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Description | Options | Required Arrays | Created Arrays | Authors

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Description

The user has the option of entering a distribution choice: Beta, LogNormal or Power. The 3-D moment invariants of second order are three numbers, represented by the symbols 0≤Ωi≤ 1 (i = 1, 2, 3), which are computed starting from the shape of an object. The moment invariants are invariant with respect to either similarity or affine coordinate transformations, which renders them particularly useful as quantitative shape descriptors that are independent of the reference frame used to represent the object(s).
Omega1 and Omega2 are related to aspect ratios, while Omega3 is useful for shape characterization. Details of the Omega3 shape descriptors are given in the Sources that include Tables of all three Omega expressions for basic geometrical shapes.
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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.

Parameters

NameType
Distribution TypeChoices

Required Arrays

TypeNameComment
CellGrainIds
FieldCentroids
FieldEquivalentDiameters
FieldVolumes

Created Arrays

TypeNameComment
FieldAspectRatios
FieldAxisEulerAngles
FieldAxisLengths
FieldOmega3s

Authors

Copyright: 2012 Michael A. Groeber (AFRL),
  2012 Michael A. Jackson (BlueQuartz Software)
Contact Info: dream3d@bluequartz.net
Version: 1.0.0
License: See the License.txt file that came with DREAM3D.

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