Pattern density function for reconstruction of three-dimensional porous media from a single two-dimensional image

Area of Science:

• Materials Science
• Computational Modeling
• Geology

Background:

• Three-dimensional (3D) reconstruction of porous media is crucial for understanding their spatial structure and physical properties.
• Existing optimal-based algorithms often use autocorrelation functions, which inadequately capture complex morphological features of porous media.
• This limitation hinders accurate 3D reconstruction and subsequent research.

Purpose of the Study:

• To develop an advanced method for accurate 3D porous media reconstruction from a single 2D training image.
• To introduce a pattern density function as a superior objective function for capturing morphological characteristics.
• To enhance the speed and accuracy of the reconstruction process.

Main Methods:

• Proposed a pattern density function, a high-order statistical function, to characterize image patterns.
• Developed an optimal-based algorithm, pattern density function simulation, utilizing the new objective function and a multiple-grid system.
• Incorporated neighborhood statistics, adjacent grid and reversed phase method, and a simplified temperature-controlled mechanism to improve reconstruction speed.

Main Results:

• The pattern density function effectively characterizes image patterns, leading to reconstructions consistent with the training image's features and statistical properties.
• Experiments demonstrated accurate 2D and 3D reconstructions using artificial structures, battery materials, and cores.
• The proposed method outperformed hierarchical simulated annealing and single normal equation simulation in quantitative measures like autocorrelation function, linear path function, and pore network model.

Conclusions:

• The novel pattern density function simulation method enables accurate 3D porous media reconstruction from a single 2D training image.
• This approach overcomes the limitations of traditional methods by better representing morphological features.
• The findings facilitate improved studies on the physical properties and spatial structures of porous media.