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Local uniqueness of the circular integral invariant

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Bauer, Martin ; Fidler, Thomas ; Grasmair, Markus:
Local uniqueness of the circular integral invariant.
In: Inverse problems and imaging : IPI. Bd. 7 (Februar 2013) Heft 1. - S. 107-122.
ISSN 1930-8337 ; 1930-8345

Volltext

Link zum Volltext (externe URL): http://dx.doi.org/10.3934/ipi.2013.7.107

Kurzfassung/Abstract

This article is concerned with the representation of curves by means of integral invariants. In contrast to the classical differential invariants they have the advantage of being less sensitive with respect to noise. The integral invariant most common in use is the circular integral invariant. A major drawback of this curve descriptor, however, is the absence of any uniqueness result for this representation. This article serves as a contribution towards closing this gap by showing that the circular integral invariant is injective in a neighbourhood of the circle. In addition, we provide a stability estimate valid on this neighbourhood. The proof is an application of Riesz--Schauder theory and the implicit function theorem in a Banach space setting.

Weitere Angaben

Publikationsform:Artikel
Schlagwörter:Integral invariants, curves, curve descriptors
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Wissenschaftliches Rechnen/Informatik
Peer-Review-Journal:Ja
Titel an der KU entstanden:Ja
Eingestellt am:25. Feb 2013 13:57
Letzte Änderung:10. Jun 2016 10:34
URL zu dieser Anzeige:http://edoc.ku-eichstaett.de/12903/