3D Segmentation of Rods from X-Ray Scans

Reconstructing individual rod positions and orientations from volumetric X-ray imaging of dense packings.

Motivation

To study entanglement experimentally, we need to measure the actual 3D configuration of rods in a packing — not just macroscopic quantities like total density or mechanical response. X-ray computed tomography (CT) provides volumetric images of opaque packings, but extracting individual rod geometries from these images is a non-trivial image analysis problem.

The challenge: in a dense packing, rods overlap in 2D projections, their X-ray contrast is similar, and artifacts from the reconstruction can blur boundaries. We need a pipeline that robustly segments individual rods in 3D and extracts their centerlines, orientations, and contact points.

What the toolkit does

The matlab-image-processing toolkit provides a MATLAB-based pipeline for this segmentation task. Key components:

Preprocessing: Noise filtering, contrast enhancement, and thresholding to binarize the volume
Individual rod segmentation: Separation of touching rods using morphological operations and watershed algorithms
Centerline extraction: Skeletonization of each segmented rod to extract its 3D centerline
Orientation analysis: Fitting a line to each centerline to extract rod orientation vector
Group analysis: SCRIPT_checkEveryGroup.m and SCRIPT_assessEveryGroup.m automate the analysis across multiple sample groups

The toolkit is organized with:

functions/ — Core analysis functions
scripts/ — High-level automation scripts
mex/ — Compiled MATLAB extensions for performance-critical steps
Data stored as .mat files for efficient I/O

Downstream use

The extracted rod configurations feed directly into the computational analyses:

Caging number computation: Given the 3D positions and orientations of all rods, compute how many rods cage each rod (see entanglement overview)
Linking number measurement: Compute pairwise \(Lk\) for all rod pairs to quantify topological entanglement
Comparison with simulation: The experimentally measured configurations can be directly compared with configurations from rod-dynamics-3d and rod-placement

Technical notes

Rod segmentation in 3D is fundamentally harder than in 2D because contact surfaces between rods in a dense packing are difficult to resolve with finite voxel resolution. The toolkit addresses this by:

Using anisotropic filtering that preserves rod-shaped features
Performing clustering analysis to group voxels into individual rod candidates
Applying geometric constraints (rod length, aspect ratio) to validate candidates

The result is a list of \(N\) rods with positions, orientations, and estimated uncertainties — a compact geometric description of the packing that can be analyzed with all the other tools in this research program.

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