As a practical application of pre-processing for the motion detector model, the difference of Gaussian (DoG) filtering provides several advantages.  It is essentially an edge-detection filter and edges are the most important factor in the detection of motion.  It also brings the average intensity of a scene to zero.

This is an unfiltered, grayscale image of a lizard in its natural habitat.




This is the same image after the application of a DoG filter.

Edges are enhanced and areas of similar intensity become black (zero).




The width of the Gaussians, determined by their standard deviations,  used for filtering can produce different results.  A gaussian with a low standard deviation appears narrow, while one with a large standard deviation appears wider.  The first filtered image  is the result of using a narrow filter (Standard deviations of one and two).  Using a broader filter will spread the edges more, which is important for avoiding aliasing effects, but also loses some precision about their exact locations.

The resulting image after application of a larger filter (Standard deviations of three and six):