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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.

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 without prior specification of the nature of the sets.

Any suggestion or reference will be greatly appreciated.

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 provides boundary points, provided we know the nature of the set (i.e., whether is it 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.

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.

Let us consider a set $S$ consisting of a collection of grid locations $(i,j),i,j=1,\ldots,n$, in 2-dimensional gridded plane. Here the point $(i,j)$ corresponds to a rectangular grid in the X-Y plane.

This set has the property that one can reach any element $(i,j)\in S$ from any other element $({i'},{j'})\in S$ through a series of neighbouring grid points which are also in $S$.

I am interested about the shape of the set $S$ in the plane, for this reason I need the boundary grid locations of the set $S$.

How can I get the boundary grid locations for the set?

I hope this give clear picture about the problem which I am interested in.

Any suggestion and reference will be greatly appreciated.

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 provides boundary points, provided we know the nature of the set (i.e., whether is it 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.