Morphological Pyramids and Wavelets Based on the Quincunx Lattice

This paper is concerned with two types of multiresolution image decompositions, pyramids and wavelets. We present an axiomatic approach for both cases, encompassing linear as well as nonlinear decompositions. A wavelet decomposition is more specific in the sense that it always involves a pyramid transform. Both families will be illustrated by means of concrete examples using the quincunx scheme in two dimensions. One nonlinear wavelet transform will be discussed in more detail: it uses the lifting scheme and has the intriguing property that it preserves local maxima over a range of scales.