Fingerprint theorems for curvature and torsion zero-crossings

It has been shown by A.L. Yuille and T. Poggio (1983) that the scale-space image of a signal determines that signal uniquely up to constant scaling. Here, generalization of the proof given by Yuille and Poggio is presented. It is shown that the curvature scale-space image of a planar curvature determines the curvature uniquely, up to constant scaling and a rigid motion. The results show that a 1-D signal can be reconstructed using only one point from its scale-space image. This is an improvement of the result obtained by Yuille and Poggio