Grouping points that represent lines

Question

I am looking for an Algorithm that is able to solve this problem.

The problem:

I have the following set points:

I want to g

Answer 1

As Micka advised, I used Sequential-RANSAC to solve my problem. Results were fantastic and exactly as I want. The idea is simple:

1. Apply RANSAC with fit-line model on the points.
2. Delete all points that are in-liers of the output of RANSAC.
3. While there are 2 or more points go to 1.

I have implemented my own fit-line RANSAC but unfortnantly I can not share code because it belongs to the company I work for. However, there is an excellent fit-line RANSAC here on SO that was implemented by Srinath Sridhar. The link of the post is : RANSAC-like implementation for arbitrary 2D sets.

It is easy to make a Sequential-RANSAC depending on the 3 simple steps I mentioned above.

Here are some results: