total variation denoising of orientation maps
The filter minimises the distance to the measured orientations plus alpha times the total variation, the sum of the misorientations between neighbouring pixels. The absolute values keep sharp steps, so a subgrain boundary survives the smoothing instead of being blurred away. The default method is half-quadratic minimisation on manifolds: R. Bergmann, R. H. Chan, R. Hielscher, J. Persch, G. Steidl, Restoration of Manifold-Valued Images by Half-Quadratic Minimization, Inverse Problems and Imaging 10 (2016). The method 'proximal' is a cyclic proximal point algorithm for the same functional; it ignores the threshold and the quality of the pixels.
Syntax
F = l1TVFilter
F = l1TVFilter(smoothingLength)
F.method = 'proximal';
ebsd = smooth(ebsd,F)Input
| smoothingLength | the wavelength damped to half its amplitude, in the units of the map; four pixel distances when empty |
Class Properties
| smoothingLength | the wavelength damped to half its amplitude |
| alpha | regularization parameter, larger means smoother; empty means the one of the smoothing length |
| method | 'halfQuadratic' or 'proximal' |
| l1DataFit | use the l1 norm for data fitting, else the l2 norm |
| l1TV | use the l1 norm for regularization, else the l2 norm |
| iterMax | maximum number of iterations |
| tol | stopping criterion of the half-quadratic iteration |
| eps | l1 relaxation parameter |
| threshold | threshold for subgrain boundaries |
| lambda | step sizes of the proximal point iteration |
| isHex | is the map on a hexagonal grid |
See also
EBSDFilter EBSD.smooth splineFilter infimalConvolutionFilter
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/l1TVFilter.l1TVFilter.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.