Simple 2 Dimensional Curve Matching

In my previous post I have explained about curvature in depth. Now to the practical side, I created a simple application which will use these curvature to compare two simple planar curves. In the following video you can see two feature vectors indicates the similarity of curves;

See the video here.
The angle difference between the feature vectors indicates how similar those shapes are.In the video, you can also see that this matching is invariant to rotation and scale(when shape gets bigger, curvature will becomes lower). Right now the algorithm I used for computing the curvature 'Feature vector' is based on centroid. It needs to be refined further,But the underlying theory is very solid.Also the first impression giving me a very good hope on the concept.

However I am stopping my work on this concept, I don't have time to refine it. Next my target is 'level set methods' or solving the thin plate spline equation. The second one is duper super hard to fully understand , I already attempted it and lost my mind and motivation.Whenever I take it , suddenly everything becomes complicated, even my life (incidents!). So it is like the book of Amun-ra  But after looking it, I knew that i need to improve my 'calculus of variation' skills , and that topic is very nice.The same thing which helps to solve missile guidance problems!.