Compressed Dynamic Mode Decomposition for Real-Time Object Detection

We introduce the method of compressive dynamic mode decomposition (cDMD) for robustly performing real-time foreground/background separation in high-definition video. The DMD method provides a regression technique for least-square fitting of video snapshots to a linear dynamical system. The method integrates two of the leading data analysis methods in use today: Fourier transforms and Principal Components. DMD modes with temporal Fourier frequencies near the origin (zero-modes) are interpreted as background (low-rank) portions of the given video frames, and the terms with Fourier frequencies bounded away from the origin are their foreground (sparse) counterparts. When combined with compression techniques, the resulting cDMD can process full HD video feeds in real-time on CPU computing platforms while still maintaining competitive video decomposition quality, quantified by F-measure, Recall and Precision. On a GPU architecture, the method is significantly faster than real-time, allowing for further video processing to improve the separation quality and/or enacting further computer vision processes such as object recognition.