Bounding Multiple Gaussians Uncertainty with Application to Object Tracking

TLDR: The uncertainty bound for the multiple Gaussian functions, termed multiple Gaussians Uncertainty (MGU), is proved, which significantly generalizes the uncertainty principle for the single Gaussian function.

Abstract: This paper proves the uncertainty bound for the multiple Gaussian functions, termed multiple Gaussians Uncertainty (MGU), which significantly generalizes the uncertainty principle for the single Gaussian function. First, as a theoretical contribution, we prove that the momentum (velocity) and position for the sum of multiple Gaussians wave function are theoretically bounded. Second, as for a practical application, we show that the bound can be well exploited for object tracking to detect anomalies of local movement in an online learning framework. By integrating MGU with a given object tracker, we demonstrate that uncertainty principle can provide remarkable robustness in tracking. Extensive experiments are done to show that the proposed MGU can significantly help base trackers overcome the object drifting and reach state-of-the-art results.