# How to estimate (if/any) displacement/rotations between 2d line segments taken from 2 data sets

I am having set of pair of line segments (2D). Though each pair should be coincided on top of each other they are not so. I derive these two line sets using image based (e.g. CD) and manual method (e.g. AB). Now I know coordinates of end vertices i.e. vector data.

So, Now I want to find is there any systematic displacements within my extraction. Also, I want to give an overall figure for the accuracy of image based method with respect to manually obtained line segments (My idea is to find the displacement or any rotations are presented in image data with respect to manual)

For that, I am not quite sure how would be my measure.. I mean should I use rmse or some other measures for this. (Actually, I can not imagine how rmse should be measured as my lines are not parallel and equidistant)

For you to get an idea, I should say that lengths and direction of corresponding pairs are not exactly same [see the figure]. (For the analysis, if you say, I need to get equidistant segments, then I can do it by projecting one on the other. I think, I should like this as I want to estimate displacements and rotations)

SO, I want your idea to estimate

any systematic errors of my extractions, in terms of displacement and rotations.