基于Laplace-Beltrami算子特征向量的三维模型特征点检测与分析

3D Feature Point Detection and Analysis Using the Eigenvectors of Laplace-Beltrami Operator

针对三维模型的特征点检测问题,提出一种基于Laplace-Beltrami算子的特征点检测算法.对于给定的三维网格模型,首先构造离散Laplace-Beltrami算子矩阵,求解特征值与特征向量,随后在不同频率的特征向量上检测局部极值点和鞍点,最后通过基于特征值的加权公式把检测结果结合起来,实现对特征点不同显著度的可视化.实验对选取自SHREC2010数据集的三维网格模型进行特征点检测,在VS2013平台上使用OpenGL进行可视化.结果表明,文中算法在三维网格模型上取得准确的检测结果,在高噪声的模型上具有鲁棒性,对等距模型能得到高度相似的结果,并且能通过分布式计算处理大尺寸的三维模型.

Aiming at the feature point detection problem of 3D models, we propose a novel feature point detection algorithm based on the Laplace-Beltrami operator. For a given 3 D mesh model, firstly the discrete Laplace-Beltrami operator is constructed, and its eigenvalues and eigenvectors are calculated. Then the local extremum and saddle points of the eigenvectors are detected and blended using the weighted formula based on the eigenvalues. Experimental models are selected from SHREC2010, and the feature points are visualized using OpenGL on VS2013. The experimental results demonstrate that our method gets ideal detection results, is applicable to models with noise, and obtains highly similar detection results on isometric models and can process large-scale data through the distributed computing.