Grain Reconstruction
Grain Reconstruction from EBSD data.
Let us first import some example EBSD data and reduce it to a subregion of interest.
plotx2east mtexdata forsterite ebsd = ebsd(inpolygon(ebsd,[5 2 10 5]*10^3)); close all plot(ebsd)

Basic grain reconstruction
We see that there are a lot of not indexed measurements. For grain reconstruction we have to three different choices how to deal with these unindexed regions:
- leaf them unindexed
- assign them to the surrounding grains
- a mixture of both, e.g., assign small notindexed regions to the surrounding grains but keep large notindexed regions
By default MTEX uses the first method.
The second parameter that is involved in grain reconstruction is the threshold misorientation angle indicating a grain boundary. By default this value is set to 10 degree.
All grain reconstruction methods in MTEX are accessable via the command calcGrains which takes as input an EBSD data set and returns a list of grain.
grains = calcGrains(ebsd,'angle',10*degree)
grains = grain2d Phase Grains Mineral Symmetry Crystal reference frame Phase 0 1139 notIndexed 1 244 Forsterite mmm 2 177 Enstatite mmm 3 104 Diopside 12/m1 X||a*, Y||b*, Z||c Properties: GOS, meanRotation
The reconstructed grains are stored in the variable grains. Note that also the notIndexed measurements are grouped into grains. This allows later to analyse the shape of these unindexed regions.
To visualize the grains we can plot its boundaries by the command plotBoundary.
% start overide mode hold on % plot the boundary of all grains plot(grains.boundary,'linewidth',1.5) % stop overide mode hold off

The grainId and how to select EBSD inside specific grains
Beside the list of grains the command calcGrains returns also two other output arguments.
[grains,ebsd.grainId,ebsd.mis2mean] = calcGrains(ebsd,'angle',7.5*degree)
grains = grain2d Phase Grains Mineral Symmetry Crystal reference frame Phase 0 1139 notIndexed 1 245 Forsterite mmm 2 177 Enstatite mmm 3 105 Diopside 12/m1 X||a*, Y||b*, Z||c Properties: GOS, meanRotation ebsd = EBSD Phase Orientations Mineral Color Symmetry Crystal reference frame 0 4052 (20%) notIndexed 1 14093 (69%) Forsterite light blue mmm 2 1397 (6.9%) Enstatite light green mmm 3 759 (3.7%) Diopside light red 12/m1 X||a*, Y||b*, Z||c Properties: bands, bc, bs, error, mad, x, y, grainId, mis2mean Scan unit : um ebsd = EBSD Phase Orientations Mineral Color Symmetry Crystal reference frame 0 4052 (20%) notIndexed 1 14093 (69%) Forsterite light blue mmm 2 1397 (6.9%) Enstatite light green mmm 3 759 (3.7%) Diopside light red 12/m1 X||a*, Y||b*, Z||c Properties: bands, bc, bs, error, mad, x, y, grainId, mis2mean Scan unit : um
�The second output argument grainId is a list with the same size as the EBSD measurements that stores for each mesurement the corresponding grainId. The above syntax stores this list directly inside the ebsd variable. This enables MTEX to select EBSD data by grains. The following command returns all the EBSD data that belong to grain number 33.
ebsd(grains(33))
ans = EBSD Phase Orientations Mineral Color Symmetry Crystal reference frame 3 5 (100%) Diopside light red 12/m1 X||a*, Y||b*, Z||c bands bc bs error mad x y grainId mis2mean 7 140 255 0 1 9750 2000 33 0.523233 7 137 234 0 1 9800 2000 33 0.663778 7 152 245 0 1.1 9850 2000 33 0.942424 7 105 153 0 0.8 9900 2000 33 1.41445 7 110 211 0 0.8 9750 2050 33 0.747032 Scan unit : um
and is equivalent to the command
ebsd(ebsd.grainId == 33)
ans = EBSD Phase Orientations Mineral Color Symmetry Crystal reference frame 3 5 (100%) Diopside light red 12/m1 X||a*, Y||b*, Z||c bands bc bs error mad x y grainId mis2mean 7 140 255 0 1 9750 2000 33 0.523233 7 137 234 0 1 9800 2000 33 0.663778 7 152 245 0 1.1 9850 2000 33 0.942424 7 105 153 0 0.8 9900 2000 33 1.41445 7 110 211 0 0.8 9750 2050 33 0.747032 Scan unit : um
Misorientation to mean orientation
The third output argument is again a list of the same size as the ebsd measurements. The entries are the misorientation to the mean orientation of the corresponding grain.
plot(ebsd,ebsd.mis2mean.angle ./ degree) hold on plot(grains.boundary) hold off colorbar

