Numerical problems with the Pascal triangle in moment computation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F16%3A00459096" target="_blank" >RIV/67985556:_____/16:00459096 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.cam.2016.03.033" target="_blank" >http://dx.doi.org/10.1016/j.cam.2016.03.033</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cam.2016.03.033" target="_blank" >10.1016/j.cam.2016.03.033</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Numerical problems with the Pascal triangle in moment computation

Popis výsledku v původním jazyce

Moments are important characteristics of digital signals and images and are commonly used for their description and classification. When calculating the moments and their derived functions numerically, we face, among other numerical problems studied in the literature, certain instabilities which are connected with the properties of Pascal triangle. The Pascal triangle appears in moment computation in various forms whenever we have to deal with binomial powers. In this paper, we investigate the reasons for these instabilities in three particular cases—central moments, complex moments, and moment blur invariants. While in the first two cases this phenomenon is tolerable, in the third one it causes serious numerical problems. We analyze these problems and show that they can be partially overcome by choosing an appropriate polynomial basis.

Název v anglickém jazyce

Numerical problems with the Pascal triangle in moment computation

Popis výsledku anglicky

Moments are important characteristics of digital signals and images and are commonly used for their description and classification. When calculating the moments and their derived functions numerically, we face, among other numerical problems studied in the literature, certain instabilities which are connected with the properties of Pascal triangle. The Pascal triangle appears in moment computation in various forms whenever we have to deal with binomial powers. In this paper, we investigate the reasons for these instabilities in three particular cases—central moments, complex moments, and moment blur invariants. While in the first two cases this phenomenon is tolerable, in the third one it causes serious numerical problems. We analyze these problems and show that they can be partially overcome by choosing an appropriate polynomial basis.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

JD - Využití počítačů, robotika a její aplikace

OECD FORD obor

—

Projekt

<a href="/cs/project/GA15-16928S" target="_blank" >GA15-16928S: Invarianty a adaptivní reprezentace digitálních obrazů</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Computational and Applied Mathematics

ISSN

0377-0427

e-ISSN

—

Svazek periodika

306

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

16

Strana od-do

53-68

Kód UT WoS článku

000378459500004

EID výsledku v databázi Scopus

2-s2.0-84964632518