I am looking for an algorithm to fit a chain of lines to a set of points/pixels. I am pretty sure that there is a suitable algorithm but I can't think of the correct search words to find it.
The figure shows a chain consisting of 3 individual lines. The lines are always connected, but their connecting points can be moved. The goal is to fit the connecting points such that the resulting lines are in a sense optimal with respect to the points/pixels (here in black with blue border), for example minimzing some distance. It would be nice if one could adapt this optimality criterion, e.g., such that the lines might snap to the point cloud coming from below the point cloud.
In my current problem I could also give some side conditions for the connecting (yellow) points, such as: point 1 has to be somewhere between x and y on the horizontal axis. Also, I could give conditions on the angles between the lines.
It would be awesome if someone could point me in the right direction and tell me actually what I am looking for :)