We can examine the misorientation to mean for one specific grain as follows
% select a grain by coordinates myGrain = grains(9075,3275) plot(myGrain.boundary,'linewidth',2) % plot mis2mean angle for this specific grain hold on plot(ebsd(myGrain),ebsd(myGrain).mis2mean.angle ./ degree) hold off colorbar
myGrain = grain2d Phase Grains Mineral Symmetry Crystal reference frame Phase 1 1 Forsterite mmm GOS meanRotation 0.0443014 66.8061

Filling not indexed holes
It is important to understand that MTEX distinguishes the following two situations
- a location is marked as not indexed
- a location does not occur in the data set
A location marked as not indexed is interpreted by MTEX as: at this position there is no crystal, whereas for a location that does not occur in the data set is interpreted by MTEX as: it is not known whether there is a crystal or not. Just to remind you, the later assumption is nothing special as it applies at all locations but the measurement points.
A location that does not occur in the data is assigned in MTEX to the same grain and phase as the closest measurement point - this may also be a not indexed point. Hence, filling holes in MTEX means to erasing them from the list of measurements, i.e., instead of telling MTEX there is no no crystal we are telling MTEX: we do not know what there is.
The exremal case is to say whenever there is a not indexed measurement we actually do not know anything and allow MTEX to freely guess what happens there. This is realized by removing all not indexed measurements or, equivalently, computing the grains only from the indexed measurements
% compute the grains from the indexed measurements only grains = calcGrains(ebsd('indexed')) plot(ebsd) % start overide mode hold on % plot the boundary of all grains plot(grains.boundary,'linewidth',1.5) % mark two grains by location plot(grains(11300,6100).boundary,'linecolor','m','linewidth',2,... 'DisplayName','grain A') plot(grains(12000,4000).boundary,'linecolor','r','linewidth',2,... 'DisplayName','grain B') % stop overide mode hold off
grains = grain2d Phase Grains Mineral Symmetry Crystal reference frame Phase 1 103 Forsterite mmm 2 32 Enstatite mmm 3 71 Diopside 12/m1 X||a*, Y||b*, Z||c Properties: GOS, meanRotation

We observe, especially in the marked grains, how MTEX fills notindexed regions and connects otherwise seperate measurements to grains. As all information about not indexed regions were removed the reconstructed grains fill the map completely
plot(grains,'linewidth',2)

Inside of grain B there is a large not indexed region and we might argue that is not very meaningfull to assign such a large region to some grain but should have kept it not indexed. In order to decide which not indexed region is large enaugh to be kept not indexed and which not indexed regions can be filled it is helpfull to know that the command calcGrains also seperates the not indexed regions into "grains" and we can standard grain functions like area or perimeter to analyze these regions.
[grains,ebsd.grainId,ebsd.mis2mean] = calcGrains(ebsd);
notIndexed = grains('notIndexed')
notIndexed = grain2d Phase Grains Mineral Symmetry Crystal reference frame Phase 0 1139 notIndexed Properties: GOS, meanRotation
We see that we have 1139 not indexed regions. A good measure for compact regions vs. cluttered regions is the quotient between the area and the boundary length.
% plot the not indexed regions colorcoded according the the quotient between % number of measurements and number of boundary segments plot(notIndexed,log(notIndexed.grainSize ./ notIndexed.boundarySize)) colorbar

Regions with a high quotient are blocks which can be hardly correctly assigned to a grain. Hence, we should keep these regions as not indexed and only remove the not indexed information from locations with a low quotient.
% the "not indexed grains" we want to remove toRemove = notIndexed(notIndexed.grainSize ./ notIndexed.boundarySize<0.8) % now we remove the corresponding EBSD measurements ebsd(toRemove) = [] % and perform grain reconstruction with the reduces EBSD data set [grains,ebsd.grainId,ebsd.mis2mean] = calcGrains(ebsd); plot(grains)
toRemove = grain2d Phase Grains Mineral Symmetry Crystal reference frame Phase 0 1134 notIndexed Properties: GOS, meanRotation ebsd = EBSD Phase Orientations Mineral Color Symmetry Crystal reference frame 0 610 (3.6%) notIndexed 1 14093 (84%) Forsterite light blue mmm 2 1397 (8.3%) Enstatite light green mmm 3 759 (4.5%) Diopside light red 12/m1 X||a*, Y||b*, Z||c Properties: bands, bc, bs, error, mad, x, y, grainId, mis2mean Scan unit : um

