Robust null space representation and sampling for view-invariant motion trajectory analysis

In this paper, we propose a novel robust retrieval and classification system for video and motion events based on null space representation. In order to analyze the robustness of the system, the perturbed null operators have been derived with the first order perturbation theory. Subsequently, the sensitivity of the null operators is discussed in terms of the error ratio and the SNR respectively. Meanwhile, the normwise bounds and componentwise bounds based on classical matrix perturbation theory are presented and discussed. Given the perturbation, uniform sampling are proposed for the convergence of the SNR and Poisson sampling are proposed for the convergence of the error ratio in the mean sense by choosing the rate parameter the same order as the number of samples. The simulation results are provided to demonstrate the effectiveness and robustness of our system in motion event indexing, retrieval and classification that is invariant to affine transformation due to camera motions.