Fast Convolution with Laplacian-of-Gaussian Masks

We present a technique for computing the convolution of an image with LoG (Laplacian-of-Gaussian) masks. It is well known that a LoG of variance a can be decomposed as a Gaussian mask and a LoG of variance σ1 < σ. We take advantage of the specific spectral characteristics of these filters in our computation: the LoG is a bandpass filter; we can therefore fold the spectrum of the image (after low pass filtering) without loss of information, which is equivalent to reducing the resolution. We present a complete evaluation of the parameters involved, together with a complexity analysis that leads to the paradoxical result that the computation time decreases when σ increases. We illustrate the method on two images.