DREAM3D User Manual
Find Field Shapes

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:

  1. Obtain the centroid for each Field.
  2. For each Cell, determine the x, y and z distance to the centroid of the Field that owns the Cell.
  3. For each Cell, calculate Ixx, Iyy, Izz, Ixy, Ixz and Iyz using the x, y and z distances determined in step 2.
  4. Sum the individual Ixx, Iyy, Izz, Ixy, Ixz and Iyz values for all Cells belonging to the same Field.
  5. Find the eigenvalues and eigenvectors of the 3x3 symmetric matrix defined by the 6 values calculated in step 4 for each Field.
  6. 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
  7. Calculate the Aspect Ratios from the Axis Lengths found in step 6.
  8. 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.
  9. Calculate the moment variant Omega3 as definied in [2] and is discussed further in [1] and [3].
    Sources:
  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. 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.
  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. _

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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