XPCorrelate

Code to register and analyse multidimensional maps e.g. nanoindentation maps vs EBSD, etc. The default setup is to analyse Nanoindentation mapping against EBSD data, and if desired, EPMA data. Data formats are expected as:

Nanoindentation: .mat file following the format given in XPImport. See below. 
EBSD: ctf or h5 file. 
EPMA: tiff file.

This reproduces the method presented in "Nanoindentation in multi-modal map combinations: A Correlative Approach to Local Mechanical Property Assessment" by CM Magazzeni et al. 2020 (arXiv / publication).

The code is provided for research proposes only. If you use this software, please cite the above paper.

Requirements, external:

• Matlab
• MTEX v5.0.3
• For second correction, ECC @ https://github.com/harshagurnani/ECC-for-Image-registration
• For CTF saving in the second correction, credit to Dr. Azdiar A. Gazder and Dr. Frank Niessen for https://github.com/frankNiessen/exportCTF

Requirements, internal:

• XPImport @ https://github.com/cmmagazz/XPressImport in order to prepare the nanoindentation data

What does XPCorrelate do?

XPCorrelate uses, as a first pass, a set of user-defined points across the property maps in order to align and interpolate the 2d datasets. Simply point, by clicking on some points you can see in both images, the scripts can set them on top of one another. The first transformation is calculated and applied to the EBSD dataset, followed by the EPMA dataset. Immediately, you can correlate each pixel against the two datasets and get structure-property scatter plots.

Following this, you can manipulate the 2d datasets which will affect your structure-property maps. In the example given in the paper, removing the datapoints near grain boundaries can significantly "clean" the declination angle vs hardness scatter plot. This is all done in the PCDM scripts bit by bit, where you can change for your dataset and requirements.

For further improvement, you can feed the "quite well" aligned maps into a second correction script (g_ scripts, nomenclature is described below), where edges are used to better align these two datasets. The description of how this works is very well described in the ECC script (from @harshagurnani), but in summary: cross-correlation can be used to determine how well the edges sit on top of one another, you can find a transformation that fits this as well as possible.

How to use XPCorrelate

Most of the process flow is described in XPC_InputDeck.m This starts with several sections:

1. Clearing workspace and loading relevant packages (MTEX and ECC etc)
2. User input section. Largely self explanatory in place and short enough to read in place
3. Loading and cleaning: loads the nanoindentation mapping and ebsd data. Formats the filepath for saving things properly, and crops nanoindentation data if need be.
4. Run the EBSD registration script. See this for details. Uses affine transformation based on User input points (>=4) This creates the variable datastack, a struct where each variable should be an array of size no of x indents * no of y indents. The convention used is that data should be structured in grids which start at 0,0, and X(2,1) is larger than X(1,1), and Y(1,2) is larger than Y(1,1). Datastack structure:

datastack.X               %X position
datastack.Y               %Y position
datastack.S               %Surface displacement
datastack.D               %Depth
datastack.L               %Load
datastack.M               %Modulus
datastack.St              %Stiffness^2/Load
datastack.H               %Hardness
datastack.phi1            %phi1  (ebsd)
datastack.Phi             %Phi   (ebsd)
datastack.phi2            %phi2  (ebsd)
datastack.phase           %phase (ebsd)
datastack.BCebsd          %Band Contrast (ebsd)

5. Save figures
6. Run step 4 and 5 for EPMA data.
7. Save the registered ebsd data
8. Grain boundary analysis: creates some new datastack.GBD %Distance to nearest grain boundary datastack.GBSZ %Size of grain in which point resides datastack.gID %ID of grain in which point resides
9. Save all variables to .mat file.

Other scripts

Naming convention:

• f_: function. Primarily related to the main XPC_InputDeck, usually run as is.
• g_: Second correction. Comes after f.
• l_: Least square function, to be edited and used post-manipulation.
• p_: post-correction data manipulators.
• v_: visualisation.
• z_: Scrap, but handy.

From here on, scripts are run ad-hoc as needed. In order as needed to recreate the results in CM Magazzeni et al 2020:

PCDM I.e. Post-Corrected Data Manipulator Needed to plot various graphs, and contains other snippets which weren't used in publication but are fun or useful.

lsqfitting-XXX lsqfitting.m : the first least square fitting script. Used to plot H vs Phi, with or without filtering based on GBD. lsqfittingOXYGEN_XXX.m : various least square fitting scripts for O vs H.