  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.
