The picture pretty much explains it. I will have a collection of line segment graphs to compare against and it's okay if it's $O(n)$ here because the set is the ASCII set or smaller .
I was thinking the algorithm would try to lay the $ in (1) with the symbols in (2), adding up total number of length change, angle change, segment addition / deletions. This is the minimum number of ops to convert one set of line segments to another, intuitively.
Any other ideas?