Papers › The moving frame method for iterated-integrals: orthogonal invariants
The moving frame method for iterated-integrals: orthogonal invariants
Joscha Diehl, Rosa Preiß, Michael Ruddy, Nikolas Tapia
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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 ℝᵈ 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 ℝᵈ under rigid motions (and tree-like extensions) and an explicit method to compare curves up to these transformations.
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