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.

中文翻译：

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流形上的有效Weingarten映射和曲率估计

在本文中，我们提出了一种有效的方法，用于估计从欧氏空间中嵌入的流形采样的点云数据的Weingarten映射。建立统计模型以分析估计量的渐近性质。特别是，随着样本量趋于无穷大，我们显示了收敛速度。我们通过模拟数据验证收敛速度，并将估计的Weingarten映射应用于曲率估计，并将点云简化应用于多个真实数据集。