# Learning Differential Invariants of Planar Curves

arXiv: https://arxiv.org/abs/2303.03458 · HTML: https://mlsanity.com/paper/2303.03458/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 17 references that are in the map.
- First posted on arXiv 6 Mar 2023.

## Builds on (most cited first, 3 of 3)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Deep Eikonal Solvers](https://mlsanity.com/paper/1903.07973/) (2019)
- [Learning Invariant Representations Of Planar Curves](https://mlsanity.com/paper/1611.07807/) (2016)

## 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 the 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 consistent 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 differential invariants. We evaluate our models qualitatively and quantitatively and propose a benchmark dataset to evaluate approximation models of differential invariants of planar curves.