A Program Code for Directional and Tensorial Extensions of Fractal, Topological, and Minkowski Functional Analysis for Segmented Multiphase 3D Microstructures

Description

This folder contains the code for phase-level, cut-response and directional/tensorial calculations needed to fulfill a topological analysis of 3D X-CT images of multiphase compositions, both natural and artificial. Numerical data calculated using this code are available at https://data.mendeley.com/drafts/34h8ygpyvb. Source data The source X-ray micro-computed tomography volume and segmented phase volumes used as the benchmark dataset are available from Mendeley Data: https://data.mendeley.com/datasets/b5t3rkn5cg/1 Calculation notes Topological and connected-component calculations use fixed 26-connectivity for foreground phases. Normalized values are reported per 1,000,000 phase voxels. This small code release provides the reference implementation of the parts of the manuscript that are especially sensitive to computational choices: 1. directional spanning and percolation indicators; 2. skeleton-based orientation weights and the orientation-weighted beta1 split; 3. extraction and orientation analysis of enclosed cavities, including the orientation-weighted beta2 split; 4. the rank-two surface Minkowski tensor W_1^{0,2}, obtained from a triangular marching-cubes surface. The release is intentionally limited to these calculations. It does not contain the full X-ray micro-computed tomography preprocessing and segmentation notebook, the source volume, the cut-response implementation, two-dimensional slice analysis, manuscript figures, or numerical result tables. Files ----- directional_metrics.py Reference implementation. requirements.txt Exact package versions used for the release checks. README.txt This description and usage information.

Steps to reproduce

# Reference environment used to validate this release (Python 3.12.2). numpy==1.26.4 pandas==2.2.2 scikit-image==0.26.0 connected-components-3d==3.18.0 openpyxl==3.1.2

Institutions

• Lomonosov Moscow State University

  Moscow, Moscow
• Kola Science Centre

  Murmansk, Apatity

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