A method of embedding.

the rotations whose images are closest to the embedding, the projection of a point of the Euclidean space back onto the orientations

Syntax

r = e.project()

The rotation of every image.

r = mean(e).project()

The rotation of the mean image.

r = e.project(maxIter=50, tol=1e-8)

Fewer steps, a coarser stop.

Description

Every target is scaled to the norm of an image (a zero target to the identity image), the best of a few seed rotations is taken, and steepest ascent of the dot product of the image with the target follows; all targets are handled at once, in blocks of chunk. The result is a rotation, e.orientation() the orientation in the crystal frame of e; MATLAB’s second output, the projected embedding, is embedding of that orientation.

Input

e embedding, the targets

Keywords

keyword default description
seeds None the rotations the ascent starts from, the best one per target; by default a few spread over the fundamental region
maxIter 200 the largest number of ascent steps
tol 1e-10 the ascent stops where the norm of the gradient falls below it
chunk 2048 the number of targets handled at once

Output

r rotation, one per image, whose image is closest to it

See also

embedding, embedding.orientation, OrientationEmbeddings

MATLAB’s embedding.project

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/embedding.project_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.