Background/foreground separation is one of the
most fundamental tasks in computer vision, especially for video
data. Robust PCA (RPCA) and its tensor extension, namely, Robust Tensor PCA (RTPCA), provide an effective framework for
background/foreground separation by decomposing the data into
low-rank and sparse components, which contain the background
and the foreground (moving objects), respectively. However, in
real-world applications, the video data is contaminated with
noise. For example, in metal additive manufacturing (AM), the
processed X-ray video to study melt pool dynamics is very noisy.
RPCA and RTPCA are not able to separate the background,
foreground, and noise simultaneously. As a result, the noise
will contaminate the background or the foreground or both.
There is a need to remove the noise from the background
and foreground. To achieve the three terms decomposition, a
smooth sparse Robust Tensor Decomposition (SS-RTD) model
is proposed to decompose the data into static background,
smooth foreground, and noise, respectively. Specifically, the static
background is modeled by the low-rank tucker decomposition,
the smooth foreground (moving objects) is modeled by the spatiotemporal continuity, which is enforced by the total variation
regularization, and the noise is modeled by the sparsity, which
is enforced by the L1 norm. An efficient algorithm based on
alternating direction method of multipliers (ADMM) is implemented to solve the proposed model. Extensive experiments on
both simulated and real data demonstrate that the proposed
method significantly outperforms the state-of-the-art approaches
for background/foreground separation in noisy cases.<br>