Orientation-invariant numerically invariant joint signatures in curve analysis

摘要

This paper investigates Group-recognition theorem, Equivalence Problem, and Signature theorem for numerically invariant joint signatures. Shape invariants must be independent of the viewpoint in which the object of interest is observed. We first show that the current formulation depends on the curve-orientation and thus is viewpoint-dependent. Next, we present the orientation-invariant version of NIJSs which guarantees the correctness of these theorems. In addition, we introduce a corrected version of the affine NIJS which is also a closer approximation compared with the current formulation.