SAMPLING ROTATION GROUPS BY SUCCESSIVE ORTHOGONAL IMAGES
SAMPLING ROTATION GROUPS BY SUCCESSIVE ORTHOGONAL IMAGES
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DOI：
10.1137/030601879
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发表时间：
2008-01-01
影响因子：
3.1
通讯作者：
Mitchell, Julie C.
中科院分区：
文献类型：
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作者：
Mitchell, Julie C.
在许多情况下，构造旋转群的统一确定性样本的能力是有用的，但存在固有的数学困难，阻碍了精确解的获得。在这里，我们提出了连续的正交图，这是正交群的均匀确定抽样的一种有效方法。该方法适用于任何维度，并给出了采样均匀性的解析界。对于SO(3)的特殊情况，给出了与其他抽样方法的数值比较。我们使用的非黎曼距离度量是群不变的，并且与Haar度量局部相容。此外，我们的结果还提供了将任何正交矩阵分解成平面旋转的乘积的半唯一分解。
The ability to construct uniform deterministic samples of rotation groups is useful in many contexts, but there are inherent mathematical difficulties that prevent an exact solution. Here, we present successive orthogonal images, an effective means for uniform deterministic sampling of orthogonal groups. The method is valid in any dimension, and analytical bounds are provided on the sampling uniformity. Numerical comparisons with other sampling methods are given for the special case of SO(3). We make use of non-Riemannian distance metrics that are group-invariant and locally compatible with the Haar measure. In addition, our results provide a semi-unique decomposition of any orthogonal matrix into the product of planar rotations.