Anisotropic Gaussian Filtering using Fixed Point Arithmetic

Gaussian filtering in one, two or three dimensions is among the most commonly needed tasks in signal and image processing. Finite impulse response filters in the time domain with Gaussian masks are easy to implement in either floating or fixed point arithmetic, because Gaussian kernels are strictly positive and bounded. But these implementations are slow for large images or kernels. With the recursive IIR-filters and FFT-based methods, there are at least two alternative methods to perform Gaussian filtering in a faster way, but so far they are only applicable when floating-point hardware is available. In this paper, a fixed-point implementation of recursive Gaussian filtering is discussed and applied to isotropic and anisotropic image filtering by making use of a non-orthogonal separation scheme of the Gaussian filter.