# Efficient Weingarten Map and Curvature Estimation on Manifolds

arXiv: https://arxiv.org/abs/1905.10725 · HTML: https://mlsanity.com/paper/1905.10725/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2019.

## Built on by (most cited first, 4 of 4)

- [Continuum Limits of Ollivier's Ricci Curvature on data clouds: pointwise consistency and global lower bounds](https://mlsanity.com/paper/2307.02378/) (2023)
- [Robust Estimation of Surface Curvature Information from Point Cloud Data](https://mlsanity.com/paper/2306.00299/) (2023)
- [Differentiable Topology Estimating from Curvatures for 3D Shapes](https://mlsanity.com/paper/2412.00140/) (2024)
- [Efficient Mean Curvature Computation on High-Dimensional Data Manifolds](https://mlsanity.com/paper/2606.06329/) (2026)

## Abstract (arXiv)

In this paper, we propose an efficient method to estimate the Weingarten map for point cloud data sampled from manifold embedded in Euclidean space. A statistical model is established to analyze the asymptotic property of the estimator. In particular, we show the convergence rate as the sample size tends to infinity. We verify the convergence rate through simulated data and apply the estimated Weingarten map to curvature estimation and point cloud simplification to multiple real data sets.