In this work we explore the use of the so-called wavelet transform in the digital image processing of micrographs. The wavelet transform of an image f(x,y) is defined as:
Wf(s,u,v)
= f(x,y) s Ψ(s(x-u),s(y-v)) dxdy
where Ψ is an analyzing function called wavelet and which is in our examples always taken to be the Mexican hat given by
Ψ(x)=(2-(x2+y2))exp(-(x2+y2)/2)
Some synthetic images are shown in which it can be clearly seen how the wavelet transform can be useful to reveal edges and to emphasize the boundaries of the clusters.
The technique is applied in the case of the CoMoS catalysts, in which the wavelet transform can be used to emphasize the hexagonal domains while filtering the noise quite effectively. The technique is next applied to electron backreflection patterns where substantial noise reduction and emphasis of the lines are achieved.
Several examples of the application of this processing tool to high resolution images of metallic particles and to quasicrystals are presented
