Exploiting the Circulant Structure of Tracking-by-detection with Kernels

WARNING: THIS POST IS UNDER CONSTRUCTION, WILL BE UPDATED SOON

TIP: Please read the paper once and use the following notes to understand the algorithm better

In this paper the author showed how dense sampling of targets can be incorporated to improve the performance of classifier, which was previously trained by taking few samples around the target^[1,2,3]

Figure 1.1: Sampling Strategies (a) Sparse Sampling (b) Dense Sampling

While dense sampling can increase the number of samples for the training, authors discovered how this type of sampling leads to pattern in the samples, which they call it as circulant structure
It is shown how this circulant structure can take advantage of Fast Fourier Transform (FFT) to train the classifier in one shot without the need to reiterate over individual samples.
It is also shown how circulant structure leads to mathematical formulation that helps to train the classifier by transforming the samples from input space to feature space using kernel trick and still run faster.

We go through the matlab code available in the link and understand the implementation.

References