I have some geological points with following distribution:

I need an algorithm to filter desultory/single points and to group points which are adjacent.
I require the algorithm create something like the following from above points for me

So after applying algorithm on first figure, I need three conglomerate of points, each one known as a critical section, be generated. (like figure 2)
I know some algorithms including Graph Partition, Convex Hull, Polygon Partitioning algorithms, but no one is typically suitable for this problem.
Do you know any specified algorithm for this question?
Look like a typical example case for density based clustering to me.
Look up DBSCAN on Wikipedia.