中文摘要：

针对现有的三维细化算法会出现断裂、不连续以及破坏物体原有的拓扑结构等问题，提出一种基于保拓扑结构和具有旋转不变性的新的三维细化算法．首先，自行设计和完善了具有各向同性的删除模板，使模板在各个方向上保持一致，保证了算法具有旋转不变性；其次，根据需要定义了真伪删除点，讨论提出的算法满足连续性保持的条件．通过假设验证法，检测候选删除点删除前后26邻域内目标体和背景组的数目变化，确认删除点的真伪，保持了原有的拓扑结构，进而确保物体旋转后细化结果的连续性不变．同时，在三维细化的基础之上，研究了基本尺寸、基准线和基准面等特征的提取方法，实现了三维非接触测量．实验结果表明：新的细化算法具有连通性保持不变，几何及拓扑性质保持不变，及旋转后细化结果保持不变的性质．

英文摘要：

Focusing on the problems that the results of the existing thinning algorithm failed to pre- serve the connectivity and destroyed the original topology structure, a novel thinning algorithm based on topology preservation and rotation invariance was proposed in this paper. First, isotropic deleting templates were designed. It made the template completely symmetrical in all directions and ensured the algorithm＇s rotation invariance. Secondly, the true and false deleting point was defined. And it was proved that the proposed algorithm could satisfy the continuity conditions. By the hypothesis tes- ting method, whether the number of objects and background components in its 26-neighborhood changed after all candidate deleting points deleted was detected, to confirm the true and false of the deleting point. It preserved the original topology structure, and ensured that the connectivity was un- changed after rotation. At the same time, on the basis of 3D thinning, the extraction methods of the basic size, baseline and datum feature were studied, then 3D non-contact measurement was realized. Experimental results show that the new method is able to preserve connectivity and topology struc- ture, and results are unchanged after rotation.