Group (Subgroup)
Statistics Filters (Morphological)
Description
This Filter calculates the second-order moments of each Field in order to determine the principal axis lengths, pricipal axis directions, aspect ratios and moment invariant Omega3. The principal axis lengths are those of a "best-fit" ellipsoid. The algorithm for determining the moments and these values is as follows:
- Obtain the centroid for each Field.
- For each Cell, determine the x, y and z distance to the centroid of the Field 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 2.
- Sum the individual Ixx, Iyy, Izz, Ixy, Ixz and Iyz values for all Cells belonging to the same Field.
- Find the eigenvalues and eigenvectors of the 3x3 symmetric matrix defined by the 6 values calculated in step 4 for each Field.
- Use the relationship of principal moments to the principal axis lengths for an ellipsoid, which can be found in [4], to determine the Axis Lengths
- Calculate the Aspect Ratios from the Axis Lengths found in step 6.
- Determine the Euler angles required to represent the principal axis directions in the sample reference frame and store them as the Field's Axis Euler Angles.
- Calculate the moment variant Omega3 as definied in [2] and is discussed further in [1] and [3].
Sources:
- Representation and Reconstruction of Three-dimensional Microstructures in Ni-based Superalloys, AFOSR FA9550-07-1-0179 Final Report, 20 Dec 2010.
- 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).
- For a full mathematical description of moment invariants and application to shapes of n-dimensional objects, see: 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.
- 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. _
Parameters
None
Required DataContainers
Voxel
Required Arrays
Type | Default Name | Description | Comment | Filters Known to Create Data |
Cell | GrainIds | Ids (ints) that specify to which Field each Cell belongs. | Values should be present from segmentation of experimental data or synthetic generation and cannot be determined by this filter. Not having these values will result in the filter to fail/not execute. | Segment Fields (Misorientation, C-Axis Misorientation, Scalar) (Reconstruction), Read Dx File (IO), Read Ph File (IO), Pack Primary Phases (SyntheticBuilding), Insert Precipitate Phases (SyntheticBuilding), Establish Matrix Phase (SyntheticBuilding) |
Field | Centroids | X, Y, Z coordinates (floats) of Field center of mass | Filter will calculate Field centroids if not previously calculated | Find Field Centroids (Generic) |
Field | Volumes | Volume (float) in um^3 of the Field. | Filter will calculate volume of each Field if not already calculated | Find Field Sizes (Statistics) |
Created Arrays
Type | Default Name | Description | Comment |
Field | AspectRatios | | |
Field | AxisEulerAngles | | |
Field | AxisLengths | | |
Field | Omega3s | | |
Authors
Copyright: 2012 Michael A. Groeber (AFRL),2012 Michael A. Jackson (BlueQuartz Software)
Contact Info: dream.nosp@m.3d@b.nosp@m.luequ.nosp@m.artz.nosp@m..net
Version: 1.0.0
License: See the License.txt file that came with DREAM3D.
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