the de la Vallee Poussin kernel on SO(3), B(3/2, 1/2) / B(3/2, kappa + 1/2) t^(2 kappa): nonnegative and concentrated at zero, the kernel recommended for texture analysis

Syntax

SO3DeLaValleePoussinKernel(20)
SO3DeLaValleePoussinKernel(halfwidth=10*degree)

Description

A nonnegative, mean-one kernel for orientation density estimation. Larger kappa gives a narrower peak. For integer kappa its harmonic series is finite; when a halfwidth produces a noninteger kappa, the stored harmonic expansion is truncated.

Evaluate psi at t=cos(omega/2), the cosine of half the rotation angle. Use psi.halfwidth() for the angular width in radians and psi.bandwidth for the maximum degree of its harmonic representation.

Keywords

keyword	default	description
`kappa`		positive concentration parameter; larger values give a sharper peak
`halfwidth`		angular halfwidth in radians, taking precedence over kappa

Output

psi SO3DeLaValleePoussinKernel

Members

halfwidth	the halfwidth in closed form, 2 acos(2^(-1 / (2 kappa)))
radon	the Radon transform: the de la Vallee Poussin kernel on the sphere of the same kappa

Used on

OrientationEmbeddings, EBSDAdvancedMaps, ODFShapes, SO3FunApproximationTheory, SO3FunConvolution, SO3FunDefinition, SO3FunOperations, SO3Kernels

MATLAB’s SO3DeLaValleePoussinKernel_index

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/SO3DeLaValleePoussinKernel_index_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

The class SO3DeLaValleePoussinKernel