=Paper=
{{Paper
|id=Vol-3702/paper37
|storemode=property
|title=Algorithms and Methods for Comparing Microstructures of Materials Based on Their Images
|pdfUrl=https://ceur-ws.org/Vol-3702/paper37.pdf
|volume=Vol-3702
|authors=Valeriia Hritskova,Oleh Semenenko,Mariia Shapovalova,Oleksii Vodka
|dblpUrl=https://dblp.org/rec/conf/cmis/HritskovaSSV24
}}
==Algorithms and Methods for Comparing Microstructures of Materials Based on Their Images==
https://ceur-ws.org/Vol-3702/paper37.pdf
Algorithms and methods for comparing microstructures
of materials based on their images
Valeriia Hritskova1, Oleh Semenenko1, Mariia Shapovalova1 and Oleksii Vodka1
1 National Technical University Β«Kharkiv Polytechnic InstituteΒ», 2, Kyrpychova str., Kharkiv, 61002, Ukraine
Abstract
The study aims to develop robust image processing algorithms capable of automatically identifying and
characterizing individual grains within material microstructures. These algorithms extract essential
grain properties, including area, shape factor, and orientation angle. Additionally, the study explores
which grain characteristics are most effective for microstructure comparison. The proposed algorithm
segments microstructure images to isolate individual grains. Grain properties (e.g., area, perimeter,
circularity) areare quantified. The distributions of grain characteristics are analyzed using violin plots.
Both visual comparisons and statistical measures (mean, variance, skewness) informs microstructure
similarity. Proposed algorithms have been tested on validation images and errors have been estimated.
Understanding microstructure properties is crucial for material design, quality control, and
performance optimization. The proposed algorithms contribute to automated microstructure analysis,
benefiting fields such as materials science, engineering, and manufacturing.
Keywords
Image Processing Algorithm, Feature Extraction, Grain Characteristics, Violin Plots, Statistical
Comparison 1
1. Introduction
Algorithms and methods for comparing the microstructures of materials based on their images
have become the object of considerable attention in modern research. The significance of this
area lies in the possibility of obtaining information about the properties of materials that affect
their functionality and application. The development of algorithms for comparing
microstructures has become an important task in the context of finding optimal solutions in
materials science. The initiation of this process involved establishing a complex for generating
microstructures; however, a challenge emerged concerning the comparison between these
generated structures and real ones. In light of this, the solution to this problem involved the
development of image processing methods for comparing the generated microstructures with
experimental data.
The microstructures of materials play a fundamental role in their properties and functionality,
determining their mechanical, thermal, and electrical characteristics. The contribution of
microstructures to the development of science and technology cannot be overstated, as their
understanding and optimization have a significant impact on the design and production of
materials. Research emphasizes not only the significant role of the microstructure itself but also
its components. Particular attention is given to the process of microstructure formation - crystal
growth. Since physical experiments are difficult to study the characteristics of microstructure
evolution during grain growth, computer modeling is used as an effective alternative.
Using the cellular automata method, various models have been considered so far: 2D modeling
of microstructures [4], [5], 3D modeling of microstructures [6]-[8], [19], [20] modeling using
probabilities [9], [10], modeling of crystal growth by recrystallization [11]-[12]. The study of
these models has allowed us to analyze various aspects of the processes of microstructure
formation, their evolution, and their influence on the properties of materials. The use of different
CMIS-2024: Seventh International Workshop on Computer Modeling and Intelligent Systems, May 3, 2024,
Zaporizhzhia, Ukraine
valeriia.hriskova@infiz.khpi.edu.ua (V. Hritskova); oleh.semenenko@infiz.khpi.edu.ua (O. Semenenko);
mariia.shapovalova@khpi.edu.ua (M. Shapovalova); oleksii.vodka@khpi.edu.ua (O. Vodka)
0009-0002-6825-726X (V. Hritskova); 0009-0003-7275-2412 (O. Semenenko); 0000-0002-4771-7485 (M.
Shapovalova); 0000-0002-4462-9869 (O. Vodka)
Β© 2024 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
modeling approaches allows for obtaining a more complete understanding of the physical and
chemical processes that occur during crystal growth and microstructure formation.
