How do I calculate the "difference" between two sequences of points?

I have two sequences of length n and m. Each is a sequence of points of the form (x,y) and represent curves in an image. I need to find how different (or similar) these sequences are given that fact that

1. one sequence is likely longer than the other (i.e., one can be half or a quarter as long as the other, but if they trace approximately the same curve, they are the same)

2. these sequences could be in opposite directions (i.e., sequence 1 goes from left to right, while sequence 2 goes from right to left)

   I looked into some difference estimates like Levenshtein as well as edit-distances in structural similarity matching for protein folding, but none of them seem to do the trick. I could write my own brute-force method but I want to know if there is a better way.

Thanks.