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中文摘要：
基于全局点签名（GPS）和格林函数表示，提出了一种由粗到细的近似等距网格曲面模型间的稀疏点对应算法．针对构建点GPS表示的对应基向量问的符号不定问题，利用Morse理论和修改的层次聚类算法，提取源网格和近似等距目标网格上的关键点作为锚点，并结合符号的组合搜索策略，提出了一种基于GPS的锚点对应鲁棒算法；针对由于网格分辨率不同导致的高维GPS坐标不一致问题，结合前面确定的锚点对，定义了一种点的格林函数表示，并在此基础上提出一种增量式稀疏点对应算法．实验结果表明，与已有网格点对应算法相比，文中算法具有更高的计算效率和准确度，可应用于刚体和非刚体对齐以及三维变形、形状匹配等．
英文摘要：
Based on global point signature and Green＇s function representation, a coarse-to-fine sparse correspondence algorithm for nearly-isometric meshes is proposed in this paper. To address the problem of undetermined signs of the corresponding basis vectors, the anchor points are extracted from the source mesh and the nearly-isometric destination mesh respectively based on the Morse theory and a modified hierarchically clustering approach. Their correspondences are then established by minimizing their GPS distances, which can be solved via a combinational searching strategy. Second, to solve the inconsistent problem of high dimensional GPS coordinates caused by different resolutions of meshes, a new Green＇s function presentation of point is proposed based on the anchor point pairs obtained. As a result, the sparse correspondence of nearly-isometric meshes is established incrementally. Experimental results demonstrate the proposed algorithm exhibits better computational efficiency and correspondence accuracy than other shape correspondence algorithms. It can be potentially applied to rigid or non-rigid mesh alignment, 3D morphing, shape matching, etc.
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