Efficient Weingarten Map and Curvature Estimation on Manifolds
Machine Learning
2021-05-17 v2 Computer Vision and Pattern Recognition
Machine Learning
Differential Geometry
Abstract
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.
Cite
@article{arxiv.1905.10725,
title = {Efficient Weingarten Map and Curvature Estimation on Manifolds},
author = {Yueqi Cao and Didong Li and Huafei Sun and Amir H Assadi and Shiqiang Zhang},
journal= {arXiv preprint arXiv:1905.10725},
year = {2021}
}
Comments
23 pages, 8 figures