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.