Correlating Fourier descriptors of local patches for road sign recognition

The Fourier descriptors (FDs) is a classical but still popular method for
contour matching. The key idea is to apply the Fourier transform to a
periodic representation of the contour, which results in a shape descriptor
in the frequency domain. Fourier descriptors are most commonly used to
compare object silhouettes and object contours; we instead use this well
established machinery to describe local regions to be used in an object
recognition framework. Many approaches to matching FDs are based on the
magnitude of each FD component, thus ignoring the information contained in
the phase. Keeping the phase information requires us to take into account
the global rotation of the contour and shifting of the contour samples. We
show that the sum-of-squared differences of FDs can be computed without
explicitly de-rotating the contours. We compare our correlation based
matching against affine-invariant Fourier descriptors (AFDs) and WARP
matched FDs and demonstrate that our correlation based approach outperforms
AFDs and WARP on real data. As a practical application we demonstrate the
proposed correlation based matching on a road sign recognition task.