Abstract
Moving object detection in a given video sequence is a pivotal step in many computer vision applications such as video surveillance. Robust Principal Component Analysis (RPCA) performs low-rank and sparse decomposition to accomplish such a task when the background is stationary and the foreground is dynamic and relatively small. A fundamental issue with the RPCA is the assumption that the low-rank and sparse components are added at each pixel, whereas in reality, the moving foreground is overlaid on the background. We propose the masked decomposition (i.e. an overlaying model) where each element either belongs to the low-rank or the sparse component, decided by a mask. We introduce the Masked-RPCA (MRPCA) algorithm to recover the mask (hence the sparse object) and the low-rank components simultaneously, via a non-convex formulation. An adapted version of the Douglas–Rachford splitting algorithm is utilized to solve the proposed formulation. Our experiments using real-world video sequences show consistently better performance for both cases of static and dynamic background videos compared to RPCA and its variants based on the additive model. Additionally, we show that utilizing non-convex priors in our formulation leads to improved results without any added complexity compared to a relaxed formulation using convex surrogates and methods based on the additive model.
Highlights
Initial approach was to model the static background using Principal Component Analysis (PCA) [1]. This method provides a model for the background and the foreground detection is achieved by thresholding the difference between the original frame and the generated background
The code for the proposed algorithms are available here [49]. For both cases of static and dynamic background, we provide visual and statistical comparisons between the proposed models and principal component pursuit (PCP) [3], Stable principal component pursuit (SPCP) [11], and DeColor [15]
MRPCA1 and MRPCA2 refer to the formulations in (6) and (7), respectively
Summary
M OVING object detection is the initial step to many video analysis applications. Given a sequence of video frames, the goal is to separate the moving object (called the “foreground”) from the static parts of each frame (called the “background”). In video surveillance applications, we may need to detect the activities that stand out from the background. Many different approaches have been proposed over the past two decades to tackle this problem. Initial approach was to model the static background using Principal Component Analysis (PCA) [1]. This method provides a model for the background and the foreground detection is achieved by thresholding the difference between the original frame and the generated background
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