repeated local averaging, the default. A Laplacian is a low pass filter with gain 1 - lk, below one everywhere but at k = 0, so it shrinks every convex region, without bound; and the count of iterations is not a physical quantity, the same call on the same sample measured at a finer step does something else. The averaging counts the vertex itself with the weight of its degree, (2V + Vl + Vr) / 4 for a degree of two, so lambda acts on half the Laplacian and the default of 0.5 is in truth a rate of 0.25

Input

iter number of smoothing steps; default 1
lambda_ smoothing parameter, with each step moving by lambda_/2 towards the neighbour mean; default 0.5

Members

smooth the vertices after iter steps of local averaging at the rate lambda_ / 2, the fixed ones kept

Used on

Grains3DSmoothing

MATLAB’s laplaceFilter_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/laplaceFilter_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.