denoises EBSD data by combined first and second order total variation
Total variation alone keeps steps but flattens a smooth gradient into a staircase. Adding a second order term through an infimal convolution lets a linear orientation gradient survive while a boundary stays sharp.
Syntax
F = infimalConvolutionFilter
F.lambda = 0.01;
ebsd = smooth(ebsd,F)Class Properties
| lambda | first order regularization parameter, in [0,1] |
| mu | second order regularization parameter, in [0,1] |
| gamma | parameter of the augmented lagrangian, > 0 |
| maxit | maximum number of iterations |
| eps_rel | relative stopping criterion |
| tol_CG | tolerance of the CG method |
| method | inner solver, 'CG' by default |
| isHex | is the map on a hexagonal grid |
| The filter minimises a matrix | valued image against the TV-norm, |
| \argmin_u{\|u | u_0\|_2^2 + \lambda \|\nabla u\|_{2,1} + \mu \|H u\|_{2,1}}, \lambda,\mu > 0 |
Authors
Johannes Persch, Ronny Bergmann, 09.06.2015, on the second order model of Markus Loeckel, 12.05.15. Later: gauss seidel replaced by mldivide, SPD no longer built by deleting half the entries, projection onto the sphere, a mask, an alternative minimisation in u by preconditioned CG, first and second order combined, and a stopping criterion.
See also
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/infimalConvolutionFilter.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.