Tensor Spectral Pyramid for Color Video Sequences Representation, Based on 3D FO-AHKLT

Abstract

AbstractIn this work, new structure is proposed aimed at the representation of color video—a sequence of RGB frames. For this, each of the color components is first transformed into a tensor, and then these tensors are represented in the reduced vector space. To achieve this, is used the Two-Layer Tensor Spectrum Pyramid (2LTSP) based on the n-level 3D Frequency-Ordered Adaptive Hierarchical KLT (3D FO-AHKLT). The new approach ensures high energy concentration of the transformed tensor into a small number of spectrum coefficients, together with low computational complexity. The 3D FO-AHKLT execution comprises three consecutive stages. In each stage, the input tensor is transformed into a vector with various spatial orientation: horizontal, vertical or lateral (in time). The computational complexity of 2LTSP is evaluated and compared with that of H-Tucker and Tensor Train decompositions and the analysis shows that it decreases together with the vector size growth. In this work is also proved that the implementation of 2LTSP based on the 3D Adaptive Fast Walsh-Hadamard Transform results into additional significant reduction of the needed calculations. The main advantages of the presented pyramidal structure are its flexibility regarding the number of retained spectrum coefficients in the first and second decomposition levels, the lack of iterative calculations, and the computational complexity. All these qualities open new implementation possibilities in application areas aimed at the information redundancy reduction in color video sequences, the use of relatively small number of features needed for objects recognition, etc.KeywordsVideo tensor representationTwo-layer tensor spectrum pyramid3D frequency-ordered adaptive hierarchical KLTAdaptive directional vectorization