Paper Info
Title
Numerical problems with the Pascal triangle in moment computation.
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.
Year
DOI
Venue
2016
10.1016/j.cam.2016.03.033
J. Computational Applied Mathematics
Keywords
Field
DocType
Stable calculations,Polynomials,Moments,Pascal triangle,Orthogonal moments,Moment invariants
Polynomial basis,Pascal's triangle,Polynomial,Mathematical analysis,Digital signal,Binomial,Invariant (mathematics),Velocity Moments,Mathematics,Computation
Journal
Volume
Issue
ISSN
306
C
0377-0427
Citations 
PageRank 
References 
0
0.34
12
Authors
2
Name
Order
Citations
PageRank
Jaroslav Kautsky110820.75
Jan Flusser23067215.61