the kernel a density estimate of orientations or directions should use, a de la Vallee Poussin kernel of the halfwidth chosen from the sample

Syntax

psi = calcKernel(ori)

By unbiased cross validation of the degree energies.

psi = calcKernel(ebsd)

A map, folded by its grain ids after calcGrains.

psi = calcKernel(ori, 'conservative', groups=grainId)

The conservative choice, pixels grouped by grain.

psi = calcKernel(ori, 'klcv', samplingSize=500)

Kullback-Leibler cross validation, as MATLAB’s default.

psi = calcKernel(v, noiseFloor=False)

An S2 kernel for directions, no lower bound.

Description

The method chooses the halfwidth:

‘UCV’, the default: the halfwidth that minimises an unbiased estimate of the error of the density, computed from the degree energies of the sample. Orientations and directions.
‘conservative’: the same error with lower confidence bounds on the energies, which gives a wider kernel that does not undersmooth. Orientations and directions.
‘klcv’: Kullback-Leibler cross validation of ten halfwidths, MATLAB’s default.
‘ruleOfThumb’: from the distances of every orientation to its nearest neighbour.
‘magicRule’: from the sample size and the symmetries alone.

‘UCV’ and ‘conservative’ never go below the halfwidth at which the noise of the sample would show as false peaks, unless noiseFloor=False.

Neighbouring pixels of one grain are no independent draws. For a map, ‘UCV’ and ‘conservative’ therefore group the pixels by their grain, which needs the grain ids that calcGrains writes into the map. ‘klcv’, ‘ruleOfThumb’ and ‘magicRule’ refuse orientations taken from a map; select from the grain mean orientations instead.

Above 5000 orientations, ‘klcv’, ‘ruleOfThumb’ and ‘magicRule’ score a random subsample and scale the result to the whole sample. MATLAB’s ‘LSCV’ and ‘BCV’ are not provided.

Input

`o`	orientation, vector3d, or EBSD
`method`	‘UCV’, ‘conservative’, ‘klcv’, ‘ruleOfThumb’ or ‘magicRule’, in any case

Keywords

keyword	default	description
`samplingSize`	`1000`	the number of orientations ‘klcv’ scores
`rng`	`None`	numpy.random.Generator of the subsamples; the energies use a fixed seed by default
`groups`	`None`	the grain id of every orientation, by which the energies fold
`weights`	`None`	the weights of the sample
`bandwidth`	`None`	the degree up to which the energies are computed, by default 64 on SO(3) (doubled when the choice lies at the edge), 256 on the sphere, 32 for ‘conservative’
`halfwidths`	`None`	the candidate halfwidths of the energies
`noiseFloor`	`True`	bound the halfwidth below by the noise of the energies

Output

psi SO3DeLaValleePoussinKernel, or S2DeLaValleePoussinKernel for directions

Used on

EBSD2ODF, OptimalKernel, VectorsDensityEstimation

MATLAB’s vector3d.calcKernel

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/vector3d.calcKernel_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.

vector3d.calcKernel