I was wondering if Riemann-Stieltjes integral still works when both of the functions $f$ and $g$ are discrete and two dimensional? Something like below: $$\int f(x,y) dg(x,y)$$
By using the parametric formula of the curve I would be able to write $x$ and $y$ in terms of one variable like angle $\alpha$ but I don't know how that would help me solve this integral which is actually a summation on discrete 2D signals. Any Suggestions?