# Deep Signatures -- Learning Invariants of Planar Curves

arXiv: https://arxiv.org/abs/2202.05922 · HTML: https://mlsanity.com/paper/2202.05922/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 32 references that are in the map.
- First posted on arXiv 11 Feb 2022.

## Builds on (most cited first, 4 of 4)

- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Deep Eikonal Solvers](https://mlsanity.com/paper/1903.07973/) (2019)
- [Learning Invariant Representations Of Planar Curves](https://mlsanity.com/paper/1611.07807/) (2016)
- [Affine Differential Invariants for Invariant Feature Point Detection](https://mlsanity.com/paper/1803.01669/) (2018)

## Built on by (most cited first, 1 of 1)

- [Neural Descriptors: Self-Supervised Learning of Robust Local Surface Descriptors Using Polynomial Patches](https://mlsanity.com/paper/2503.03907/) (2025)

## Abstract (arXiv)

We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is shown to be a preferable alternative to axiomatic constructions. Specifically, we show that DNNs can learn to overcome instabilities and sampling artifacts and produce numerically-stable signatures for curves subject to a given group of transformations in the plane. We compare the proposed schemes to alternative state-of-the-art axiomatic constructions of group invariant arc-lengths and curvatures.