10.2. Align Sections (Mutual Information)
Group (Subgroup)
Reconstruction (Alignment)
Description
This Filter segments each 2D slice, creating Feature Ids that are used when determining the mutual information between neighboring slices. The slices are shifted relative to one another until the position of maximum mutual information is determined for each section. The Feature Ids are temporary, they apply to this Filter only and are not related to the Feature Ids generated in other Filters. The algorithm of this Filter is listed below:
Segment Features on each ‘section’ of the sample perpendicular to the Z-direction. This is done using the same algorithm in the [Segment Features (Misorientation)](@ref alignsectionsmisorientation) Filter (only in 2D on each section)
Calculate the mutual information between neighboring sections and store that as the misalignment value for that position. Mutual information is related to the ratio of joint probability to individual probabilities of variables (i.e., p(x,y)/p(x)p(y) ). Details of the actual mutual information calculation can be found in the references below, but can be thought of as the inherent dependence between variables (here the Feature Ids on neighboring sections).
Repeat step 2 for each position when shifting the second slice (relative to the first) from three (3) Cells to the left to three (3) Cells to the right, as well as from three (3) Cells up to three (3) Cells down Note that this creates a 7x7 grid
Determine the position in the 7x7 grid that has the highest mutual information value
Repeat steps 2-4 with the center of each (new) 7x7 grid at the best position from the last 7x7 grid until the best position in the current/new 7x7 grid is the same as the last 7x7 grid
Repeat steps 2-5 for each pair of neighboring sections
Note that this is similar to a downhill simplex and can get caught in a local minimum!
The user choses the level of misorientation tolerance by which to align Cells, where here the tolerance means the misorientation cannot exceed a given value. If the rotation angle is below the tolerance, then the Cell is grouped with other Cells that satisfy the criterion.
The approach used in this Filter is to group neighboring Cells on a slice that have a misorientation below the tolerance the user entered. Misorientation here means the minimum rotation angle of one Cell’s crystal axis needed to coincide with another Cell’s crystal axis. When the Features in the slices are defined, they are moved until disks in neighboring slices align with each other.
If the user elects to use a mask array, the Cells flagged as false in the mask array will not be considered during the alignment process.
Optional Output Data
The user can optionally have the shifts that are generated by the filter stored in various DataArrays in a new Attribute Matrix.
The structure for which looks like this
|-- Image Geometry
|-- Alignment Shifts Data
|-- Slices
|-- Relative Shifts
|-- Cumulative Shifts
In this new structure, what follows is what the created structures represent:
Alignment Shifts Data (Attribute Matrix) - The tuple size here is defined by the number of slices [ie the Z Dimension of the Image Geometry]
Slices (DataArray | 2 component) - The slice indices (stored as uint32s)
Relative Shifts (DataArray | 2 component) - The slices shift relative to previous shift (stored as int64s) [previously known as
newxshiftandnewyshift]Cumulative Shifts (DataArray | 2 component) - The slice’s accumulated shift (stored as int64s)
In previous versions a file would have been produced instead. If you wish to recreate this, you can write the Attribute Matrix as a CSV/Text file.
Input Parameter(s)
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Misorientation Tolerance (Degrees) |
Scalar Value |
Float32 |
Tolerance used to decide if Cells above/below one another should be considered to be the same. The value selected should be similar to the tolerance one would use to define Features (i.e., 2-10 degrees). |
Optional Data Mask
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Use Mask Array |
Bool |
Whether to remove some Cells from consideration in the alignment process. |
|
Cell Mask Array |
Array Selection |
Allowed Types: uint8, boolean Comp. Shape: 1 |
Specifies if the Cell is to be counted in the algorithm. Only required if Use Mask Array is checked. |
Input Cell Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Selected Image Geometry |
Geometry Selection |
Image |
The target geometry on which to perform the alignment |
Cell Quaternions |
Array Selection |
Allowed Types: float32 Comp. Shape: 4 |
Specifies the orientation of the Cell in quaternion representation. |
Cell Phases |
Array Selection |
Allowed Types: int32 Comp. Shape: 1 |
Specifies to which Ensemble each Cell belongs. |
Input Ensemble Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Crystal Structures |
Array Selection |
Allowed Types: uint32 Comp. Shape: 1 |
Enumeration representing the crystal structure for each Ensemble. |
Optional Alignment Output
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Store Alignment Shifts |
Bool |
Whether to store the shifts applied to each section to a collection of Arrays in a new Attribute Matrix |
|
Alignment Attribute Matrix Name |
DataObjectName |
The output attribute matrix where the shifts applied to the section to be stored as DataArrays. |
|
Alignment Slices Data Array Name |
DataObjectName |
The output array name where the slice information related to shifts will be stored. |
|
Alignment Relative Shifts Data Array Name |
DataObjectName |
The output array name where the new shifts relative to previous slice information will be stored. |
|
Alignment Cumulative Shifts Data Array Name |
DataObjectName |
The output array name where the accumulated shift information will be stored. |
References
Journal articles on Mutual Information that are useful:
Elements of information theory. John Wiley & Sons, New York, NY.Gray, R.M. (1990).
Entropy and Information Theory. Springer-Verlag, New York, NY. Nirenberg, S. and Latham, P.E. (2003).
Decoding neuronal spike trains: how important are correlations? Proc. Natl. Acad. Sci. 100:7348-7353. Shannon, C.E. and Weaver, W. (1949).
The mathematical theory of communication. University of Illinois Press, Urbana, Illinois. M zard, M. and Monatanari, A. (2009).
Information, Physics, and Computation. Oxford University Press, Oxford.
Example Pipelines
AlignSectionsMutualInformation
License & Copyright
Please see the description file distributed with this Plugin
DREAM3D-NX Help
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