For one of the lectures on 2D planar differential geometry in the series "Image and Video Processing: From Mars to Hollywood With a Stop at The Hospital", the lecturer discusses differential signatures based on parameterization of a 2D planar curve (starts at approx minute 17 in the link attached). I'm not sure if there is some other terminology used but I'm having a hard time finding a software library that can extract such differential signatures once a curve has been segmented/identified in an image. Is there some other name that such a process is called or is there some other method that can extract similar features? I tried searching the OpenCV library but I wasn't certain.
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.
And this work might be quite nice to take a look, if you are concerned about numerics and invariance.