Extracting informations from a graphic

I’m currently working on a data processing algorithm which involve (for now) grabing values from bidimentional graphs (x;y values) by hand. It is used to do polynomial fitting. I speak about this kind of graph: enter image description here

Because the amount of data to extract from these graphics can be very huge (multiple lines with different parameters) I realised that it could be really time consuming for the user. All the graphs we have are pictures.

I would like to know if in the huge world of image processing something exist for extracting a finite number of points with their coordinates from a graph.

Thank you.