Cartan's moving frame method and its application to the geometry and evolution of curves in the Euclidean, affine and projective planes
Abstract
This article is a general introduction to Cartan's moving frame method which is elegant, simple and of an algorithmic nature. We have demonstrated how to use it systematically on three examples relevant to computer vision, curves in the euclidean, affine and projective planes, and derived the corresponding Frenet equations. We have then used these equations to show that the analysis of the deformation of plane curves according to an intrinsic heat equation could be done in a common framework, yielding very similar expressions for the evolution of the three curvature invariants.