Variety-Based Background Subtraction for Nonlinear Trajectory Tracking

Abstract

In this paper, the incorporation of algebraic varieties is considered for structured estimation of nonlinear trajectories. The background subtraction model is extended beyond sparse and low-rank decompositions. The algebraic varieties model is introduced via an additional low-rank constraint. The proposed method is applied to single object tracking in video wherein the trajectory locations in space belong to an algebraic variety. The optimization is solved via the Iteratively Reweighted Least Squares method, adapted to the proposed problem. The algorithm is numerically shown to be convergent, given proper tuning of system parameters. Perfect recovery is observed for noiseless measurements. For noisy measurements, a performance improvement on order of 2.4 dB, on average, is observed over previous background subtraction methods that do not consider the side structure, i.e., the variety.