Digital image reduction for the analysis of topological changes in the pore space of rock matrix

The paper presents an original algorithm for reducing three-dimensional digital images to improve the computing performance of persistence diagrams. These diagrams represent changes in pore space topology during essential or artificial changes in the structure of porous materials. The algorithm has linear complexity because during reduction, each voxel is checked not more than seven times. This check, as well as the removal of voxels, takes a constant number of operations. We illustrate that the algorithm's efficiency depends on the complexity of the original pore space and the size of filtration steps. The application of the reduction algorithm allows the computation of one-dimensional persistence Betti numbers for models of up to 5003 voxels by using a single computational node. Thus, it can be used for routine topological analysis and the topological optimization of porous materials.

Automated summary

The paper introduces an original algorithm for reducing three-dimensional digital images to enhance the computing performance of persistence diagrams, which can be used for topological optimization of porous materials. The algorithm has linear complexity and is efficient in calculating one-dimensional persistence Betti numbers for models of up to 5003 voxels.