Local Uniqueness of the Circular Integral Invariant

Details Local Uniqueness of the Circular Integral Invariant Local Uniqueness of the Circular Integral Invariant

2011-07-21

arxiv.org/abs/1107.4257v2

Mathematics

Numerical Analysis

Scientific paper

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 locally unique in a neighbourhood of the circle. The proof is an application of Riesz-Schauder theory and the implicit function theorem in a Banach space setting.

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