You are mostly correct. You can compute the global coordinates from only a few point correspondences, but the system is not linear. If we expand the equation that described the relationship between the local and global coordinates (in 2D for simplicity), we have
After considerable I was able to figure out how to use the Falkolib library. So, after you download the source code from github, you will have a folder called test. In that folder, there will be sample code for using the various detectors.
In my case I experimented with the Falko detector and the OC detector. However I found some issues with the OC ...
The process you are referring to is called point cloud registration (or point matching). The goal of point cloud registration is find the spatial transformation that aligns two point clouds (i.e., sets of points). One of the most popular methods is iterative closest point (ICP), and many variants of ICP exist. Other methods exist as well such as robust point ...