基于分层策略的三维非刚性模型配准算法

在三维非刚性模型分析中，通常需要对不同姿态下的模型进行配准。针对传统配准算法存在复杂度高、计算量大、精确度低等问题，提出一种新的基于分层策略的三维非刚性模型配准算法。首先，定义热核签名函数为模型的标量域，使用同源聚类算法提取模型的特征点和特征区域，进而提出三维几何模型的树形表示方法:它的根节点为三维几何模型，内部节点为模型的特征区域，叶节点为包含在相应区域的特征点。然后，根据三维几何模型的树形表示提出模型的分层配准算法。在SHREC 2010模型配准数据集上对比分析了分层配准算法、推广的多维尺度变换算法（GMDS）和博弈论方法在等距变换、孔洞、小孔洞、尺度变换、局部尺度变换、重采样、噪声、散粒噪声以及拓扑变换等情况下的性能。实验结果表明，在以上三维几何模型数据受干扰的情况下，分层配准算法的准确性明显优于GMDS方法和博弈论方法，同时具有较低的计算复杂度。

Hierarchical approach for 3D non-rigid shape registration

Shape registration is a common task in non-rigid 3D shape analysis. In order to solve the problems of high complexity, large computation cost and low accuracy of the traditional algorithms, a new hierarchical shape registration method was proposed. Firstly, the heat kernel signature function was defined as the scalar field for a model, and persistence-based clustering was used to extract feature points and salient regions of the model. Then, a novel tree-based shape representation was proposed, whose root node, internal nodes and leaf nodes were defined as the model, the salient regions and the corresponding feature points, respectively. Finally, a new hierarchical shape registration method was designed to make full use of the tree-based shape representation. The hierarchical shape registration algorithm was tested on the SHREC 2010 correspondence dataset and compared with the Generalized Multi-Dimensional Scaling (GMDS) and game theory algorithms. Experimental results show that the proposed hierarchical shape registration method achieves higher accuracy than GMDS and game theory under various shape transformations, including isometric transformation, holes, micro holes, scaling, local scaling, resampling, noise, shot noise and topological transformation; in addition, the computational complexity is reduced significantly.