# Rotation invariants of two dimensional curves based on iterated integrals

arXiv: https://arxiv.org/abs/1305.6883 · HTML: https://mlsanity.com/paper/1305.6883/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2013.

## Built on by (most cited first, 2 of 2)

- [Logsig-RNN: a novel network for robust and efficient skeleton-based action recognition](https://mlsanity.com/paper/2110.13008/) (2021)
- [Deep Signature: Characterization of Large-Scale Molecular Dynamics](https://mlsanity.com/paper/2410.02847/) (2024)

## Abstract (arXiv)

We introduce a novel class of rotation invariants of two dimensional curves based on iterated integrals. The invariants we present are in some sense complete and we describe an algorithm to calculate them, giving explicit computations up to order six. We present an application to online (stroke-trajectory based) character recognition. This seems to be the first time in the literature that the use of iterated integrals of a curve is proposed for (invariant) feature extraction in machine learning applications.