10.12. Compute Feature Shapes
Group (Subgroup)
Statistics (Morphological)
Description
This Filter calculates the second-order moments of each Feature in order to determine the principal axis lengths, principal axis directions, aspect ratios and moment invariant Omega3s. The principal axis lengths are those of a “best-fit” ellipsoid. The algorithm for determining the moments and these values is as follows:
For each Cell, determine the x, y and z distance to the centroid of the Feature that owns the Cell
For each Cell, calculate Ixx, Iyy, Izz, Ixy, Ixz and Iyz using the x, y and z distances determined in step 1.
Sum the individual Ixx, Iyy, Izz, Ixy, Ixz and Iyz values for all Cells belonging to the same Feature
Find the eigenvalues and eigenvectors of the 3x3 symmetric matrix defined by the 6 values calculated in step 3 for each Feature
Use the relationship of principal moments to the principal axis lengths for an ellipsoid, which can be found in [4], to determine the Semi-Axis Lengths
Calculate the Aspect Ratios from the Semi-Axis Lengths found in step 5.
Determine the Euler angles required to represent the principal axis directions in the sample reference frame and store them as the Feature’s Axis Euler Angles.
Calculate the moment variant Omega3 as definied in [2] and is discussed further in [1] and [3]
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] On the use of moment invariants for the automated classifcation of 3-D particle shapes, J. MacSleyne, J.P. Simmons and M. De Graef, Modeling and Simulations in Materials Science and Engineering, 16, 045008 (2008).
[3] n-Dimensional Moment Invariants and Conceptual Mathematical Theory of Recognition n-Dimensional Solids, Alexander G. Mamistvalov, IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 20, NO. 8, AUGUST 1998, p. 819-831.
[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 (2008), 1257-1273.
Example Pipelines
(01) SmallIN100 Morphological Statistics
(06) SmallIN100 Synthetic
License & Copyright
Please see the description file distributed with this Plugin
DREAM3D-NX Help
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