Numerical problems with the Pascal triangle in moment computation

Jaroslav Kautsky, J Flusser

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)53-68
    Number of pages16
    JournalJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
    Volume306
    DOIs
    Publication statusPublished - 2016

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