  Scene Background Initialization (SBI) is one of the challenging problems in
computer vision. Dynamic mode decomposition (DMD) is a recently proposed method
to robustly decompose a video sequence into the background model and the
corresponding foreground part. However, this method needs to convert the color
image into the grayscale image for processing, which leads to the neglect of
the coupling information between the three channels of the color image. In this
study, we propose a quaternion-based DMD (Q-DMD), which extends the DMD by
quaternion matrix analysis, so as to completely preserve the inherent color
structure of the color image and the color video. We exploit the standard
eigenvalues of the quaternion matrix to compute its spectral decomposition and
calculate the corresponding Q-DMD modes and eigenvalues. The results on the
publicly available benchmark datasets prove that our Q-DMD outperforms the
exact DMD method, and experiment results also demonstrate that the performance
of our approach is comparable to that of the state-of-the-art ones.
