I have a set of points $S=\{(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)\}$. Then how to find the boundary points (which is a subset of $S$) of $S$?

There are methods like convex hull, concave hull and $\alpha$-hull, which produce boundary points, provided we know the nature of the set (i.e. whether it is convex or concave).

But I have lots of sets with different sizes and I need boundary points for each of the set. So it is not convenient to know the nature of each set. Rather I need a method which will give the boundary points of each set with out prior specification of the nature of the sets.

Any suggestion and reference will be greatly appreciated.