grain2d.smoothBoundary

A method of grain2d.

the grains with the pixel staircase of their boundaries turned into smooth curves; MATLAB’s grain2d.smoothBoundary

Syntax

grains = smoothBoundary(grains)

grains = smoothBoundary(grains, 5, moveTriplePoints=True)

grains = smoothBoundary(grains, 3, simplify=False, refine=False)

grains = smoothBoundary(grains, 3, simplify=0.5, refine=1)

grains = smoothBoundary(grains, taubinFilter())

grains = smoothBoundary(grains, curvatureFilter(smoothingLength=3))

Description

calcGrains gives a boundary as a staircase of pixel edges, every segment along a grid axis. The smoothing repairs it in three steps:

• simplify: drops every vertex whose removal moves the boundary by less than a tolerance, by default d / sqrt(2) for the pixel spacing d, which removes the staircase and nothing else.
• refine: resamples what is left at equal arc length, by default d, so that the vertices are evenly spaced and no longer tied to the grid.
• the boundaryFilter smooths, by default laplaceFilter(iter), iter steps of local averaging.

The first two steps matter: simplifying alone leaves a curve as a few long chords whose corners the smoothing cuts off, and smoothing alone leaves straight boundaries scattered around the grid axes. They change the segments, though, and a resampled segment no longer lies between one pair of pixels: where gB.ebsdId is read per segment, as calcGBND does, switch them off with simplify=False, refine=False.

The junctions (triple and quadruple points, and the ends of the inner boundary on the outer one) stay fixed unless moveTriplePoints=True, the outer boundary of the map unless moveOuterBoundary=True. MATLAB’s second output, the filter used, is the one passed or laplaceFilter(iter).

Input

Keywords

Output

Example

Compare reconstructed and smoothed boundaries on the small Forsterite sample. The sample file is downloaded and cached on first use.

import matplotlib.pyplot as plt
from mtex import mtexdata, calcGrains, smoothBoundary, degree, plot, hold

ebsd = mtexdata('small', verbose=False)['Forsterite']
grains = calcGrains(ebsd, angle=10*degree, minPixel=5)
smoothed = smoothBoundary(grains, 5)
plot(grains.boundary, lineColor='black', lineWidth=2, displayName='Reconstructed')
hold(True)
plot(smoothed.boundary, lineColor='red', lineWidth=1, displayName='Smoothed')
hold(False)
print('Grains before and after:', grains.size, smoothed.size)
plt.show()

Black shows the pixel-derived outlines and red the smoothed geometry. Smoothing changes the curves, while the pixel grain ids and the grain membership remain those of the reconstruction.

Grains before and after: 15 15

See also

grain2d.simplifyBoundary, grain2d.refineBoundary, grain2d.reduceBoundary, boundaryFilter, laplaceFilter, taubinFilter, curvatureFilter, huberFilter, GrainSmoothing

MATLAB’s grain2d.smoothBoundary

@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}
}