The wavelet enhancement method highlights features in an image at the size-scale of the wavelet. There are a large set of possible wavelets—that generally chosen for structure enhancement is the so-called Mexican Hat (Maar) wavelet (e.g. ). This is defined as the second derivative of the classical Gaussian function:
where a determines the size of the wavelet and, therefore, the scale which is probed. The 2-D wavelet transform, obtained by correlating ip(x,y,a) with an image f(x,y), is given by
In practice, for speed of execution, this correlation is performed by a convolution in discrete Fourier space.
A notable feature of W(x, y, a) are the regions of negative amplitude surrounding positive cores—the latter correspond to under-densities while the former correspond to over-densities in the original image at the size-scale under study.
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