Tensor Voting Algorithm And Its Application

This paper mainly introduces a novel algorithm of data analysis, i.e. tensor voting. This algorithm makes full use of data, encodes and decodes them in terms of geometry according to the theories of tensor analysis, matrix and geometry. After setting up a rule for communicating information based on the Gestalt principles, we can infer some salient geometric structures. There are lots of advantages for this algorithm: it's local, robust to noise, noniterative, able to proceed large amounts of data, and able to represent all structure types simultaneously. The paper makes a detailed description of the algorithm in terms of mathematics, and generalizes it into higher dimensions.This algorithm is distinctive from those current popular image processing methods based on partial differential equations, and the difference can be seen in the Chapter 3 with regard to its applications in three aspects: 1.image denoising; 2.image segmentation; 3.image sequences. Image denoising takes advantage of the input data by tensor voting, which proves the efficiency of the algorithm. Though lots of work based on energy functional and partial differential equations before relate to the boundary inference in given images, this paper in another perspective obtains the same or even more precise equation by combining the saliency information which arises in the tensor voting. Because of the limited time, we do not supply multiple comparisons and analysis between the method and the previous ones. Finally, we do some experimental work about producing the transient image among a image sequence, which is not accurately solved in literature [23] but figured out partially in our method.