The Moving-Frame Method for the Iterated-Integrals Signature: Orthogonal Invariants

Geometric, robust-to-noise features of curves in Euclidean space are of great interest for various applications such as machine learning and image analysis. We apply 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 [Formula omitted] from the iterated-integrals 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 [Formula omitted] under rigid motions (and tree-like extensions) and an explicit method to compare curves up to these transformations.
Author(s): Joscha Diehl [sup.1], Rosa Preiß [sup.2], Michael Ruddy [sup.3], Nikolas Tapia [sup.2] [sup.4] Author Affiliations: (1) grid.5603.0, Universität Greifswald, Institut für Mathematik und Informatik, , Walther-Rathenau-Str. 47, 17489, Greifswald, [...]