The smoothing is applied by the way of a bi-exponential filter, itself realized by a pair of one-tap recursions. It is therefore very fast; moreover, its computational cost is truly independent of the amount of smoothing. Meanwhile, the preservation of edges is obtained by a range filter akin to the range filter found in a bilateral filter. More technical details are available here.
The plugin allows one to control the amount of smoothing, the type of range filter, its broadness, and to iterate the filter several times if desired. We illustrate in Figure 2 a possible outcome of this filter. Here, we iterated the BEEPS 10 times with a Gaussian range filter, σ = 10, and the spatial decay λ = 0.1.