A special application MatViz3D (https://github.com/MME-NTU-KhPI/MatViz3D) has been
developed for computer modelling of the crystallization process and generation of
microstructures. The main advantages of the application are the three-dimensional generation of
microstructures, which allows to obtain detailed and realistic images of the material structure,
the selection of cell neighborhoods for the diversity of generation, and the ability to follow the
step-by-step crystallization process. Overall, MatViz3D is a powerful tool for modeling, analyzing,
and visualizing material microstructures using a variety of approaches and techniques.
Once the microstructure is generated, it is necessary to conduct research and identify the
characteristics inherent in the model. The identification of model characteristics is carried out
through data processing and systematization. Among the tools that can be used for this purpose,
a special place is occupied by processing data in the form of images. Using techniques such as
image analysis and image processing, it is possible to identify the main features of
microstructures, such as grain size, shape, and distribution of grains in space. For example, the
use of segmentation algorithms can automatically identify individual grains in microstructure
images, which simplifies further analysis. In addition, the use of image processing techniques to
determine various characteristics, such as grain size, shape, and texture, provides quantitative
data that can be used for further analysis and comparison with experimental data or other
models. This approach to image processing is becoming increasingly common in the study of
material microstructures and plays an important role in the development of the fields of materials
science and mechanics [14]-[18].
Having processed the image and obtained the grain properties of the microstructures, it
becomes necessary to develop an algorithm for their comparison. In this context, a special
emphasis is placed on comparing the distributions and statistical characteristics of each of the
grain properties. This approach will allow for a deeper analysis and comparison of material
microstructures, contributing to the further development of the fields of materials science and
mechanics.
Although there are already software tools, such as CLEMEX [21] and Fiji [22], designed to
process images and detect regions on them, this study developed a system for comparing grain
characteristics that goes beyond the capabilities of these programs. The developed system allows
for automated comparison of the distribution of microstructure characteristics and determines
statistical parameters that are not available in existing software. This expands the analytical
capabilities and provides a deeper understanding of the microstructures of materials.
2. Problem statement
The objective of this study is to develop image processing algorithms for automatically identifying
regions in an image that correspond to individual grains in the microstructure of a material. The
resulting algorithms should also provide the calculation of the characteristics of each grain, such
as area, shape factor, orientation angle, etc.
Further, the developed algorithms will be tested on test images of microstructures, after which
the results will be presented. Based on the analysis of these results, recommendations should be
made as to which grain characteristics can be used for more effective comparison of
microstructures and which may have limited variability and therefore be less important for
comparison.
In addition, the study will develop an algorithm for comparing microstructures by analyzing
the distributions of grain characteristics. For this purpose, violin plots will be used to visualize
the distributions of grain size and other characteristics. In addition to comparing the visual
characteristics, the statistical properties of the distributions will be analyzed, which will provide
additional data on the similarity or difference of microstructures in different cases.
3. Methodology
The study and reproduction of microstructures plays a key role in the development of new
materials with unique properties that will find applications in a wide range of industries,
including electronics, aviation, medicine, and energy. Microstructures are defined as the
organization and arrangement of materials at the microscopic level, and they have a significant
impact on the properties and behavior of materials. It is important to note that the formation of
microstructures is a complex and multifactorial problem, which is influenced by a variety of
factors, including chemical composition, temperature, pressure, cooling rate, and others.
Furthermore, microstructures can exhibit extreme diversity depending on the type of material,
the number of impurities, the manufacturing process, and the conditions.
The key stage is the formation of the internal structure of the material, as it allows analyzing
the interaction between its elements, such as location, quantity, and nature. This helps to
determine the optimal conditions for achieving the desired material parameters (e.g. strength,
wear resistance, thermal conductivity, etc.). The detailed analysis and presentation of such
material information can enable modeling and simulation with an accurate description of specific
microstructural features. It also opens up the possibility of performing highly accurate
engineering calculations using well-known methods, such as the finite element method.
The ability to characterize microstructural features using statistical methods is a significant
advance in materials science. This helps to increase the accuracy of material property predictions.
