High Speed Tracking With A Fourier Domain Kernelized Correlation Filter

It is challenging to design a high speed tracking approach using l1-norm due to its non-differentiability. In this paper, a new kernelized correlation filter is introduced by leveraging the sparsity attribute of l1-norm based regularization to design a high speed tracker. We combine the l1-norm and l2-norm based regularizations in one Huber-type loss function, and then formulate an optimization problem in the Fourier Domain for fast computation, which enables the tracker to adaptively ignore the noisy features produced from occlusion and illumination variation, while keep the advantages of l2-norm based regression. This is achieved due to the attribute of Convolution Theorem that the correlation in spatial domain corresponds to an element-wise product in the Fourier domain, resulting in that the l1-norm optimization problem could be decomposed into multiple sub-optimization spaces in the Fourier domain. But the optimized variables in the Fourier domain are complex, which makes using the l1-norm impossible if the real and imaginary parts of the variables cannot be separated. However, our proposed optimization problem is formulated in such a way that their real part and imaginary parts are indeed well separated. As such, the proposed optimization problem can be solved efficiently to obtain their optimal values independently with closed-form solutions. Extensive experiments on two large benchmark datasets demonstrate that the proposed tracking algorithm significantly improves the tracking accuracy of the original kernelized correlation filter (KCF) while with little sacrifice on tracking speed. Moreover, it outperforms the state-of-the-art approaches in terms of accuracy, efficiency, and robustness.