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.
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¶
License & Copyright¶
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