Real-time Background Subtraction via L1 Norm Tensor Decomposition

Currently, background subtraction is being actively studied in many image processing applications. Nuclear Norm Minimization (NNM) and Weighted Nuclear Norm Minimization (WNNM) are commonly used background subtraction methods based on Robust Principal Component Analysis (RPCA). However, these techniques approximate the RPCA rank function and take the form of an iterative optimization algorithm. Therefore, due to the approximation, the NNM solution can not converge if the number of frames is small. In addition, the NNM and WNNM processing times are delayed because of their iterative optimization schemes. Thus, NNM and WNNM are not suitable for real-time background subtraction. In order to overcome these limitations, this paper presents a real-time background subtraction method using tensor decomposition in accordance with the recent tensor analysis research trend. In this study, we used the closed form TUCKER2 decomposition solution to omit the iterative process while retaining the L1 norm of the RPCA rank function. This proposed method allows for convergence even when the number of frames is small. Compared to NNM and WNNM, the proposed method reduces the processing time by more than 80 times and has a higher precision even when the number of frames are less than 10.