TY - JOUR

T1 - Digital image reduction for the analysis of topological changes in the pore space of rock matrix

AU - Prokhorov, Dmitriy

AU - Lisitsa, Vadim

AU - Bazaikin, Yaroslav

N1 - Funding Information: D. Prokhorov and Y. Bazaikin implemented the retraction algorithm, constructed the persistence diagrams, and performed clustering under the support of the Mathematical Center in Akademgorodok, the agreement with the Ministry of Science and High Education of the Russian Federation number 075-15-2019-1675. V. Lisitsa performed the numerical estimation of the formation factors of the rock samples under the support of Russian Science Foundation Grant No. 19-77-20004. Numerical simulations were performed using the NKS-1P cluster of the Siberian Supercomputer Center. Publisher Copyright: © 2021 Elsevier Ltd Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/8

Y1 - 2021/8

N2 - 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.

AB - 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.

KW - Digital image reduction

KW - Persistence homology

KW - Porous materials

UR - http://www.scopus.com/inward/record.url?scp=85105499527&partnerID=8YFLogxK

U2 - 10.1016/j.compgeo.2021.104171

DO - 10.1016/j.compgeo.2021.104171

M3 - Article

AN - SCOPUS:85105499527

VL - 136

JO - Computers and Geotechnics

JF - Computers and Geotechnics

SN - 0266-352X

M1 - 104171

ER -