Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements

TL;DR

This paper introduces a novel tensor-based robust PCA method utilizing total variation regularization for background subtraction directly from compressive measurements, effectively capturing spatial-temporal correlations in video data.

Contribution

The paper proposes two new tensor RPCA models, H-TenRPCA and PG-TenRPCA, that incorporate 3D total variation and Tucker decomposition for improved background subtraction from compressive measurements.

Findings

Outperforms existing methods on simulated videos

Effective in real-world video background subtraction

Demonstrates robustness to compressive measurement noise

Abstract

Background subtraction has been a fundamental and widely studied task in video analysis, with a wide range of applications in video surveillance, teleconferencing and 3D modeling. Recently, motivated by compressive imaging, background subtraction from compressive measurements (BSCM) is becoming an active research task in video surveillance. In this paper, we propose a novel tensor-based robust PCA (TenRPCA) approach for BSCM by decomposing video frames into backgrounds with spatial-temporal correlations and foregrounds with spatio-temporal continuity in a tensor framework. In this approach, we use 3D total variation (TV) to enhance the spatio-temporal continuity of foregrounds, and Tucker decomposition to model the spatio-temporal correlations of video background. Based on this idea, we design a basic tensor RPCA model over the video frames, dubbed as the holistic TenRPCA model (H-TenRPCA). To characterize the correlations among the groups of similar 3D patches of video background, we further design a patch-group-based tensor RPCA model (PG-TenRPCA) by joint tensor Tucker decompositions of 3D patch groups for modeling the video background. Efficient algorithms using alternating direction method of multipliers (ADMM) are developed to solve the proposed models. Extensive experiments on simulated and real-world videos demonstrate the superiority of the proposed approaches over the existing state-of-the-art approaches.