Abstract: 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.

Key words: tensor voting, unorganized point cloud, feature extraction, analytical solution