Context
This article outlines a method for evaluating particle spacing by calculating the average distance between particles in a segmented image. The approach computes the average thickness of the continuous phase, which can be interpreted as the average distance between particles.
Quantifying the distance between particles is a common requirement in microstructural analysis, especially in materials science, composites, porous media, and multiphase systems. While several methods exist to evaluate particle spacing, a simple and robust approach is to compute a thickness map of the matrix phase (i.e., the phase without particles).
Prerequisites
An Amira-Avizo 3D Pro license.
Description
The simplest approach is to compute a “thickness map” of the phase without particles, then obtain “image statistics” restricted to that phase. This provides the average thickness, which can be interpreted as the average distance between particles.
1. Load the Data
Start the application with units deactivated and load the tutorial dataset <installation folder>\data\tutorials\PNM\Sponceram.am.
Set the Voxel size to 1, 1, 1:
1.1 Select the dataset.
1.2 Open the Crop Editor.
1.3 Set the Voxel size to 1, 1, 1.
2. Image Segmentation
Perform segmentation of the multiphase dataset to distinguish the dispersed particle phase from the continuous matrix phase, and retain only the matrix phase for further analysis. To do this:
2.1 Attach an Interactive Thresholding module to the dataset.
2.2 Using the preview, adjust the Intensity Range until the matrix phase is correctly segmented. In this example, the selected intensity range is [3070, 9530].
2.3 Apply the module. The image below shows the segmented result (right) compared with the original image (left).
3. Compute Thickness Map
Attach a Thickness Map module to the segmented image, keep the default settings, and apply the module.
Instead of measuring distances directly between particle centroids or surfaces, this method analyzes the void or matrix phase surrounding the particles. By computing the thickness map for this phase, each voxel is assigned the diameter of the largest sphere that fits locally within the matrix.
4. Result Analysis
The average thickness obtained from the matrix phase can be interpreted as the average interparticle distance. Since the thickness map captures the local size of the void space between particles, it provides a meaningful and orientation-independent measure of particle spacing.
Attach an Image Statistics module to the output of the Thickness Map, keep the default parameters, and click Apply. The 3D statistics are then computed. The image below shows the workflow on the left and the results on the right.
Related Links
- Tutorial:
Help > User's Guide >Tutorials > Image Quantification and Analysis Tutorials > Further Image Analysis - Average Thickness of Material in Foam > Further Image Analysis - Average Thickness of Material in Foam
- Module:
Reference Guide > Module Index > Chessboard Distance Map Module