How to convolve a Gaussian function super-accurately with linear computational complexity

Abstract

Gaussian convolution is a fundamental and important tool in CG, CAD, and image processing applications. In this research, we propose a novel, fast, and accurate approximation algorithm to convolve a Gaussian function with images. Our algorithm is based on splitting a pixel domain into representative regions where we can efficiently perform discrete convolutions. Our algorithm is applicable to non-uniform pixels with linear computational complexity. We examine our algorithm numerically in terms of speed, precision, and quality.