Moving-window mean and variance

Efficient computation of moving-window mean and moving-window variance

This function computes the moving-window mean (also know as moving average) and moving-window variance of a sequence of one-dimensional or two-dimensional data frames (e.g. a sequence of images). For two-dimensional data, the moving-window mean and variance are computed per individual entry (e.g. per pixel).
The expressions were derived using the approach of [Welford, 1962], who provides expressions for the running mean and running variance.
The running mean and variance are calculated during start-up (i.e. while the window is not yet full).
References:
Welford, BP, "Note on a method for calculating corrected sums of squares and products." Technometrics, 4(3), pp.419-420, 1962.
NOTE: In the present implementation a moving history is maintained (similar to a shift register). This might still represent quite a computational burden. If memory size permits, one could maintain a longer history that is shifted only when full. This will be implemented in a future release.