An adjustable Gaussian filter for Fourier transformation of arbitrary image regions

The ability to analyse an arbitrary region of an image has not yet been satisfactorily solved. Classical Fourier techniques are only suited to analysing rectangular, and preferably square, regions. Furthermore, analysing regions that comprise less than the full image, particularly regions of arbitrary shape and size, results in sets of coefficients in the frequency domain that are also of arbitrary size. This makes it extremely difficult to compare the results in the frequency domain.; The shortcomings in Fourier techniques have led to development of wavelet based techniques that are inherently suited to analysis of sub-regions of an image. This makes wavelet methods more useful for working with sub-regions of an image. However, even wavelet based techniques have limitations on the exact size and shape of the sub-regions that are available for analysis and comparison.; Although both Fourier and wavelet approaches have shortcomings, Fourier techniques still offer better immunity to the problems of rotation, translation, and scaling.; This work explores the development of an Adjustable Gaussian Filter that is used to process an arbitrary (non-rectangular) region of an image using Fourier techniques. The filter is applied to a Fourier Transform in a manner that leaves the frequency domain amenable to comparison and is reasonably independent of the shape and size of the region.