A new geometric approach to the affine geometry of curves in the plane and to affine-invariant curve shortening is presented. We describe methods of approximating the affine curvature with discrete finite difference approximations, based on a general theory of approximating differential invariants of Lie group actions by joint invariants. Applications to computer vision are indicated.
Bibliographical noteFunding Information:
* Supported in part by NSF Grant DMS 92-03398. E-mail address: calabi math.upenn.edu. -Supported in part by NSF Grant DMS 95-00931. E-mail address: olver ima.umn.edu. Supported in part by NSF Grant ECS-9122106, by the Air Force Office of Scientific Research Grant F49620-94-1-00S8DEF, by Army Research Office Grants DAAL03-91-G-0019, DAAH04-93-G-0332, and DAAH04-94-G-0054, and by Image Evolutions, Ltd. E-mail address: tannenba ee.umn.edu.