9.38. Compute Grouping Densities
Group (Subgroup)
Statistics (Reconstruction)
Description
This Filter computes a Grouping Density value for each Parent Feature in a hierarchical reconstruction. Hierarchical reconstructions involve more than one level of segmentation, creating a Feature to Parent Feature relationship (e.g., grains grouped into reconstructed parent grains).
The Grouping Density quantifies how spatially concentrated the child Features of a Parent Feature are relative to the surrounding microstructure. A higher density value indicates the Parent Feature’s volume is large relative to the region its child Features and their neighbors occupy, suggesting a tightly packed grouping. A lower density value indicates the child Features are spread out among many neighbors, suggesting a more dispersed grouping.
How It Works
For each Parent Feature, the filter:
Identifies all child Features that belong to the Parent Feature (via the Parent IDs array).
Collects all contiguous neighbors of those child Features (and optionally non-contiguous neighbors).
Accumulates the volumes of all collected (“checked”) Features into a total checked volume. Each Feature is only counted once, even if it is a neighbor of multiple child Features.
Computes the Grouping Density as:
Grouping Density = Parent Volume / Total Checked Volume
If a Parent Feature has no child Features (total checked volume is zero), the Grouping Density is set to -1.0 to indicate an invalid or empty parent.
Optional Parameters
Use Non-Contiguous Neighbors
When enabled, the filter also queries the Non-Contiguous Neighbor List for each child Feature in addition to the standard Contiguous Neighbor List. This expands the set of checked Features to include neighbors that are nearby but do not share a direct face/edge/vertex with the child Feature. Enable this option if non-contiguous neighbors were used during the original grouping step. Typically the filter “Compute Feature NeighborHoods” is used to generate the Non-contiguous Neighbors lists. That filter’s parameter for the “Multiples of Average Diameter can have a large effect on the final Grouping Density value that is computed.
Find Checked Features
When enabled, the filter produces an additional output array (Checked Features) at the Feature level. For each Feature that was checked during the density computation, this array records which Parent Feature checked it. Since a Feature may be checked by multiple Parent Features (as a neighbor of children belonging to different parents), the assignment goes to the Parent Feature with the largest Parent Volume. This provides a way to see which parent had the strongest influence over each region of the microstructure.
Worked Example
Consider a 20x5 2D Image Geometry with unit spacing (1.0 x 1.0 x 1.0), containing 5 Features arranged as vertical bands and 2 Parent Features:
Features 1, 2, 3 belong to Parent 1 (Parent Volume = 45, i.e. 10 + 20 + 15 cells)
Features 4, 5 belong to Parent 2 (Parent Volume = 55, i.e. 25 + 30 cells)
Feature |
Cells |
Volume |
Parent |
Contiguous Neighbors |
|---|---|---|---|---|
1 |
10 |
10.0 |
1 |
{2} |
2 |
20 |
20.0 |
1 |
{1, 3} |
3 |
15 |
15.0 |
1 |
{2, 4} |
4 |
25 |
25.0 |
2 |
{3, 5} |
5 |
30 |
30.0 |
2 |
{4} |
Parent 1: Child features {1, 2, 3} plus their contiguous neighbors include feature 4 (neighbor of feature 3). Total checked volume = 10 + 20 + 15 + 25 = 70. Density = 45 / 70 = 0.6429.
Parent 2: Child features {4, 5} plus their contiguous neighbors include feature 3 (neighbor of feature 4). Total checked volume = 25 + 30 + 15 = 70. Density = 55 / 70 = 0.7857.
Note that both densities are less than 1.0 because each parent’s children have neighbors belonging to the other parent, expanding the total checked volume beyond the parent’s own volume.
Interpreting Results
Density Value |
Interpretation |
|---|---|
> 1.0 |
Parent volume exceeds the total checked region; the grouping is compact and dense |
= 1.0 |
Parent volume equals the total checked region |
0.0 < d < 1.0 |
Parent volume is smaller than the total checked region; the grouping is dispersed |
-1.0 |
No child features found for this parent (invalid/empty parent) |
Input Parameter(s)
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Find Checked Features |
Bool |
Find checked features |
Non-Contiguous Neighborhood Option
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Use Non-Contiguous Neighbors |
Bool |
Use non-contiguous neighborhoods for computations |
|
Non-Contiguous Neighborhoods |
NeighborListSelection |
List of non-contiguous neighbors for each Feature. |
Input Feature Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Feature Parent Ids |
Array Selection |
Allowed Types: int32 Comp. Shape: 1 |
Input Feature level ParentIds |
Feature Volumes |
Array Selection |
Allowed Types: float32 Comp. Shape: 1 |
The Feature Volumes Data Array |
Contiguous Neighbor List |
NeighborListSelection |
List of contiguous neighbors for each Feature. |
Input Parent Feature Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Parent Volumes |
Array Selection |
Allowed Types: float32 Comp. Shape: 1 |
Input Parent feature level volumes data array |
Output Feature Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Checked Features Name |
DataObjectName |
Output feature level data array to hold ‘Checked Features’ values |
Output Parent Feature Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Grouping Densities Name |
DataObjectName |
Output feature level data array to hold ‘Grouping Densities’ values |
Algorithm Flowchart
References
Example Pipelines
License & Copyright
Please see the description file distributed with this Plugin
DREAM3D-NX Help
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