Given any two discrete curves, we would like to compare them and want to find the difference between them. It might be a very easy job for human eyes, but the computers are not as good as human brains.

In our curves matching project, we try to figure out the orientation of the curves at first One general way to do that is to use the average point or the mean. The problem of this method is that when there is a perturbation on the curves, the result change a lot and becomes not as accurate. Instead, we use our new median point, the stability is improved significantly.

The following are general two curves without any perturbation: