Modeling irregular-shaped pores based on the brightness of pixels in a digital image

Damdinova Tatiana Tsybikovna ORCID: 0000-0002-3597-3262 PhD in Technical Science Associate Professor, East-Siberian State University of Technology and Management 670000, Russia, Republic of Buryatia, Ulan-Ude, Klyuchevskaya str., 40 V dtatyanac@mail.ru Other publications by this author     Damdinov Zorigto Shiripovich ORCID: 0009-0002-1614-3746 Master's degree; Department of Software Engineering and Artificial Intelligence; East Siberian State University of Technology and Management 670013, Russia, Republic of Buryatia, Ulan-Ude, Klyuchevskaya str., 40 V vdzorigto@mail.ru Prudova Lyudmila Yur'evna PhD in Technical Science Associate Professor, Department of Engineering and Computer Graphics, East Siberian State University of Technology and Management 670013, Russia, Buryatiya oblast', g. Ulan-Ude, ul. Klyuchevskaya, 40 prudova456@mail.ru Other publications by this author

Bubeev Innokentii Trofimovich PhD in Technical Science Associate Professor; Department of Engineering and Computer Graphics; East Siberian State University of Technology and Management 670013, Russia, Republic of Buryatia, Ulan-Ude, Klyuchevskaya str., 40b it_bubeev@mail.ru Other publications by this author

Introduction

One of the relevant directions in the field of materials science is the study and modeling of processes occurring in capillary-porous bodies. These facilities play an important role in areas such as oil production, medicine, construction, production of filters and batteries, and the creation of new materials, where accurate understanding and control of processes occurring in porous media is required.

Modern modeling methods and existing models for the representation of porous objects often do not take into account the irregularity of structures, which leads to a decrease in modeling accuracy and limits their application. In this regard, there is a need to develop new methods and tools for modeling processes in irregular structures of capillary-porous bodies.

Setting the task

Capillary-porous bodies are materials characterized by the presence of multiple pores filled with liquid or gas. These materials are widely used in various fields, such as medicine (in terms of the penetration of drugs into tissues), the production of filters (for determining pore sizes that affect filtration quality), the creation of new building materials with specified properties (for example, moisture permeability and heat transfer), the creation of new composite high-strength, lightweight materials. Understanding and modeling the processes occurring in porous structures is an important task, as it allows to improve the characteristics and efficiency of these materials when they are used ^[1].

The porosity of a material is defined as the ratio of the pore volume to the total volume of the material and is an important characteristic affecting its physical and mechanical properties ^[2]. Porous systems can vary significantly in shape, size, and pore distribution. According to geometric features, porous bodies are divided into regular porous structures with regular alternation of individual pores or cavities and channels connecting them in the body volume, as well as structures with random shapes, sizes, orientation and mutual arrangement. Depending on the geometric and topological characteristics, pores can be classified into several types: open, closed, dead-end and through ^[3].

The methods of studying porous structures are considered in ^[4]. The classification of the porous structure of materials by origin and dimensional and geometric features is presented here. The authors emphasize that "There are more than 60 analytical methods for studying the porous structure of solids, systematized according to the physical principles of determining its characteristics." Irregular structures of capillary-porous bodies have complex geometric shapes, which complicates their analysis and modeling of processes in them ^[5]. Instrumental methods for determining porosity are known, which are labor-intensive and material-intensive ^[6]. These methods require significant time and resources for conducting experiments and subsequent data processing. As a result, the process of studying capillary-porous bodies becomes extremely expensive, which limits the possibilities for conducting extensive research. The main problem is the lack of universal methods that could accurately describe and predict the condition of such materials. Existing models are often based on simplified assumptions, which leads to a decrease in the accuracy of modeling and evaluation in order to obtain an adequate understanding of the method or principles of operation of the objects under study.

Modern modeling methods include the use of well-developed computer vision methods ^{[7, 8]}, computational methods for analyzing images of porous structures and creating appropriate models ^[9]. Solving modern scientific problems, such as the creation of new materials with the necessary characteristics, require more accurate data, which can be obtained by analyzing their digital images. Digital image processing methods make it possible to automate the process of data collection and processing, which significantly reduces research time.

Note that traditionally, simplified models are used in pore modeling, representing instead shapes of known shapes ^[9-11] – circles, spheres, squares, cubes, etc., and the structure of a porous object is defined in the form of lattices, cells, etc. (Fig.1, Fig.2)

Figure 1 – Three-dimensional model of a porous body in spherical shape

Figure 2 – Simplified voxel model of a porous body

The main directions of modern methods of modeling porous materials can be represented using computer modeling programs - PoreSpy and OpenPNM. (Fig.3, fig.4). The PoreSpy application describes the pores on the plane, and OpenPNM describes the structure of a porous object in 3D.

