论文标题
迭代构成的移动框架方法：正交不变性
The moving frame method for iterated-integrals: orthogonal invariants
论文作者
论文摘要
对于诸如机器学习和图像分析等各种应用，欧几里得空间中曲线的几何特征，强大的噪声，曲线非常有趣。我们将Fels-Olver的移动框架方法（用于几何特征）与对数符号变换（用于健壮功能）配对，以构建一组整体不变式在$ \ Mathbb {r}^d $中的曲线下，从迭代 - 积分签名中构造。特别是我们表明，可以算法构建一组不变性，这些不变性表征在正交转换下截断的迭代迭代综合签名的等价类别，从而在$ \ mathbb {r}^d $中产生曲线在刚性运动（以及类似树状的扩展）和expecress andecress crudves crecrevers crecrevers crecrevers crecrevers中，以这些曲线的特征。
Geometric features, robust to noise, of curves in Euclidean space are of great interest for various applications such as machine learning and image analysis. We apply the Fels-Olver's moving frame method (for geometric features) paired with the log-signature transform (for robust features) to construct a set of integral invariants under rigid motions for curves in $\mathbb{R}^d$ from the iterated-integral signature. In particular we show that one can algorithmically construct a set of invariants that characterize the equivalence class of the truncated iterated-integrals signature under orthogonal transformations which yields a characterization of a curve in $\mathbb{R}^d$ under rigid motions (and tree-like extensions) and an explicit method to compare curves up to these transformations.
