# Shape Analysis of Surfaces Using General Elastic Metrics

arXiv: https://arxiv.org/abs/1910.02045 · HTML: https://mlsanity.com/paper/1910.02045/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2019.

## Built on by (most cited first, 8 of 8)

- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)
- [A Riemannian Framework for Analysis of Human Body Surface](https://mlsanity.com/paper/2108.11449/) (2021)
- [Basis restricted elastic shape analysis on the space of unregistered surfaces](https://mlsanity.com/paper/2311.04382/) (2023)
- [Deep neural networks on diffeomorphism groups for optimal shape reparameterization](https://mlsanity.com/paper/2207.11141/) (2022)
- [Shape-Graph Matching Network (SGM-net): Registration for Statistical Shape Analysis](https://mlsanity.com/paper/2308.06869/) (2023)
- [A function space perspective on stochastic shape evolution](https://mlsanity.com/paper/2302.05382/) (2023)
- [Gaussian Differentially Private Human Faces Under a Face Radial Curve Representation](https://mlsanity.com/paper/2409.08301/) (2024)
- [Investigating Image Manifolds of 3D Objects: Learning, Shape Analysis, and Comparisons](https://mlsanity.com/paper/2503.06773/) (2025)

## Abstract (arXiv)

In this article we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the space of vector valued one-forms. We provide a numerical framework for the computation of geodesics with respect to these metrics. The family of metrics is invariant under rigid motions and reparametrizations; hence it induces a metric on the "shape space" of surfaces. This new class of metrics generalizes a previously studied family of elastic metrics and includes in particular the Square Root Normal Function (SRNF) metric, which has been proven successful in various applications. We demonstrate our framework by showing several examples of geodesics and compare our results with earlier results obtained from the SRNF framework.