Robust Low Rank Dynamic Mode Decomposition for Compressed Domain Crowd and Traffic Flow Analysis

In this paper, we develop a dynamic mode decomposition algorithm that is robust to both inlier and outlier noise in the data. One application of our algorithm is the identification of multiple crowd or traffic flows from compressed video streams. Our method uses motion vectors that are readily available in the compressed bitstream, and do not require computationally expensive optical flow. These motion vectors are known to be very noisy, however, our algorithm is able to extract the underlying dynamical systems that define the flows. We formulate a rank regularized dynamic mode decomposition problem with total least squares constraints to estimate the Koopman modes of the motion dynamics. The estimated Koopman modes are then used to analyze the stability of the system and extract steady state and transient flows. We demonstrate the improved performance of our approach compared to state of the art schemes and illustrate it applicability in identifying transient and steady-state flows in real video sequences.