Figure 3 – Example of PoreSpy processing of a porous body

OpenPNM is an open source project that also focuses on modeling porous materials. Unlike PoreSpy, in OpenPNM, the porous structure is represented as connected spheres (Fig.4). This approach is more realistic from the point of view of modeling porous materials, since spheres can more accurately match the shape and size of pores in porous structures. However, this representation is also abstract, since the spheres representing the pores are interconnected by straight lines, which leads to limitations in modeling accuracy, especially for porous materials of irregular shape.

Figure 4 – Example of processing a porous body by the OpenPNM project

Algorithm for modeling pores of irregular structure

The software solution for modeling pores of irregular structure is user input of images of sections of a porous body, similar to ^{[12, 13]}. According to the processed image of the pore, the boundaries of the slices are distinguished based on information on the brightness of the pixels, followed by the construction of a 3D model based on the selected boundary points of the slices.

To model real processes, first of all it is necessary to get the most approximate idea of the shape of a porous object. One of the main methods for modeling porous objects is surface modeling methods for creating smooth and continuous surfaces, which allows for a more accurate description of the shape of the pores and their distribution in the material. It should be noted that the surface modeling apparatus is quite well developed^{[14, 15]}.

There are various methods for constructing surface models, each of which has its own characteristics and applications ^{[16, 17]}. The method using analytical models involves the creation of surfaces based on equations describing known geometric shapes - cylindrical, canonical, spherical and elliptical surfaces. Surfaces can also be constructed based on curves. Curves obtained from cross-sections of an object can be used to create a three-dimensional model by extrusion or rotation. Surfaces can also be constructed from existing surfaces using interpolation and extrapolation techniques. For example, to create a surface model from several known surfaces, you can use the bilinear interpolation method, which allows you to smoothly transition between specified surfaces. This approach is used to model complex objects.

Another approach to constructing surfaces is to use data based on an array of points. An array of points for constructing a surface can be processed using methods that include the creation of polygonal meshes, binomial surfaces, bicubic Koons surfaces, as well as quadrangular and triangular Bezier surfaces ^[15]. In practice, many curves and surfaces are composed of relatively simple smooth parts - segments (curves) or fragments of surfaces, each of which can be described with sufficient accuracy by an elementary function of one or two variables. These methods are suitable for solving the problem of restoring irregularly shaped objects, where an array of points is used as the source data.

Results

To solve the problem of modeling a three–dimensional pore model, we selected, as before ^[12], the most accessible porous object, cheese, with irregularly shaped pores (Fig.5). After the binarization stage of the initial digital image of the slice, the most pronounced pores were identified, from which one large pore was selected to create its volumetric model.

a b c

Figure 5 – Digital image of a cheese slice with pores irregular pore model a is the original image, b is the pores isolated after binarization, c is the time for creating a 3D model

Based on the brightness of the pixels of the selected pore, it is possible to assume the estimated pore size in depth ^[18]. To do this, a brightness histogram is constructed from the grayscale image of the pore, on which global and local maxima are programmatically determined (Fig.6).

Figure 6 - Pore pixel brightness histogram with maxima

Arrays of boundary points of the pore sections are obtained from the pore points grouped at the level of these luminosities (Fig. 7).

Figure 7 – Grouping of points at selected brightness levels

Further, cubic spline interpolation was performed for each of the arrays of boundary points, the transverse and longitudinal sections of which are shown in Figure 8. (Note that for the convenience of visual representation of the simulation result, the lowest part of the pore was omitted.) Then, in the next step, surface modeling is performed based on the calculated splines (Fig. 9).

a b

Figure 8 – Spline interpolation of the boundary points of the cheese pore

a – cross sections, b – longitudinal sections

Figure 9 – Surface model of irregular pores

According to the developed method of geometric modeling of irregular pores, it is possible to obtain further information for analysis about the size and volume of pores, the porosity of the object as a whole, as well as to analyze processes in porous objects ^{[19, 20]}. If necessary, to increase the accuracy of the shape, the number of brightness levels for grouping points can be increased.

Conclusion

Solving the problem of modeling the pores of objects with an irregular structure has shown that the computing power of modern computers and modern methods of geometric modeling make it possible to obtain an adequate three-dimensional model of the pore surface of a real object. The application of this solution will make it possible to reproduce with a high degree of accuracy the complex geometric structures characteristic of porous materials, which will allow us to develop this field further for the analysis of porous bodies with irregular structures and processes in them.