Author:
Diehl Joscha,Preiß Rosa,Ruddy Michael,Tapia Nikolas
Abstract
AbstractGeometric, 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 $${\mathbb {R}}^d$$
R
d
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 $${\mathbb {R}}^d$$
R
d
under rigid motions (and tree-like extensions) and an explicit method to compare curves up to these transformations.
Funder
Weierstraß-Institut für Angewandte Analysis und Stochastik, Leibniz-Institut im Forschungsverbund Berlin e.V.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Computational Mathematics,Analysis
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