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A Simple Standard Orientation Density Function: The Hyperspherical de la Vallée Poussin Kernel
Author(s) -
Schaeben H.
Publication year - 1997
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/1521-3951(199704)200:2<367::aid-pssb367>3.0.co;2-i
Subject(s) - simple (philosophy) , series (stratigraphy) , orientation (vector space) , harmonics , mathematics , representation (politics) , spherical harmonics , kernel (algebra) , mathematical analysis , series expansion , kernel density estimation , fourier series , function (biology) , pure mathematics , physics , geometry , quantum mechanics , statistics , philosophy , epistemology , estimator , paleontology , voltage , evolutionary biology , politics , political science , law , biology
The hyperspherical de la Vallée Poussin kernel ν k (ω) = C ( k ) cos 2 k (ω/2) is introduced as a simple standard orientation density function for texture modeling. The finiteness of its harmonic series expansion advantageously distinguishes it from other known standard functions. Given its halfwidth, the de la Vallée Poussin standard orientation density function allows, for example, to tabulate the degree of series expansion into harmonics required for its exact representation.