  This paper introduces a fast algorithm for randomized computation of a
low-rank Dynamic Mode Decomposition (DMD) of a matrix. Here we consider this
matrix to represent the development of a spatial grid through time e.g. data
from a static video source. DMD was originally introduced in the fluid
mechanics community, but is also suitable for motion detection in video streams
and its use for background subtraction has received little previous
investigation. In this study we present a comprehensive evaluation of
background subtraction, using the randomized DMD and compare the results with
leading robust principal component analysis algorithms. The results are
convincing and show the random DMD is an efficient and powerful approach for
background modeling, allowing processing of high resolution videos in
real-time. Supplementary materials include implementations of the algorithms in
Python.
