Since no library functions exist for wavelet transformation, we
had to make our own implementation. We used Mallat's fast wavelet transform
algorithm, stated in
Castleman's Wavelet Transform notes, in order to eliminate matrix multiplication.
Filters are similar to those used in the previous part except that they have rectangular form rather than being circular.
Function of the filter used for blurring is :
Function of the filter used for sharpening is :
Graph of these filters are given in this page.
In the implementation part, two extra command line arguments are added
(optional) for
changing D0 and n values in the filtering functions in order
to obtain better results for
different kinds of images. After the standard --sharpen or --blur argument,
one or two
numbers first of which is the new D0 value and second is the
new n value can be entered.