moving window rms slope

I am trying to calculate the rms slope of a moving window:

zc = elevation of central cell

zb = elevation of cells along the border of the window size

sb = distance of central cell to a border cell

N is the width of window size

To add, I am looking at a 2D matrix

I am having trouble computing the slope.. I have thought of using convolution and diff functions, but they lead to nowhere.

Please advice.

Thanks in advanced!