Abstract: This paper proposes a greedy optimal algorithm based on the initialization of spectral embedding of extreme points in order to calculate optimal correspondence between two given 3D isometric shapes after non-rigid transformation. Firstly, a group of sample points with same quantity and relatively consistent position are obtained by using FPS (farthest point sampling) algorithm based on Gaussian curvature. Then, an improved matching algorithm of spectral embedding is adopted to establish initial correspondence between the sampling point sets. Finally, sparse correspondence between isometric shapes is iteratively computed by a greedy optimal algorithm based on global metrics (geodesic distance). According to experimental results, the proposed algorithm can get robust sparse correspondence and improve the efficiency of the matching algorithm in a certain extent.

Key words: non-rigid transformation, extreme point, global metrics, sparse correspondence, greedy optimal algorithm

摘要： 针对非刚性变换后两个三维等距模型间的对应关系问题，提出了基于极点谱植入初始化的贪婪优化算法。首先运用基于高斯曲率的最远点采样算法，获得一组数目相同和位置相对一致的采样点；其次改进初始谱植入匹配算法建立两模型采样点集间的初始对应关系；最后使用基于全局度量（测地距离）的贪婪优化算法进行迭代优化，从而得到三维模型间的稀疏对应关系。实验结果表明，改进的非刚性匹配算法能够获得强健的稀疏对应关系，并在一定程度上提高了匹配算法的效率。

关键词: 非刚性变换, 极点, 全局度量, 稀疏对应关系, 贪婪优化算法