library for computing differential signatures from 2D planar curves
Recently I have worked on a projective invariant line signature:


  Projective splines and estimators for planar curves
  Thomas Lewiner and Marcos Craizer International Journal of Computer Vision, 2000
  http://thomas.lewiner.org/pdfs/projective_splines_jmiv.pdf


That paper proposes a projective length and a projective curvature estimators for plane curves, when the curves are represented by points together with their tangent directions. The goal of the paper is an invariant spiral construction in the canonical projective frame. 

If you like to implement this paper, the paper is pretty self contained. And I posted the details which are kind of hidden in my blog along with some code.

If you don't need projective invariance then I would suggest Fourier Descriptors or Elliptical Fourier Descriptors. There are many MATLAB implementations available for that.

And this work might be quite nice to take a look, if you are concerned about numerics and invariance.