IEEE Trans Vis Comput Graph. 2011 Jun;17(6):743-56. doi: 10.1109/TVCG.2010.261. Epub 2010 Dec 17.
We present an efficient and robust method for extracting curvature information, sharp features, and normal directions of a piecewise smooth surface from its point cloud sampling in a unified framework. Our method is integral in nature and uses convolved covariance matrices of Voronoi cells of the point cloud which makes it provably robust in the presence of noise. We show that these matrices contain information related to curvature in the smooth parts of the surface, and information about the directions and angles of sharp edges around the features of a piecewise-smooth surface. Our method is applicable in both two and three dimensions, and can be easily parallelized, making it possible to process arbitrarily large point clouds, which was a challenge for Voronoi-based methods. In addition, we describe a Monte-Carlo version of our method, which is applicable in any dimension. We illustrate the correctness of both principal curvature information and feature extraction in the presence of varying levels of noise and sampling density on a variety of models. As a sample application, we use our feature detection method to segment point cloud samplings of piecewise-smooth surfaces.
我们提出了一种从点云采样中提取分片光滑表面曲率信息、锐利特征和法向方向的高效、鲁棒方法，该方法在统一框架内具有积分性质，并使用点云 Voronoi 单元格的卷积协方差矩阵，使其在存在噪声时具有可证明的鲁棒性。我们表明，这些矩阵包含与表面光滑部分曲率相关的信息，以及有关分片光滑表面特征周围锐边方向和角度的信息。我们的方法适用于二维和三维，并且可以轻松并行化，从而可以处理任意大的点云，这是基于 Voronoi 的方法的一个挑战。此外，我们还描述了我们的方法的蒙特卡罗版本，该版本适用于任何维度。我们在各种模型上展示了在不同噪声水平和采样密度下的主曲率信息和特征提取的正确性。作为一个示例应用，我们使用我们的特征检测方法对点云采样的分片光滑表面进行分割。
