Applying the top hat filter to the inner and outer edges of a region

Applying the top hat filter to the inner and outer edges of a region

I'm looking forward to applying the top hat filtering to some region using
MATLAB. The region will have borders. If we imagine the borders, there is
an inside to the border, and an outside.
So, when I want to apply the filter, how can I determine that I want to do
that to the inside of the border for instance?
Thanks.