2-DIMENSIONAL DIRECTIONAL WAVELETS AND THE SCALE-ANGLE REPRESENTATION

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