Feature Representation And Typical Applications Based On The Tensor Eigenvalue Analysis

Tensor mainly has two attractive research areas:tensor decomposition and the representation of tensor eigenvalue. Tensor is a natural representation of high dimensional data, which can ensure the internal structure of the data and has the absolute advantage of data mining and feature extraction. Images and video are the most common high-dimensional data, How to use tensor theory in image and video researches is a hot topic. This thesis mainly makes the following contributions:(1) A brief introduction of tensor’s two main analysis methods and a comprehensive introduction of the conception of gradient skewness tensor’s D eigenvalue and tensor’s Tucker decomposition are made firstly.(2) Based on the fact of a larger change of gradient at the edge of one image, this information of gradient difference can be used to combine the directional derivative of horizontal and vertical directions into a tensor presentation, which means gradient skewness tensor’s D eigenvalue facilitates the presentation of the image’s edge features. Simulations verify the effectiveness and accuracy of this method.(3) The concept is similar to radar range profile, this paper based on the gradient skewness tensor proposed the concept of skewness one-dimensional image.(4) According to the conception of tensor’s compact representation, in the area of the application of video compression, this paper proposes a multiple Tucker-ALS algorithm with the tensor’s Tucker decomposition. During the realization of video compression algorithm, several improvement are made as follows:every decomposition result is quantized and these quantized data are used to recovery tensor, then a tensor difference can be obtained, which is continued tensor decompose. This method can dramatically reduce the effect of quantization error; according to the specific video, each test sequence are chunked. Then more iterationis allocated to low-redundancy chunk and less to high-redundancy chunk; in view of the YUV video’s special format, the Y, U and V are compressed separately and using the property of high correlation between U and V, largely reduce the final data size. With the simulations of 9 group test sequences under the metric of BD-rate, the proposed method shows an improved performance compared with H.264, especially for the video which has the obvious textural features.