ABSTRACT

In the paper, we derive Procrustes-based closed-form solutions to the point-wise weighted rigid-body transformation under different adjustment scenarios. We treat both asymmetric and symmetric cases. By asymmetric (or Gauss–Markov) models we mean those in which either a source system or a target system is subject to random errors. On the other hand, by the symmetric model (Gauss-Helmert or errors-in-variables) we mean the one in which points of both coordinate systems are considered erroneous. The solutions are universal in the sense that they fit both 2D and 3D transformation cases without modifications of computational algorithms. Presented results are also attractive because the solutions require neither linearisation nor iteration.

摘要

在论文中，我们推导出了不同调整场景下逐点加权刚体变换的基于 Procrustes 的封闭形式解。我们处理非对称和对称情况。非对称（或高斯-马尔可夫）模型是指源系统或目标系统受随机误差影响的模型。另一方面，对称模型（Gauss-Helmert 或errors-in-variables）是指两个坐标系的点都被认为是错误的。这些解决方案是通用的，因为它们适合 2D 和 3D 转换情况，而无需修改计算算法。呈现的结果也很有吸引力，因为解决方案既不需要线性化也不需要迭代。