Estimating 3-D rigid body transformations: A comparison of four major algorithms
Estimating 3-D rigid body transformations: A comparison of four major algorithms
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DOI：
10.1007/s001380050048
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发表时间：
1997-01-01
影响因子：
3.3
通讯作者：
Fischer, RB
中科院分区：
文献类型：
--
作者：
Eggert, DW;Lorusso, A;Fischer, RB
机器视觉中的一个常见需求是计算3-D刚体变换，该变换将已知对应关系的两组点对齐。这里提出了一个比较分析的四个流行的和有效的算法，每一个计算的平移和旋转组件的转换在封闭的形式，作为解决方案的最小二乘制定的问题。它们在所使用的变换表示和解的数学推导方面不同，分别使用基于标准[R，T]表示的奇异值分解或特征系统计算，以及从变换的单位和对偶四元数形式导出的矩阵的特征系统分析。这种比较呈现了几个实验的定性和定量结果，这些实验旨在确定（1）存在不同水平噪声时每种算法的准确性和鲁棒性，（2）相对于退化数据集的稳定性，以及（3）不同条件下每种方法的相对计算时间。结果表明，在“理想”的数据条件下（无噪声），可以看出在精度和稳定性方面的某些区别。但是对于“典型的真实的世界”噪声水平，最终解的鲁棒性没有差异（与某些先前发表的结果相反）。效率，在执行时间方面，被发现是高度依赖于计算机系统的设置。
A common need in machine vision is to compute the 3-D rigid body transformation that aligns two sets of points for which correspondence is known. A comparative analysis is presented here of four popular and efficient algorithms, each of which computes the translational and rotational components of the transform in closed form, as the solution to a least squares formulation of the problem. They differ in terms of the transformation representation used and the mathematical derivation of the solution, using respectively singular value decomposition or eigensystem computation based on the standard [R, T] representation, and the eigensystem analysis of matrices derived from unit and dual quaternion forms of the transform. This comparison presents both qualitative and quantitative results of several experiments designed to determine (1) the accuracy and robustness of each algorithm in the presence of different levels of noise, (2) the stability with respect to degenerate data sets, and (3) relative computation time of each approach under different conditions. The results indicate that under ''ideal'' data conditions (no noise) certain distinctions in accuracy and stability can be seen. But for ''typical, real world'' noise levels, there is no difference in the robustness of the final solutions (contrary to certain previously published results). Efficiency, in terms of execution time, is found to be highly dependent on the computer system setup.