# Elastic analysis of irregularly or sparsely sampled curves

arXiv: https://arxiv.org/abs/2104.11039 · HTML: https://mlsanity.com/paper/2104.11039/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2021.

## Built on by (most cited first, 6 of 6)

- [Uncertainty quantification in metric spaces](https://mlsanity.com/paper/2405.05110/) (2024)
- [Nonparametric Multi-shape Modeling with Uncertainty Quantification](https://mlsanity.com/paper/2206.09127/) (2022)
- [Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces](https://mlsanity.com/paper/2507.15741/) (2025)
- [A geometric framework for outlier detection in high-dimensional data](https://mlsanity.com/paper/2207.00367/) (2022)
- [Classification ensembles for multivariate functional data with application to mouse movements in web surveys](https://mlsanity.com/paper/2205.13380/) (2022)
- [Deep Shape Regression for Planar Curves with Multimodal Covariates](https://mlsanity.com/paper/2607.19600/) (2026)

## Abstract (arXiv)

We provide statistical analysis methods for samples of curves when the image but not the parametrisation of the curves is of interest. A parametrisation invariant analysis can be based on the elastic distance of the curves modulo warping, but existing methods have limitations in common realistic settings where curves are irregularly and potentially sparsely observed. We provide methods and algorithms to approximate the elastic distance for such curves via interpreting them as polygons. Moreover, we propose to use spline curves for modelling smooth or polygonal Fr'echet means of open or closed curves with respect to the elastic distance and show identifiability of the spline model modulo warping. We illustrate the use of our methods for elastic mean and distance computation by application to two datasets. The first application clusters sparsely sampled GPS tracks based on the elastic distance and computes smooth means for each cluster to find new paths on Tempelhof field in Berlin. The second classifies irregularly sampled handwritten spirals of Parkinson's patients and controls based on the elastic distance to a mean spiral curve computed using our approach. All developed methods are implemented in the textttR-package textttelasdics and evaluated in simulations.