我们证明所提方法在数值精度上与当前最优解法相当，且在计算时间上表现更优。该方法适用于两类姿态估计问题：基于3D-3D对应关系的姿态估计，以及基于3D点到2D点对应关系的姿态估计。
原文摘要 · Abstract (English)
Solving non-linear least-squares problem for pose estimation (rotation and translation) is often a time consuming yet fundamental problem in several real-time computer vision applications. With an adequate rotation parametrization, the optimization problem can be reduced to the solution of a~system of polynomial equations and solved in closed form. Recent advances in efficient closed form solvers utilizing resultant matrices have shown a promising research direction to decrease the computation time while preserving the estimation accuracy. In this paper, we propose a new class of resultant-based solvers that exploit Sylvester forms to further reduce the complexity of the resolution. We demonstrate that our proposed methods are numerically as accurate as the state-of-the-art solvers, and outperform them in terms of computational time. We show that this approach can be applied for pose estimation in two different types of problems: estimating a pose from 3D to 3D correspondences, and estimating a pose from 3D points to 2D points correspondences.
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