Suppose that I have a reference polygon, $P_1$, and a test polygon, $P_2$. Both are defined by a certain number of ordered points:
$P_1$ = {$(x_1, y_1), (x2, y2)...(x_{n1}, y_{n1})$}
$P_2$ = {$(x_1, y_1), (x2, y2)...(x_{n2}, y_{n2})$}
$P_2$ is an approximation of $P_1$ and I want to compute the similarity between them. I read that I could compare their turn functions to do it. However, $P_2$ is very noisy and I am afraid that this solution would not work in this case. For example, I expect the following two polygons to result similar (the noise here is exaggerated). What could be the best approach?
