针对传统张量投票算法在散乱点云特征提取过程中计算复杂、算法效率低等问题,提出了基于解析张量投票的散乱点云特征提取.首先,深入分析张量投票理论的基本思想,分析传统张量投票算法的不足及其根源.其次,设计了一种新的解析棒张量投票机制,实现了解析棒张量投票的直接求取,在此基础上,利用解析棒张量投票不依赖参考坐标系的特性,设计并求解了解析板张量投票和解析球张量投票表达式,而传统张量投票理论仅能通过迭代数值进行估算,过程复杂、效率低、精度与效率存在矛盾.然后,对解析张量投票后的散乱点云张量矩阵进行特征分解,根据特征显著性值实现特征提取.最后,通过仿真分析和对比实验验证了该算法在精度和计算效率方面的性能均优于传统张量投票算法,能够实现散乱点云的鲁棒特征提取.%A novel analytical tensor voting algorithm was proposed to reduce the complexity and heavy computational burden in traditional tensor voting for extracting featured points from unorganized point cloud. Firstly, basic thoughts of tensor voting theory were investigated, shortcomings and corresponding reasons were analyzed. Secondly, new voting mechanism for stick tensor was proposed and the analytical solution to proposed stick tensor voting mechanism was solved. Owing to the analytical stick tensor voting being independent of particular reference coordinates system, mechanisms for plate tensor voting and ball tensor voting were proposed and the analytical solutions were also solved. Thus, the problems of iterated numerical approximation, complicate computational process and the confliction between accuracy and efficiency in traditional tensor voting, which were caused by the lack of analytical solutions, were soundly solved. Then, the tensor of unorganized point cloud was decomposed. The feature points were extracted according to significance eigenvalue. At last, the correctness, accuracy and efficiency of the proposed algorithm were validated through simulated analysis and comparative experimental results, the proposed method can extract feature points from unorganized point cloud robustly.
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