Numerical problems with the Pascal triangle in moment computation
| Autor: | Jaroslav Kautsky, Jan Flusser |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Binomial (polynomial)
Applied Mathematics Computation Mathematical analysis 010103 numerical & computational mathematics 02 engineering and technology Pascal's triangle 01 natural sciences Moment (mathematics) Computational Mathematics symbols.namesake Polynomial basis Velocity Moments Face (geometry) 0202 electrical engineering electronic engineering information engineering symbols Applied mathematics 020201 artificial intelligence & image processing 0101 mathematics Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 306:53-68 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2016.03.033 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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