  Sampling and budgeting training examples are two essential factors in
tracking algorithms based on support vector machines (SVMs) as a trade-off
between accuracy and efficiency. Recently, the circulant matrix formed by dense
sampling of translated image patches has been utilized in correlation filters
for fast tracking. In this paper, we derive an equivalent formulation of a SVM
model with circulant matrix expression and present an efficient alternating
optimization method for visual tracking. We incorporate the discrete Fourier
transform with the proposed alternating optimization process, and pose the
tracking problem as an iterative learning of support correlation filters (SCFs)
which find the global optimal solution with real-time performance. For a given
circulant data matrix with n^2 samples of size n*n, the computational
complexity of the proposed algorithm is O(n^2*logn) whereas that of the
standard SVM-based approaches is at least O(n^4). In addition, we extend the
SCF-based tracking algorithm with multi-channel features, kernel functions, and
scale-adaptive approaches to further improve the tracking performance.
Experimental results on a large benchmark dataset show that the proposed
SCF-based algorithms perform favorably against the state-of-the-art tracking
methods in terms of accuracy and speed.
