Stable and efficient differential estimators on oriented point clouds
Stable and efficient differential estimators on oriented point clouds
复制标题
DOI：
10.1111/cgf.14368
复制
发表时间：
2021-08
影响因子：
2.5
通讯作者：
T. Lejemble;Nicolas Mellado
中科院分区：
文献类型：
--
作者：
T. Lejemble;Nicolas Mellado
点云现在在计算机图形和计算机视觉中无处不在。点采样曲面的微分特性（如主曲率）对于估计扫描形状的局部特征非常重要。为了从配备法向量的非结构化点近似表面，我们依赖于代数点集表面（APSS）[GG07]，我们为平均曲率估计器提供了收敛性和稳定性证明。使用积分不变的观点，这第一个贡献链接的代数球回归参与的APSS算法的几个表面衍生物不同的订单。作为第二个贡献，我们提出了一种分析方法来计算形状算子和它的主曲率从拟合代数球。我们将我们的方法与最先进的方法进行了比较，并在合成采样表面上进行了几次收敛性和鲁棒性测试。实验表明，我们的曲率估计是更准确和稳定的，同时计算速度比以前的方法。我们的差分估计器很容易实现，内存占用很少，只需要一个唯一的范围邻居查询每个估计。它的高度并行性使其适合处理大量采集的数据，正如我们在几个真实的世界实验中所展示的那样。
Point clouds are now ubiquitous in computer graphics and computer vision. Differential properties of the point‐sampled surface, such as principal curvatures, are important to estimate in order to locally characterize the scanned shape. To approximate the surface from unstructured points equipped with normal vectors, we rely on the Algebraic Point Set Surfaces (APSS) [GG07] for which we provide convergence and stability proofs for the mean curvature estimator. Using an integral invariant viewpoint, this first contribution links the algebraic sphere regression involved in the APSS algorithm to several surface derivatives of different orders. As a second contribution, we propose an analytic method to compute the shape operator and its principal curvatures from the fitted algebraic sphere. We compare our method to the state‐of‐the‐art with several convergence and robustness tests performed on a synthetic sampled surface. Experiments show that our curvature estimations are more accurate and stable while being faster to compute compared to previous methods. Our differential estimators are easy to implement with little memory footprint and only require a unique range neighbors query per estimation. Its highly parallelizable nature makes it appropriate for processing large acquired data, as we show in several real‐world experiments.