12.21. Compute Kernel Average Misorientations

Group (Subgroup)

Statistics (Crystallography)

Description

This Filter determines the Kernel Average Misorientation (KAM) for each Cell. This Filter requires an Image Geometry, and the output KAM values are stored in degrees. The user can select the size of the kernel (in voxels) to be used in the calculation. The kernel size entered by the user is the radius of the kernel (i.e., entering values of 1, 2, 3 will result in a kernel that is 3, 5, and 7 Cells in size in the X, Y and Z directions, respectively; see Understanding the Kernel Radius below). The algorithm for the determination of KAM is as follows:

Calculate the misorientation angle between each Cell in a kernel and the central Cell of the kernel only if the kernel cell belongs to the same FeatureId.
Average all of the misorientations for the kernel and store at the central Cell

The Use Feature Ids option controls which Cells within the kernel are included in the average:

Checked (default): only Cells that belong to the same Feature (same Feature Id) as the central Cell are considered — the calculation will not cross grain boundaries. This is the traditional per-grain KAM.
Unchecked: the Feature Id grouping is ignored and the average may cross grain boundaries, producing a per-voxel KAM. A kernel Cell is still excluded if its Feature Id is 0 (invalid/background data) or if its Phase differs from the central Cell’s Phase (averaging is restricted to Cells of the same Phase).

In both modes, Cells with a Feature Id of 0 or a Phase of 0 are considered invalid and receive a KAM value of 0.

Note

All Cells in the kernel are weighted equally during the averaging, though they are not equidistant from the central Cell.

Understanding the Kernel Radius

The Kernel Radius parameter has three components (X, Y, Z), and each value specifies how many Cells to extend outward from the center Cell along that axis. The resulting kernel size along each axis is:

Fig. 1: The kernel radius to kernel size formula.

The kernel extends the specified radius in both directions (e.g., left and right) along each axis, plus includes the center Cell itself – hence the formula. The radius can be set independently for each axis. For example, a Kernel Radius of (1, 2, 3) produces a kernel that is 3 × 5 × 7 Cells in the X, Y, and Z directions, respectively.

1D Examples

Consider a single row of Cells. With a radius of 1, the kernel extends 1 Cell in each direction from the center, giving a kernel of size 3:

Fig. 2: 1D kernel with radius 1 produces a kernel size of 3.

Increasing the radius to 2 extends 2 Cells in each direction, giving a kernel of size 5:

Fig. 3: 1D kernel with radius 2 produces a kernel size of 5.

2D Examples

In 2D, the kernel forms a rectangular region around the center Cell. With a symmetric radius of (1, 1), the kernel is a 3 × 3 square:

Fig. 4: 2D kernel with radius (1, 1, 0) produces a 3x3 kernel of 9 cells.

When different radii are used per axis, the kernel becomes non-square. With X Radius = 1 and Y Radius = 2, the kernel is 3 Cells wide and 5 Cells tall:

Fig. 5: 2D kernel with radius (1, 2, 0) produces a 3x5 kernel of 15 cells.

In 3D, the Z Radius works the same way, extending into adjacent slices above and below the center Cell.

Quick Reference

Fig. 6: Common radius values and their resulting kernel sizes.

Required Input Sources

Cell Feature Ids – produced by a segmentation filter such as Segment Features (Misorientation).
Cell Quaternions – typically read from EBSD data via Read H5EBSD, Read CTF Data, or Read ANG Data.
Cell Phases – typically read from EBSD data alongside the quaternions.
Crystal Structures – ensemble-level array read from EBSD data or created by Create Ensemble Info.

For related per-feature misorientation metrics, see the Compute Feature Reference Misorientations and Compute Misorientation filters.

Input Parameter(s)

Parameter Name	Parameter Type	Parameter Notes	Description
Kernel Radius	Vector of Int32 Values	Order=X,Y,Z	Size of the kernel in the X, Y and Z directions (in number of Cells)
Use Feature Ids	Bool		When checked (default), only kernel Cells belonging to the same Feature as the central Cell are included in the average (per-grain KAM). When unchecked, every in-bounds kernel Cell with a Feature Id greater than 0 and the same phase as the central Cell is included, allowing the average to cross Feature boundaries (per-voxel KAM).

Input Cell Data

Parameter Name	Parameter Type	Parameter Notes	Description
Selected Image Geometry	Geometry Selection	Image	Path to the target geometry
Cell Feature Ids	Array Selection	Allowed Types: int32 Comp. Shape: 1	Specifies to which feature each cell belongs.
Cell Phases	Array Selection	Allowed Types: int32 Comp. Shape: 1	Specifies to which Ensemble each Cell belongs
Cell Quaternions	Array Selection	Allowed Types: float32 Comp. Shape: 4	Specifies the orientation of the Cell in quaternion representation

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

Output Cell Data

Parameter Name	Parameter Type	Parameter Notes	Description
Kernel Average Misorientations	DataObjectName		The name of the array containing the average misorientation (in Degrees) for all Cells within the kernel and the central Cell

Example Pipelines

MassifPipeline
(05) SmallIN100 Crystallographic Statistics

License & Copyright

Please see the description file distributed with this Plugin

DREAM3D-NX Help

If you need help, need to file a bug report or want to request a new feature, please head over to the DREAM3DNX-Issues GitHub site where the community of DREAM3D-NX users can help answer your questions.