Many current medical image processing algorithms utilize Fourier Transform techniques that represent images as sums of translationally invariant complex exponential basis functions. Selective removal or enhancement of these translationally invariant components can be used to effect a number of image processing operations such as edge enhancement or noise attenuation. An important characteristic of many natural phenomena, including the structures of interest in medical imaging is spatial self-similarity. In this work a filtering technique that represents images as sums of scale invariant self-similar basis functions will be presented. The decomposition of a signal or image into scale invariant components can be accomplished using the Mellin Transform, which diagonalizes changes of scale in a manner analogous to the way the Fourier Transform diagonalizes translation.