The use of intensity-dependent weight functions to "Weberize" L2-based methods of signal and image approximation
Authors:
- Ilona A. Urbaniak,
- Amelia Kunze,
- Dongchang Li,
- Davide La Torre,
- Edward R. Vrscay
Abstract
We consider the problem of modifying L2-based approximations so that they “conform” in a better way to Weber’s model of perception: Given a greyscale background intensity I>0, the minimum change in intensity ΔI perceived by the human visual system is ΔI/Ia=C, where a>0 and C>0 are constants. A “Weberized distance” between two image functions u and v should tolerate greater (lesser) differences over regions in which they assume higher (lower) intensity values in a manner consistent with the above formula. In this paper, we Weberize the L2 metric by inserting an intensity-dependent weight function into its integral. The weight function will depend on the exponent a so that Weber’s model is accommodated for all a>0. We also define the "best Weberized approximation" of a function and also prove the existence and uniqueness of such an approximation.
- Record ID
- CUT75911b29760e4e1ebd90ea15039cb042
- Publication categories
- ;
- Author
- Journal series
- Optimization and Engineering, ISSN 1389-4420, e-ISSN 1573-2924
- Issue year
- 2021
- Vol
- 22
- No
- 4
- Pages
- 2349-2365
- Other elements of collation
- wykr.; Bibliografia (na s.) - 2364-2365; Oznaczenie streszczenia - Abstr.; Data udostępnienia on-line - 2021-04-19; Numeracja w czasopiśmie - Vol. 22, Iss. 4
- Keywords in English
- Weber model of perception, range-dependent weight functions, weberized image metrics, best weberized approximation
- DOI
- DOI:10.1007/s11081-021-09630-2 Opening in a new tab
- URL
- https://link.springer.com/article/10.1007/s11081-021-09630-2 Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 70
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT75911b29760e4e1ebd90ea15039cb042/
- URN
urn:pkr-prod:CUT75911b29760e4e1ebd90ea15039cb042
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.