The implemented standard deviation filter is based on calculation two integral images and subsequent common calculation of the variance by:
var(X) = E[X^2] - (E[X])^2.
The advantage of this implementation is that the computation time is independent of the kernel size. In comparison to stdfilt from Image Processing Toolbox, whose computation time increases linearly, usage of the integral image method is beneficial for kernels bigger 15 pixels.
The disadvantage of integral based computation is that it doesn't allow easy changing of the kernel shape (triangle, cross, circle,...) and as a consequence only rectangular kernels are supported