TABLE OF CONTENTS The next step is to choose an analyzing wavelet ?. At this point, there are two possibilities, depending whether one is interested or not in detecting oriented features in an image, i.e., regions where the amplitude is regular along one direction and has a sharp variation along the perpendicular direction.
Isotropic wavelets
If one wants to perform a pointwise analysis, i.e., when no oriented features are present or relevant in the signal, one may choose an analyzing wavelet ? which is invariant under rotation. Then the ? dependence drops out, for instance, in the reconstruction formula (2.26). The most familiar example is the isotropic 2-D Mexican hat wavelet (2.21).
Anisotropic wavelets
When the aim is to detect oriented features in an image (for instance, in the classical problem of edge detection or in directional filtering), one has to use a wavelet which is not rotation invariant. The best angular selectivity will be obtained if ? is directional, which means that the (essential) support of 
in spatial frequency space is contained in a convex cone with apex at the origin (by which we mean that the wavelet is numerically negligible outside the cone). Typical directional wavelets are the 2-D Morlet wavelet (2.22) or the conical wavelets.
There are many ways of designing wavelets of either kind, but in fact almost all of those available on the market may be obtained by a general procedure, outlined in the proposition below. The starting...
