基于离散流形调和基的保特征谱几何处理方法

Approach of feature-preserving spectral geometry processing with discrete manifold harmonic bases

提出一种离散点云的Laplace算子的估计方法,利用离散化积分以及空间Voronoi图来构造拉普拉斯算子。为使Voronoi图近似更加精确,考虑在切空间投影生成Voronoi图时引入法向约束,相对于直接在切空间中构造Voronoi图,在切空间中生成的各向异性Voronoi图在近似精度上更加逼近于曲面流形上的Voronoi图。几何滤波、骨架提取等实验结果表明,该离散Laplace-Beltrami算子在局部特征的保持上效果更加明显,收敛速度更加迅速。

An approximation of Laplace-Beltrami operator for point clouds by discretizing integration was proposed.To improve the accuracy of the approximation,a normal constraint was introduced to control the projection on tangent spaces.As a result,the anisotropic Voronoi diagram acted better than the one directly constructed on tangent spaces in the terms of accuracy.The results of experiments of geometry filtering and skeleton extraction show the better performance of the proposed operator in the preservation of local features and speed.