Fast Recursive Implementation of the Gaussian Filter

摘要

On one hand, the convolution with the truncated impulse response (IR) of Gaussian filters leads to a high computation cost when the standard deviation σ of the Gaussian increases. On the other hand, recursive filters that approximate the Gaussian filters reduce the computation cost but can only be applied to finite length signals due to the infinity of the IR on both sides. In this paper, we present a new filter: PAOG. Its IR is a polynomial which is an accurate approximation of the truncated Gaussian m. Then, we derive a simple and fast recursive implementation of the PAOG filter. The computation cost is independent on σ. PAOG is particularly suitable for very high speed hardware architecture because the recursive part of the filter uses only adders (without multiplier) which can be implemented in carry-save. This filter can be used with signal of infinite duration (real time). Simultaneously, the first and second derivative of the Gaussian filter are computed without any extra computation cost.