We see that there are some not indexed regions are left blank. Finally, the image with the raw EBSD data and on top the grain boundaries.
% plot the raw data plot(ebsd) % start overide mode hold on % plot the boundary of all grains plot(grains.boundary,'linewidth',1.5) % mark two grains by location plot(grains(11300,6100).boundary,'linecolor','m','linewidth',2,... 'DisplayName','grain A') plot(grains(12000,4000).boundary,'linecolor','r','linewidth',2,... 'DisplayName','grain B') % stop overide mode hold off

Grain smoothing
The reconstructed grains show the typicaly staircase effect. This effect can be reduced by smoothing the grains. This is particulary important when working with the direction of the boundary segments
% plot the raw data plot(ebsd) % start overide mode hold on % plot the boundary of all grains plot(grains.boundary,angle(grains.boundary.direction,xvector)./degree,'linewidth',3.5) colorbar % stop overide mode hold off

We see that the angle between the grain bounday direction and the x-axis takes only values 0, 45 and 90 degree. After applying smoothing we obtain a much better result
% smooth the grain boundaries grains = smooth(grains) % plot the raw data plot(ebsd) % start overide mode hold on % plot the boundary of all grains plot(grains.boundary,angle(grains.boundary.direction,xvector)./degree,'linewidth',3.5) colorbar % stop overide mode hold off
grains = grain2d Phase Grains Mineral Symmetry Crystal reference frame Phase 0 5 notIndexed 1 115 Forsterite mmm 2 33 Enstatite mmm 3 77 Diopside 12/m1 X||a*, Y||b*, Z||c Properties: GOS, meanRotation

Grain reconstruction by the multiscale clustering method
When analyzing grains with gradual and subtle boundaries the threshold based method may not lead to the desired result.
Let us consider the following example
mtexdata single
oM = ipdfHSVOrientationMapping(ebsd);
oM.inversePoleFigureDirection = mean(ebsd) * oM.whiteCenter;
oM.colorStretching = 5;
plot(ebsd,oM.orientation2color(ebsd.orientations))
Hint: You might want to use the point group "432" for colorcoding!

We obeserve that the are no rapid changes in orientation which would allow for applying the threshold based algorithm. Setting the threshold angle to a very small value would include many irrelevant or false regions.
grains_high = calcGrains(ebsd,'angle',1*degree); grains_low = calcGrains(ebsd,'angle',0.5*degree); figure plot(ebsd,oM.orientation2color(ebsd.orientations)) hold on plot(grains_high.boundary) hold off figure plot(ebsd,oM.orientation2color(ebsd.orientations)) hold on plot(grains_low.boundary) hold off


As an alternative MTEX includes the fast multiscale clustering method (FMC method) which constructs clusters in a hierarchical manner from single pixels using fuzzy logic to account for local, as well as global information.
Analogous with the threshold angle, a single parameter, C_Maha controls the sensitivity of the segmentation. A C_Maha value of 3.5 properly identifies the subgrain features. A C_Maha value of 3 captures more general features, while a value of 4 identifies finer features but is slightly oversegmented.
grains_FMC = calcGrains(ebsd,'FMC',3.5) % smooth grains to remove staircase effect grains_FMC = smooth(grains_FMC);
grains_FMC = grain2d Phase Grains Mineral Symmetry Crystal reference frame Phase 1 13 Al m-3m GOS meanRotation 0.0084358 153.098 0.0060217 153.427 0.01229 153.367 0.016496 67.4424 0.00481028 165.006 0.0141737 165.398 0.00276888 165.437 0.012498 124.393 0.0215271 167.311 0.0196901 164.93 0.0190118 130.205 0.019412 131.038 0.0124594 166.019
We observe how this method nicely splits the measurements into clusters of similar orientation
plot(ebsd,oM.orientation2color(ebsd.orientations)) % start overide mode hold on plot(grains_FMC.boundary,'linewidth',1.5) % stop overide mode hold off

MTEX 4.0.10 |