This paper surveys and evaluates some popular state of the art methods for algorithmic curvature and normal estimation. In addition to surveying existing methods we also propose a new method for robust curvature estimation and evaluate it against existing methods thus demonstrating its superiority to existing methods in the case of significant data noise. Throughout this paper we are concerned with computation in low dimensional spaces (N < 10) and primarily focus on the computation of the Weingarten map and quantities that may be derived from this; however, the algorithms discussed are theoretically applicable in any dimension. One thing that is common to all these methods is their basis in an estimated graph structure. For any of these methods to work the local geometry of the manifold must be exploited; however, in the case of point cloud data it is often difficult to discover a robust manifold structure underlying the data, even in simple cases, which can greatly influence the results of these algorithms. We hope that in pushing these algorithms to their limits we are able to discover, and perhaps resolve, many major pitfalls that may affect potential users and future researchers hoping to improve these methods

翻译：本文综述并评估了当前主流的曲率与法向量估计算法。除系统梳理现有方法外，我们还提出了一种新型稳健曲率估计方法，并在显著数据噪声条件下与现有方法进行对比评估，证明了该方法相较于现有方法的优越性。本文重点关注低维空间（N<10）中的计算问题，主要研究Weingarten映射及其衍生量的计算方法；然而，文中讨论的算法在理论上适用于任意维度空间。所有方法的共同基础在于依赖估计的图结构。为实现这些方法，必须利用流形的局部几何特性；但面对点云数据时，即使对于简单情形，也难以发现数据底层稳健的流形结构，这将对算法结果产生重大影响。我们希望通过将这些算法推向极限，能够发现并可能解决影响潜在用户及未来研究者的诸多关键难题。