Recursive implementation of the Gaussian filter

Abstract In this paper we propose a recursive implementation of the Gaussian filter. This implementation yields an infinite impulse response filter that has six MADDs per dimension independent of the value of σ in the Gaussian kernel. In contrast to the Deriche implementation (1987), the coefficients of our recursive filter have a simple, closed-form solution for a desired value of the Gaussian σ. Our implementation is, in general, faster than (1) an implementation based upon direct convolution with samples of a Gaussian, (2) repeated convolutions with a kernel such as the uniform filter, and (3) an FFT implementation of a Gaussian filter.