Compute MomentInvariants (2D)

Group (Subgroup)

Statistics (Statistics)

Description

This Filter computes the 2D Omega-1 and Omega 2 values from the Central Moments matrix and optionally will normalize the values to a unit circle and also optionally save the Central Moments matrix as a DataArray to the Cell Feature Attribute Matrix. Based off the paper by MacSleyne et. al [1], the algorithm will calculate the 2D central moments for each feature starting at feature id = 1. Because feature id 0 is of special significance and typically is a matrix or background it is ignored in this filter. If any feature id has a Z Delta of > 1, the feature will be skipped. This algorithm works strictly in the XY plane and is meant to be applied to a 2D image. Using the research from the cited paper certain shapes can be detected using the Omega-1 and Omega-2 values. An example usage is finding elliptical shapes in an image:

See below figure from [1] that can help the user classify objects.

Example appllication of filter to identify elliptical particales (red) which are differentiated from non-elliptical particals (purple)

Example appllication of filter to identify elliptical particales (red) which are differentiated from non-elliptical particals (purple)

Parameters

Name Type Description
Normalize MomentInvariants Bool Should the algorithm normalize the results to unit circle.
Save Central Moments Bool Write the Central Moments to a new Data Array

Required Geometry

ImageGeom

CentralMomentsArrayPath 2

Required Objects

Kind Default Name Type Component Dimensions Description
Cell Attribute Array FeatureIds int32_t (1) The Feature Ids array to analyze for ellipsoids
Cell Attribute Array FeatureRectArray int32_t (4) Array holding the min xy and max xy pixel coordinates of each feature id

Created Objects

Kind Default Name Type Component Dimensions Description
Cell Attribute Array Omega1 float (1) Omega1 value
Cell Attribute Array Omega2 float (1) Omega2 value
Cell Attribute Array CentralMoments float (3)(3) Central Moments value

Citations

[1] J.P. MacSleyne, J.P. Simmons, M. De Graef, On the use of 2-D moment invariants for the automated classification of particle shapes, Acta Materialia, Volume 56, Issue 3, February 2008, Pages 427-437, ISSN 1359-6454, http://dx.doi.org/10.1016/j.actamat.2007.09.039. http://www.sciencedirect.com/science/article/pii/S1359645407006702

Acknowledgements

The authors would like to thank Dr. Marc De Graef from Carnegie Mellon University for enlightening discussions and a concrete implementation from which to start this filter.

Example Pipelines

Please see the description file distributed with this plugin.

DREAM3D Mailing Lists

If you need more help with a filter, please consider asking your question on the DREAM3D Users mailing list: https://groups.google.com/forum/?hl=en#!forum/dream3d-users