Computing An Exact Gaussian Scale-Space

Gaussian convolution is one of the most important algorithms in image processing. The present work focuses on the computation of the Gaussian scale-space, a family of increasingly blurred images, responsible, among other things, for the scale-invariance of SIFT, a popular image matching algorithm. We discuss and numerically analyze the precision of three different alternatives for defining a discrete counterpart to the continuous Gaussian smoothing operator. This study is focused on low blur levels, that are crucial for the scale-space accuracy.