This is a presentation of the work that we have done in the field of 1D, 2D, 3D and 4D spatial filtering. We have focused on the convolution with Gaussian filter. The results were achieved with our in-house developed LinearFilters library .

Motivation

The motivation for fast and accurate computation of Gaussian filtering was to be able to compute certain optical flow algorithms efficiently. Such group of algorithms employ several Gabor filters (filtering banks) what can be turned into computation of many convolutions with Gaussian filters [1]. The filtering has always been the major slowdown factor of the approach.

The overall goal is to equip such methods with fast and accurate implementation of algorithms which should be able to compute truly arbitrary, i.e. anisotropic with generaly-oriented main axis, Gaussian (and Gabor as well) filtering for 3D and time lapse 3D images. The LinearFilters library should serve this purpose.