CAJ | 학술논문

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。
제출일충리산점운적Laplace산자적고계방법，이용리산화적분이급공간Voronoi도래구조랍보랍사산자。위사Voronoi도근사경가정학，고필재절공간투영생성Voronoi도시인입법향약속，상대우직접재절공간중구조Voronoi도，재절공간중생성적각향이성Voronoi도재근사정도상경가핍근우곡면류형상적Voronoi도。궤하려파、골가제취등실험결과표명，해리산Laplace‐Beltrami산자재국부특정적보지상효과경가명현，수렴속도경가신속。
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 re‐sults of experiments of geometry filtering and skeleton extraction show the better performance of the proposed operator in the preservation of local features and speed .