Neighborhood Filters and the NL-means algorithm

[parazit]

Hi friends.

I am working on Neighborhood Filters and the NL-means algorithm but it's not going for me.

I got the expression to figure out but do not know about the function and its variables.
(you may check at here: http://mathbrain.risc.cnrs.fr/actes_pdf/andi/morel_p.pdf)

I need your help to get some result and figure out the mathematical expression with its variables and constants.

Thank you so much.