the von Mises Fisher kernel on SO(3), proportional to e^(kappa cos omega), kappa > 0

Syntax

SO3vonMisesFisherKernel(90)
SO3vonMisesFisherKernel(halfwidth=10*degree)

Description

A nonnegative kernel with mean one on orientation space, concentrated around the identity rotation. Larger kappa narrows the peak. The direct evaluation uses the closed form, while its harmonic representation 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 SO3vonMisesFisherKernel

Members

halfwidth	the halfwidth in closed form, acos(1 - log(2) / kappa)
radon	the Radon transform: the kernel on the sphere of the same coefficients, in closed form

Used on

ODFModeling, ODFShapes, RadialODFs, SO3Kernels

MATLAB’s SO3vonMisesFisherKernel_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/SO3vonMisesFisherKernel_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 SO3vonMisesFisherKernel