Two-Dimensional Directional Wavelets and the Scale-Angle Representation

Abstract

The two-dimensional continuous wavelet transform (CWT), derived from a square integrable representation of the similitude group of IR 2 , 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 review the general properties of the 2D 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. UCL--IPT--95--03 May 1995 3 Supported by ONR (Office of Naval Research), Grant Nr.N0014-93-10561 and by ARPA (Advanced Research Project Agency), Grant Nr.MDA 972-93-1-0013 1. Introduction The wavele..