Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/26206
Title: | A space-based method for the generation of a SchwartzFunction with infinitely many vanishing moments of higher order with applications in image processing |
Author: | Fink, Thomas Kahler, Uwe |
Keywords: | Edge detection q-calculus Shearlets |
Issue Date: | 1-Apr-2019 |
Publisher: | Birkhäuser |
Abstract: | In this article we construct a function with infinitely many vanishing (generalized) moments. This is motivated by an application to the Taylorlet transform which is based on the continuous shearlet transform. It can detect curvature and other higher order geometric information of singularities in addition to their position and the direction. For a robust detection of these features a function with higher order vanishing moments, ∫ℝ𝑔(𝑥𝑘)𝑥𝑚𝑑𝑥=0, is needed. We show that the presented construction produces an explicit formula of a function with ∞ many vanishing moments of arbitrary order and thus allows for a robust detection of certain geometric features. The construction has an inherent connection to q-calculus, the Euler function and the partition function. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/26206 |
DOI: | 10.1007/s11785-018-0832-3 |
ISSN: | 1661-8254 |
Publisher Version: | https://link.springer.com/article/10.1007/s11785-018-0832-3 |
Appears in Collections: | CIDMA - Artigos CHAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Fink-Kähler2019_Article_ASpace-BasedMethodForTheGenera.pdf | 1.12 MB | Adobe PDF |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.