Find 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]
Parameters¶
None
Required Geometry¶
Image
Required Objects¶
| Kind | Default Name | Type | Component Dimensions | Description |
|---|---|---|---|---|
| Cell Attribute Array | FeatureIds | int32_t | (1) | Specifies to which Feature each Cell belongs |
| Feature Attribute Array | Centroids | float | (3) | X, Y, Z coordinates of Feature center of mass |
| Attribute Matrix | CellFeatureData | Cell Feature | N/A | Feature Attribute Matrix of the selected Feature Ids |
Created Objects¶
| Kind | Default Name | Type | Component Dimensions | Description |
|---|---|---|---|---|
| Feature Attribute Array | AspectRatios | float | (2) | Ratio of semi-axis lengths (b/a and c/a) for best-fit ellipsoid to Feature |
| Feature Attribute Array | AxisEulerAngles | float | (3) | Euler angles (in radians) necessary to rotate the sample reference frame to the reference frame of the Feature, where the prinicpal axes of the best-fit ellipsoid are (X, Y, Z) |
| Feature Attribute Array | SemiAxisLengths | float | (3) | Semi-axis lengths (a, b, c) for best-fit ellipsoid to Feature |
| Feature Attribute Array | Omega3s | float | (1) | 3rd invariant of the second-order moment matrix for the Feature, does not assume a shape type (i.e., ellipsoid) |
| Feature Attribute Array | Volumes | float | (1) | 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
DREAM.3D Mailing Lists¶
If you need more help with a Filter, please consider asking your question on the DREAM.3D Users Google group!