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This paper introduces a fast algorithm for randomized computation of alow-rank Dynamic Mode Decomposition (DMD) of a matrix. Here we consider thismatrix to represent the development of a spatial grid through time e.g. datafrom a static video source. DMD was originally introduced in the fluidmechanics community, but is also suitable for motion detection in video streamsand its use for background subtraction has received little previousinvestigation. In this study we present a comprehensive evaluation ofbackground subtraction, using the randomized DMD and compare the results withleading robust principal component analysis algorithms. The results areconvincing and show the random DMD is an efficient and powerful approach forbackground modeling, allowing processing of high resolution videos inreal-time. Supplementary materials include implementations of the algorithms inPython.

Randomized Low-Rank Dynamic Mode Decomposition for Motion Detection