Metrics for 3D Rotations: Comparison and Analysis
Metrics for 3D Rotations: Comparison and Analysis
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DOI：
10.1007/s10851-009-0161-2
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发表时间：
2009-10-01
影响因子：
2
通讯作者：
Huynh, Du Q.
中科院分区：
文献类型：
--
作者：
Huynh, Du Q.
3D旋转出现在许多计算机视觉，计算机图形学和机器人问题中，并且两个3D旋转之间的距离的评估通常是一项基本任务。本文详细分析了文献中提出的用于测量3D旋转之间距离的六个函数。基于三维旋转背后的成熟理论，我们证明了其中五个是SO（3）上的双不变度量，但只有四个是有界等价的。我们的结论是，它是空间和计算效率更高，使用四元数的三维旋转。最后，通过将两个旋转作为真实的和估计的旋转矩阵来处理，我们说明了与等误差测量相关的几何形状。
3D rotations arise in many computer vision, computer graphics, and robotics problems and evaluation of the distance between two 3D rotations is often an essential task. This paper presents a detailed analysis of six functions for measuring distance between 3D rotations that have been proposed in the literature. Based on the well-developed theory behind 3D rotations, we demonstrate that five of them are bi-invariant metrics on SO(3) but that only four of them are boundedly equivalent to each other. We conclude that it is both spatially and computationally more efficient to use quaternions for 3D rotations. Lastly, by treating the two rotations as a true and an estimated rotation matrix, we illustrate the geometry associated with iso-error measures.