# An inexact matching approach for the comparison of plane curves with general elastic metrics

arXiv: https://arxiv.org/abs/2001.02858 · HTML: https://mlsanity.com/paper/2001.02858/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2020.

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

- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)
- [VariGrad: A Novel Feature Vector Architecture for Geometric Deep Learning on Unregistered Data](https://mlsanity.com/paper/2307.03553/) (2023)

## Abstract (arXiv)

This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar curves. Our approach combines the general simplifying transform for first-order elastic metrics that was recently introduced by Kurtek and Needham, together with a relaxation of the matching constraint using parametrization-invariant fidelity metrics. The main advantages of this formulation are that it leads to a simple optimization problem for discretized curves, and that it provides a flexible approach to deal with noisy, inconsistent or corrupted data. These benefits are illustrated via a few preliminary numerical results.