IEEE Trans Pattern Anal Mach Intell. 2005 Mar;27(3):434-449. doi: 10.1109/TPAMI.2005.62.
Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.
尽管从给定网格或规则采样点集估计曲率是一个已得到充分研究的问题，但当输入由因未对准误差和离群噪声而损坏的非结构化点云组成时，仍然具有挑战性。这种输入在计算机视觉中很常见。在本文中，我们提出了一种三通道张量投票算法，以稳健地估计曲率张量，从中可以计算出准确的主曲率和方向。我们的定量估计是对先前两通道算法的改进，后者仅进行定性曲率估计（高斯曲率的符号）。为了克服未对准误差，我们改进的方法以亚体素精度自动校正输入点位置，这也会剔除无法校正的离群点。为了在局部适应不同尺度，我们定义曲率张量的RadiusHit来量化估计精度和适用性。我们的曲率估计算法已通过详细的定量实验得到验证，在存在大量未对准噪声的情况下，在各种标准误差指标（曲率大小的百分比误差、曲率方向的绝对角度差）方面表现更好。
