Orientation-invariant numerically invariant joint signatures in curve analysis. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Aghayan, R.
• Is Part Of: International journal of computer mathematics. Volume 3:Issue 1(2018)
• Page Start: 13
• Page End: 30
• Publication Date: 2018-01-02
• Subjects: Differential and numerically invariant signatures -- group-recognition theorem -- the reparameterization equivalence problem -- signature theorem and its inverse -- curve analysis; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2017.1411394
• Languages: English
• ISSNs: 2379-9927

Abstract

ABSTRACT: 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.