Efficient Weingarten Map and Curvature Estimation on Manifolds

Yueqi Cao; Didong Li; Huafei Sun; Amir H Assadi; Shiqiang Zhang

doi:10.1007/s10994-021-05953-4

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arXiv · 1905.10725

Efficient Weingarten Map and Curvature Estimation on Manifolds

Yueqi Cao·Didong Li·Huafei Sun·Amir H Assadi·Shiqiang Zhang

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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.

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Yueqi Cao, Didong Li, Huafei Sun, Amir H Assadi, Shiqiang Zhang. 2020-09-07. Efficient Weingarten Map and Curvature Estimation on Manifolds. https://doi.org/10.1007/s10994-021-05953-4

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