Algorithm to find the boundary grid points

Question

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.

Note: R-code

data=read.csv(file="trial.csv")

require('ggplot2')

pred.points <- ggplot(data = data,
                      aes(x = lat,
                          y = lon,
                          colour = variable)) + 
  geom_point()

print(pred.points) 

I need an algorithm to find the boundary grid locations for the set?

Here I don't know whether the set is concave or convex.