Detecting set of planes from point cloud

I have a set of point cloud, and I would like to test if there is a corner in a 3D room. So I would like to discuss my approach and if there is a better approach or not in terms of speed, because I want to test it on mobile phones.

I will try to use hough tranform to detect lines, then I will try to see if there are three lines that are intersecting and they make a two plane that are intersecting too.