12.12. Compute Feature Shapes (Image Geometry)
Group (Subgroup)
Statistics (Morphological)
Description
This Filter characterizes the 3D shape of each Feature (grain or particle) by fitting a best-fit ellipsoid to its voxels. The result is a set of shape descriptors including axis lengths, aspect ratios, axis orientations, and a shape invariant (Omega3).
What This Filter Produces
Semi-Axis Lengths – The half-lengths of the three principal axes of the best-fit ellipsoid (a ≥ b ≥ c). These describe the size and elongation of the grain.
Aspect Ratios – The ratios b/a and c/a, which describe the grain’s shape independent of its size. An equiaxed (roughly spherical) grain has aspect ratios near 1.0; an elongated grain has lower values.
Axis Euler Angles – The orientation of the ellipsoid’s principal axes in the sample reference frame, stored as Euler angles. These describe which direction the grain is elongated.
Omega3 – A dimensionless shape invariant derived from the second-order moments [2]. Omega3 is 1.0 for a perfect sphere and decreases for shapes that deviate from spherical. It provides a single-number summary of how “round” a grain is, independent of its size or orientation.
How This Filter Works
For each Cell, compute the x, y, and z distances from the cell center to the centroid of its parent Feature
Accumulate the second-order moment terms (Ixx, Iyy, Izz, Ixy, Ixz, Iyz) for all Cells in each Feature
Solve for the eigenvalues and eigenvectors of the resulting 3x3 moment tensor for each Feature
Convert eigenvalues to ellipsoid semi-axis lengths using the relationship between principal moments and axis lengths [4]
Compute aspect ratios, axis orientation angles, and the Omega3 shape invariant
Note
For shape analysis on triangle geometry meshes rather than voxelized image geometry, see the Compute Feature Shapes (Triangle Geometry) filter.
Required Input Sources
Cell Feature Ids – produced by a segmentation filter such as Segment Features (Misorientation) or Segment Features (Scalar).
Feature Centroids – produced by Compute Feature Centroids.
Filter Parameters
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Selected Image Geometry |
Geometry Selection |
Image |
The target geometry |
Input Cell Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Cell Feature Ids |
Array Selection |
Allowed Types: int32 |
Specifies to which feature each cell belongs. |
Input Feature Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Feature Centroids |
Array Selection |
Allowed Types: float32 Comp. Shape: 3 |
X, Y, Z coordinates of Feature center of mass |
Output Feature Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Omega3s |
DataObjectName |
3rd invariant of the second-order moment matrix for the Feature, does not assume a shape type (i.e., ellipsoid) |
|
Axis Lengths |
DataObjectName |
Semi-axis lengths (a, b, c) for best-fit ellipsoid to Feature |
|
Axis Euler Angles |
DataObjectName |
Euler angles (in radians) necessary to rotate the sample reference frame to the reference frame of the Feature, where the principal axes of the best-fit ellipsoid are (X, Y, Z) |
|
Aspect Ratios |
DataObjectName |
Ratio of semi-axis lengths (b/a and c/a) for best-fit ellipsoid to Feature |
|
Volumes |
DataObjectName |
The volume of each Feature |
References
[1] Representation and Reconstruction of Three-dimensional Microstructures in Ni-based Superalloys, AFOSR FA9550-07-1-0179 Final Report, 20 Dec 2010.
[2] J. MacSleyne, J.P. Simmons, and M. De Graef. On the use of moment invariants for the automated classification of 3-D particle shapes. Modeling and Simulations in Materials Science and Engineering, 16, 045008 (2008).
[3] A.G. Mamistvalov. n-Dimensional Moment Invariants and Conceptual Mathematical Theory of Recognition n-Dimensional Solids. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(8), 819-831 (1998).
[4] M. Groeber, M. Uchic, D. Dimiduk, and S. Ghosh. A Framework for Automated Analysis and Simulation of 3D Polycrystalline Microstructures, Part 1: Statistical Characterization. Acta Materialia, 56, 1257-1273 (2008).
Example Pipelines
(03) Small IN100 Morphological Statistics(06) SmallIN100 Synthetic
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.