Real-Time Motion Detection Using Dynamic Mode Decomposition

TL;DR

This paper introduces a real-time motion detection algorithm for streaming video based on Dynamic Mode Decomposition, which decomposes video data into modes to identify movement effectively under various conditions.

Contribution

The work presents a simple, interpretable motion detection method rooted in DMD, specifically designed for streaming video and optimized using cross-validation.

Findings

Effective detection of motion in security-like videos

High accuracy demonstrated through ROC analysis

Robustness under varying realistic conditions

Abstract

Dynamic Mode Decomposition (DMD) is a numerical method that seeks to fit timeseries data to a linear dynamical system. In doing so, DMD decomposes dynamic data into spatially coherent modes that evolve in time according to exponential growth/decay or with a fixed frequency of oscillation. A prolific application of DMD has been to video, where one interprets the high-dimensional pixel space evolving through time as the video plays. In this work, we propose a simple and interpretable motion detection algorithm for streaming video data rooted in DMD. Our method leverages the fact that there exists a correspondence between the evolution of important video features, such as foreground motion, and the eigenvalues of the matrix which results from applying DMD to segments of video. We apply the method to a database of test videos which emulate security footage under varying realistic conditions. Effectiveness is analyzed using receiver operating characteristic curves, while we use cross-validation to optimize the threshold parameter that identifies movement.