how can I accurately select some of the intersection points of interest from a set of lines in a plot?

I have a plot that includes several intersecting lines. Some intersection points should be selected accurately by a user, and finally, the coordinates of selection points extracted. I should add the “ginput” function hasn’t accuracy, so I can’t use it. How can I solve this problem?

(In the picture you can see the plot, for instance, I should be able to select the blue points.)