Abstract: This paper aims to resolve the problem of 3D shape correspondence under large deformation by isometry. Based on the proposed idea, the optimizing correspondence can be reduced to solve minimizing energy of Markov model. It initially aligns two shapes after performing spectral transformation. The spectral distance and geodesic distance are used to define potential energy and pairwise energy of Marko model respectively. In this way, the corresponding problem is reduced to solve an energy minimizing problem. There are many fast algorithms used to solve the problem. The final correspondence is obtained by alpha expansion. Experimental results show the proposed algorithm can output correct results under large deformation and topological changing. 

Key words: 3D shape correspondence, isometry, geodesic distance, spectral transformation, Markov model

摘要： 针对大尺度变形下的三维形状对齐问题，提出根据三维形状的等距性构造马尔可夫能量最小化模型，得到最优对齐结果。算法对三维模型进行谱变换，在变换空间中对三维模型进行初始化对齐。以谱距离和测地距离分别定义马尔可夫模型的单点势能函数和点对势能函数，形成可用于形状对齐的能量最小化模型。通过Alpha扩展算法对模型进行求解，得到最终的对齐结果。实验结果表明，算法在大尺度变形和拓扑变化等情况都能够输出很好的对齐结果。

关键词: 三维形状对齐, 等距性, 测地距离, 谱变换, 马尔可夫模型