Abstract
Nowadays material science involves powerful 3D imaging techniques such as X-ray computed tomography that generates high-resolution images of different structures. These methods are widely used to reveal information about the internal structure of geological cores; therefore, there is a need to develop modern approaches for quantitative analysis of the obtained images, their comparison, and classification. Topological persistence is a useful technique for characterizing the internal structure of 3D images. We show how persistent data analysis provides a useful tool for the classification of porous media structure from 3D images of hydrocarbon reservoirs obtained using computed tomography. We propose a methodology of 3D structure classification based on geometry-topology analysis via persistent homology.
Highlights
Complex structure analysis is a rapidly developing branch that comprises a broad spectrum of applications and modern data analysis methods
We propose an automated porous media 3D image classification method based on its topological properties using persistent data analysis
We used the proposed algorithm to find and plot the distances between persistent diagrams of selected samples: An—the A Formation type (A), n refers to different binarization threshold and resolution as follows:
Summary
Complex structure analysis is a rapidly developing branch that comprises a broad spectrum of applications and modern data analysis methods. Such structures encompass many spatial features of various scales. Many mathematical methods aim to describe such objects as of statistical origin, this work focuses on the approach based on topological data analysis. Statistical methods are often frequency-based and are well suited for capturing some regularities enclosed in the structure. When it comes to the analysis of significantly irregular formations (mostly naturally occurring), statistical methods may lack the ability to reflect the variety of spatial features present in such objects. The main advantage of the topology-based approach is that it allows for the capture of the main structural features (such as tied parts, tunnels, and cavities) expressed through topological invariants, which appears to be extremely useful when describing such natural objects as core, soil samples, etc
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