Research On Background Subtraction Via Low-rank Matrix Recovery Algorithm

Background subtraction,separating the foreground in the video frame sequence from the background,is an important field in video analysis.It can be used in various visual tasks such as video surveillance,human-computer interaction,and medical image processing.However,it remains still a challenging task due to complex scenes and lack of the prior knowledge.To solve these problems,the low-rank matrix recovery has become an effective method in recent years.This paper mainly studies the low-rank matrix recovery method for background subtraction,which mainly focuses on the problem of convex relaxation penalty imbalance and low degree of dispersion of data recovery in the low-rank matrix recovery.To overcome the problem of the convex relaxation penalty imbalance in the low-rank matrix recovery,a continuous approximated non-convex relaxation model of continuous approximation is proposed and is used for background subtraction.To overcome the problem of small difference in the degree of dispersion of the restored part in the low-rank matrix recovery,a low-rank matrix recovery model based on the variance constraint is proposed and is verified on the background subtraction.The innovation of this paper manly includes:1.A low-rank matrix recovery model based on continuous minimization.In this paper,we focus on the non-convex relaxation model and its convergence analysis for the rank function convex relaxation penalty imbalance in the low-rank matrix recovery.The aim is to propose a more stringent approximation of the rank function and apply the proposed model to the background subtraction.Specifically,this paper proposes a stricter non-convex relaxation model,tanh-RPC A.By introducing a continuous strategy in the hyperbolic tangent(tanh)function,tanh-norm is more strictly approximated to the real rank.The low-rank matrix recovery on the simulated data and background subtraction on the real data show that tanh-RPCA significantly improves the performance of the low-rank matrix recovery and overcomes the problem of penalty imbalance compared to the latest and representative low-rank matrix recovery models.2.A low-rank matrix recovery model based on variance constraint.In this paper,the problem of small difference in the degree of dispersion between the low-rank recovery and the low-rank matrix recovery is studied.This paper introduces the optimization and solution of low-rank matrix to recover the low-rank partial maximal variance constraint model,aiming at maximizing the dispersion degree of low-rank part,to ensure that the background of the neighbor frame is more stable.And the proposed model is applied to background subtraction.Specifically,this paper proposes a model based on the maximum variance constraint,var-RPCA,which restores the original low-rank attribute of the low-rank part by restoring the maximum variance constraint of the low-rank part to the low-rank matrix,thereby realizing the low-rank matrix recovery.The low-rank matrix recovery on the simulated data and the background subtraction on the real data show that var-RPC A improves the performance of the low-rank matrix recovery and guarantees the low-rank partiality Smoothness compared to the latest and representative low-rank matrix recovery models.