Efficient Weingarten Map and Curvature Estimation on Manifolds
This work addresses a domain-specific problem in computational geometry and manifold learning, offering incremental improvements in efficiency for curvature estimation.
The paper tackles the problem of estimating the Weingarten map from point cloud data on manifolds, establishing a statistical model with proven convergence rates and applying it to curvature estimation and point cloud simplification on real datasets.
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.