I know this is more bit of a cartographic issue, but maybe somebody would be able to help. I have an old map georeferenced to the openstreetmap with 50 identical points. I want to get the scale of the old map.
I am using Helmert 4-parameter tranformation (similarity) with the equations:
where x and y are the old map coordinates in meters (same as coordinates used from openstreetmap), X0 and Y0 are translations and then there is one scaling and rotation.
Scaling parameter m could be obtained as:
The resolution of the old map is 400 dpi (0.0635 mm per pixel).
I have all the parameters counted now with the least squares method.
Does anybody know how to get the scale of the old map from these parameters? I want the scale in a common form 1 : M (1 : 600 000).
EDIT: Further on I will use iteratively reweighted least squares and I will be omitting those identical points with the biggest spatial error (I am working with very old maps which have mistakes). I will do this to make the definition of scale more accurate. That's why I need to use the transformation parameters for the map scale definition and not only to compare the distances.
Thanks a lot.