Real-Time Motion Detection Using Dynamic Mode Decomposition

2024-05-08

arXiv.org

AI Summary

This work addresses the challenge of real-time motion detection in streaming video—particularly under low signal-to-noise ratio and dynamic illumination conditions typical of simulated surveillance scenarios. We propose a lightweight, unsupervised detection framework based on Dynamic Mode Decomposition (DMD). Our method models video frame sequences as linear dynamical systems and establishes, for the first time, an interpretable mapping between foreground motion characteristics and the temporal evolution of DMD eigenvalues. By analyzing the eigenvalue spectrum to identify salient motion responses, and integrating sliding-window segmentation with ROC-driven adaptive thresholding, we achieve efficient online detection. Evaluated on a simulated surveillance dataset, our approach achieves an AUC exceeding 0.92, demonstrating high accuracy, low latency, and strong robustness. This work introduces a novel paradigm for unsupervised, real-time motion detection grounded in spectral system identification.

Technology Category

• Computer Vision: Motion & Tracking
• Machine Learning: Unsupervised & Self-Supervised Learning
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• Develops a real-time motion detection algorithm
• Uses Dynamic Mode Decomposition for video analysis
• Optimizes movement identification in security footage

Innovation

• Dynamic Mode Decomposition for motion detection
• Eigenvalues link video features to motion
• Cross-validation optimizes movement detection threshold