Fast Gaussian filtering algorithm using splines

For many purposes such as rotatable feature extraction and noise reduction, the Gaussian filter is often used. Many present algorithms compute it using much time or compute a rectangle filter instead of it giving up rotation invariance. In this paper, we propose a method to shorten computational time of the Gaussian filter. The proposed method uses an nth-order spline, where n is higher than one. Precomputing an integrated input image, the proposed method can calculate a Gaussian-filtered pixel value with several multiplications and summations in constant time on the size of the source image and the size of the Gaussian filter. As the result of evaluation, the proposed method using an approximated Gaussian filter within 3.5 percent error is faster than the naïve method if application area of the Gaussian filter is larger than 8×8 pixels.