Hypercomplete circular harmonic pyramids

In this contribution we present a steerable pyramid based on a particular set of complex wavelets named circular harmonic wavelets (CHW). The proposed CHWs set constitutes a generalization of the smoothed edge wavelets introduced by Mallat, consisting of extending the local differential representation of a signal image from the first order to a generic n-th order. The key feature of the proposed representation is the use of complex operators leading to an expansion in series of polar separable complex functions, which are shown to possess the space-scale representability of the wavelets. The resulting tool is highly redundant, and for this reason is called hypercomplete circular harmonic pyramid (HCHP), but presents some interesting aspects in terms of flexibility, being suited for many image processing applications. In the present contribution the main theoretical aspects of the HCHPs are discussed along with some introductory applications. ©2005 Copyright SPIE - The International Society for Optical Engineering.