Two-dimensional directional wavelets and the scale-angle representation

The two-dimensional continuous wavelet transform (CWT) is characterized by a rotation parameter, in addition to the usual translations and dilations. This enables it to detect edges and directions in images, provided a directional wavelet is used. First we briefly review the general properties of the 2-D CWT and describe several classes of wavelets, including the directional ones. Then we turn to the problem of wavelet calibration. We show, in particular, how the reproducing kernel may be used for defining and evaluating the scale and angle-resolving power of a wavelet. Finally, we illustrate the usefulness of the scale-angle representation of the CWT on the problem of disentangling a train of damped plane waves.