What algorithm to use to find (x,y) ends of lines or their intersection?

Question

Image processing

For example:

How can this be done more efficiently?
Thanks in advance for your replies

Answer 1

Well, in general, classically, the problem of finding the intersection of two lines is solved by solving (tautology?) a system of two equations, each of which describes a line.
It is possible to offer you a more accurate solution only if you have some sane data on the task. For example, how do you describe line segments?

Answer 2

Use one of the feature detector .
I think FAST will do