In recent years, correlation filter based trackers (CF trackers) have attracted much attention from the vision community because of their top performance in both localization accuracy and efficiency. The society of visual tracking, however, still needs to deal with the following difficulty on CF trackers: avoiding or eliminating the boundary effect completely, in the meantime, exploiting non-linear kernels and running efficiently. In this paper, we propose a fast kernelized correlation filter without boundary effect (nBEKCF) to solve this problem. To avoid the boundary effect thoroughly, a set of \emph{real} and \emph{dense} patches is sampled through the traditional sliding window and used as the training samples to train nBEKCF to fit a Gaussian response map. Non-linear kernels can be applied naturally in nBEKCF due to its different theoretical foundation from the existing CF trackers'. To achieve the fast training and detection, a set of cyclic bases is introduced to construct the filter. Two algorithms, ACSII and CCIM, are developed to significantly accelerate the calculation of kernel correlation matrices. ACSII and CCIM fully exploit the density of training samples and cyclic structure of bases, and totally run in space domain. The efficiency of CCIM exceeds that of the FFT counterpart remarkably in our task. Extensive experiments on six public datasets, OTB-2013, OTB-2015, NfS, VOT2018, GOT10k, and TrackingNet, show that compared to the CF trackers designed to relax the boundary effect, BACF and SRDCF, our nBEKCF achieves higher localization accuracy without tricks, in the meanwhile, runs at higher FPS.
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