  Correlation filters (CFs) are a class of classifiers that are attractive for
object localization and tracking applications. Traditionally, CFs have been
designed in the frequency domain using the discrete Fourier transform (DFT),
where correlation is efficiently implemented. However, existing CF designs do
not account for the fact that the multiplication of two DFTs in the frequency
domain corresponds to a circular correlation in the time/spatial domain.
Because this was previously unaccounted for, prior CF designs are not truly
optimal, as their optimization criteria do not accurately quantify their
optimization intention. In this paper, we introduce new zero-aliasing
constraints that completely eliminate this aliasing problem by ensuring that
the optimization criterion for a given CF corresponds to a linear correlation
rather than a circular correlation. This means that previous CF designs can be
significantly improved by this reformulation. We demonstrate the benefits of
this new CF design approach with several important CFs. We present experimental
results on diverse data sets and present solutions to the computational
challenges associated with computing these CFs. Code for the CFs described in
this paper and their respective zero-aliasing versions is available at
http://vishnu.boddeti.net/projects/correlation-filters.html
