由粗到精的三维等距模型对应关系计算

针对不同姿态下的三维等距模型对应关系计算问题，提出了一种基于初始谱植入的稠密对应关系计算方法。计算源模型与目标模型上各点的高斯曲率，利用空间一致采样算法获得一组数目相同的采样点，通过初始谱植入构建源模型与目标模型间的初始对应关系，使用空间一致采样法并结合二分图匹配算法迭代获取每一层的对应关系，利用贪婪优化算法进行优化，得到三维模型间的稠密对应关系。实验结果表明，以初始谱植入匹配算法计算得到的稀疏对应关系为基础，通过由粗到精的求解过程，能构建更为准确的稠密对应关系，并在一定程度上减小了等距误差。与已有算法相比，基于初始谱植入的稠密匹配算法适用于计算等距或近似等距的三维模型之间的对应关系；与单一使用测地距离度量相比，可以得到更加准确的稠密对应关系。

Coarse-to-fine calculation for 3D isometric shape correspondence

Aiming at the problem of three dimensional isometric shape correspondence under different posture, a dense correspondence calculation method based on initial spectral embedding is presented in this paper. Firstly, the Gaussian curvatures of vertices on source and target models are calculated respectively, and a set of sampling points are obtained by using the curvature-oriented evenly-spaced (COES) sampling algorithm. Secondly, the initial correspondence between the source and the target model is constructed by the initial spectral embedding matching algorithm. And then the COES sampling algorithm and the bipartite graph matching algorithm are applied to iteratively obtain corresponding relations of each layer. Finally, the greedy optimization algorithm is used to optimize resulting in obtaining dense correspondences between three dimensional models. The experimental results show that, based on the sparse correspondence calculated by an initial spectral embedding algorithm, a more accurate dense correspondence can be constructed through a coarse-to-fine method and the isometric error is reduced to a certain extent. Compared with the existing algorithms, the dense matching algorithm presented in this paper is applicable to calculate correspondences between 3D isometric or similar isometric models. Moreover, compared with the algorithms merely based on geodesic distance metric, the correspondences obtained by the initial spectral embedding are more accurate in this paper.