Efficient Weingarten map and curvature estimation on manifolds

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...

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Bibliographic Details
Published inMachine learning Vol. 110; no. 6; pp. 1319 - 1344
Main Authors Cao, Yueqi, Li, Didong, Sun, Huafei, Assadi, Amir H., Zhang, Shiqiang
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2021
Springer Nature B.V
Subjects
Artificial Intelligence
Asymptotic properties
Computer Science
Control
Convergence
Curvature
Euclidean geometry
Euclidean space
Machine Learning
Manifolds
Mechatronics
Natural Language Processing (NLP)
Robotics
Simulation and Modeling
Statistical models
Curvature estimation
Weingarten map
Point cloud data
Unsupervised learning
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0885-6125
1573-0565
DOI:10.1007/s10994-021-05953-4