# Learning Invariant Representations Of Planar Curves

arXiv: https://arxiv.org/abs/1611.07807 · HTML: https://mlsanity.com/paper/1611.07807/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2016.

## Built on by (most cited first, 3 of 3)

- [Deep Signatures -- Learning Invariants of Planar Curves](https://mlsanity.com/paper/2202.05922/) (2022)
- [Learning Differential Invariants of Planar Curves](https://mlsanity.com/paper/2303.03458/) (2023)
- [Length Learning for Planar Euclidean Curves](https://mlsanity.com/paper/2102.01895/) (2021)

## Abstract (arXiv)

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural networks to compute these geometric quantities. In comparison with axiomatic constructions, we show that the invariants approximated by the learning architectures have better numerical qualities such as robustness to noise, resiliency to sampling, as well as the ability to adapt to occlusion and partiality. Finally, we develop a novel multi-scale representation in a similarity metric learning paradigm.