Sum-box technique for fast linear filtering

Abstract

Linear filters are widely used in signal processing and in image processing, and the fast realization of large kernel filters has been an important research subject. Traditional fast algorithms try to decompose the initial kernel into the convolution of smaller kernels, and a lot of multiplications are still needed to realize all the convolutions with the small kernels. Box technique can realize the Gaussian filters with little multiplications, but it cannot realize linear filters other than the Gaussians. In the present paper, by use of the analysis on the scaled Spline functions, we propose the sum-box filter technique to approximately realize a given large kernel linear filter (even non Gaussian type) to a factor by the sum of the translated outputs of sum-box filters, requiring no multiplications. This original sum-box technique presented opens thus a new orientation for linear filter fast realization: realizing to a factor the convolution with a large filter kernel by additions only. From the viewpoint of computational complexity, this method is highly efficient in image and signal processing, in particular, for large filter kernels. Experimental results are reported.