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摘要: 针对传统张量投票(Tensor voting)算法计算过程复杂、算法效率低的问题, 本文提出了一种二维解析张量投票算法.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, 设计了一种二维解析棒张量投票新机制, 实现了二维解析棒张量投票的直接求取; 在此基础上, 利用二维解析棒张量投票不依赖参考坐标系的特性, 设计并求解了二维解析球张量投票表达式, 解决了长期困扰张量投票理论中球张量投票无法解析求解, 仅能通过迭代数值计算, 计算过程复杂、算法效率低、算法精度与算法效率存在矛盾的难题.最后, 通过仿真分析和对比实验验证了本文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.Abstract: A novel 2D analytical tensor voting algorithm is proposed to reduce the complexity and heavy computational burden in traditional tensor voting. Firstly, basic thoughts of tensor voting theory are investigated, and shortcomings and corresponding reasons are analyzed. Secondly, a new voting mechanism for 2D stick tensor is proposed and an analytical solution to the proposed 2D stick tensor voting mechanism is presented. Owing to the analytical 2D stick tensor voting being independent of the particular reference coordinate system, the mechanism for 2D ball tensor voting is proposed and the analytical solution is also provided. Thus, the problems of iterated numerical approximation, complicate computational process and the confliction between accuracy and efficiency in traditional 2D tensor voting, all caused by lack of analytical solutions, are soundly solved. At last, the correctness, accuracy and efficiency of the proposed algorithm are validated through simulated analysis and comparative experimental results.
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Key words:
- Tensor voting /
- structure inference /
- analytical solution /
- feature extraction
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图 4 传统张量投票中的衰减函数特性
Fig. 4 Demonstration of decay function in traditional tensor voting
图 5 任意两点间棒张量投票坐标变换示意图
Fig. 5 Illustration of stick voting coordinate transformation between any two points
图 12 二维棒张量投票运行时间对比实验结果
Fig. 12 Running time comparison between 2D stick tensor voting method
图 13 二维球张量投票运行时间对比实验结果
Fig. 13 Running time comparison between 2D ball tensor voting method
图 15 本文算法用于灰度图像结构推理
Fig. 15 Utilization of the proposed method in structure inference of gray scale image
表 1 算法运行时间比较
Table 1 Running time comparison between the methods
投票 棒投票时间(ms) 球投票时间(ms) 点数 传统方法 本文方法 传统方法 本文方法 4 225 9.123 3.775 222.619 1.549 6 241 11.820 6.137 292.801 2.273 16 641 36.184 13.621 979.026 7.407 
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