  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.
