Image Analysis Using a Generalised Wavelet Transform

The suitability of wavelet transforms (WT) for use in image analysis is well established: a representation in terms of the frequency content of local regions over a range of scales provides an ideal framework for the analysis of image features, which in general are of di erent size and can often be characterised by their frequency domain properties [1]. However, the standard form of wavelet decomposition, based on the translation and scaling of a single mother wavelet [2], has its limitations when considering general analysis problems. Apart from its lack of shift invariance [3], it also necessarily links scale and frequency: the size of a given region determines its representative frequencies within the transform. This latter property seems particularly restrictive given that there is no reason in general to assume that the frequency content of an image region should be related to its size. Thus, although the basic advantages of a wavelet approach are well-founded, the need exists for a form which addresses these limitations.