Conventional techniques and methodologies employed for the quantitative analysis of three-
dimensional structures using data derived from two-dimensional images or their cross-sections
enable the prediction and determination of three-dimensional structural attributes. These
encompass parameters such as volume, surface area, boundary length, and other descriptors
derived from the analysis of images acquired from various orientations or viewpoints. Such
approaches facilitate the evaluation of geometric and morphological characteristics of structures
and materials.
However, there are microstructural parameters that cannot be determined from a single two-
dimensional section, such as the connectivity of features, the true shape of inclusions, and the
number of inclusions per unit volume. The need for a more complete characterization of
microstructures has led to the development of techniques that allow for the direct acquisition of
three-dimensional microstructural data of grain structures, such as serial sectioning,
intergranular corrosion, and various X-ray tomography-based techniques. This includes
references [2] and [3], where the authors quantify a set of microstructural parameters and their
relationships to determine morphological characteristics using the serial sectioning technique to
collect 3D crystallographic data. Many of the parameters have been quantified in two-
dimensional space, while only a few have been determined in three-dimensional space, but the
study of the relationships between these parameters has remained limited [1].
Thus, despite the significant progress in microstructure generation and the development of
related applications, this topic requires further research and development. There is potential for
improving generation algorithms, expanding the functionality of applications, and improving the
accuracy of microstructure visualization. This study aims to analyze and compare the structures
obtained experimentally with similar structures generated by artificial methods in an analytical
context. The paper uses a set of metrics to compare such structures. Features such as sample and
inclusion areas, their perimeters, and the ratio of these parameters are analyzed. The concept of
area equivalence is introduced, and equivalent radii are found. Based on these indicators, the
results are visualized using histograms and Kernel Density Estimation (KDE). By performing a
statistical analysis of the results, using mathematical expectation and variance of values, a
comparison is made, and a conclusion is drawn about the adequacy of the use of computer
modeling of microstructure and artificial sample generation in comparison with experimental
data.
3.1. Metrics for comparing experimental and generated structures
Several parameters are employed to ascertain the characteristics of grains, facilitating the
evaluation of their shape and size.
β’ The normalized grain area is determined by the ratio of the grain area to the total image
area using the formula (1):
π΄ππ
π΄π = , (1)
π΄
where, π΄ππ - is the grain area, and π΄ - is the total area of the image.
β’ The grain shape coefficient is calculated as the ratio of the grain area to the square of its
perimeter according to (2):
π΄ππ
πΆπ = 4π 2 , (2)
πππ
where πππ - is the perimeter of the grain.
β’ The equivalent circle radius of the grain, as the value of the radius of a circle having the
same area as the area of the grain projection onto the plane, is calculated by (3):
π΄π
πΡπ = β , (3)
π
β’ In addition, the orientation angle π which is reflected in the deviation of the major axis of
the grain ππ₯ from the horizontal axis.
β’ The scale factor of the grain is defined as the ratio of the large to the small grain axes
according to (4):
ππ₯
ππ = , (4)
ππ¦
where ππ₯ - is the major axis, and ππ¦ - is the minor axis of the grain.
An example of the appearance of an arbitrary grain with the designation of the minor and
major axes and the orientation angle is shown in Figure 1.
β’ The grain inertia tensor is represented as (5):
πΌπ₯π₯ πΌπ₯π¦
πΌ=( ), (5)
πΌπ¦π₯ πΌπ¦π¦
where πΌπ₯π₯ and πΌπ¦π¦ - are the principal moments of inertia, and πΌπ₯π¦ (or πΌπ¦π₯ since the inertia tensor is
symmetric) - is the element representing the moment of inertia between the x and y axes.
β’ The grain aspect ratio, which indicates how closely a shape coincides with the rectangle
described around it, is calculated using the formula (6):
π΄π
π΄π
= , (6)
π΄ππ
where π΄π - is the area of the described grain rectangle. The closer the value of the coefficient is to
1 means the more rectangular the shape. In the ideal case, when the shape is a pure rectangle,
this coefficient will be equal to 1.
β’ The grain compactness ratio is calculated using formula (7):
π΄π
Π‘π = , (7)
π΄ππ
where π΄π - is the area of the convex polygon that is described around the grain. This coefficient
provides information on how close the grain is to a round or uniform shape: the larger the
coefficient, the more compact the grain shape.
β’ The ratio of the area to the grain axes, which indicates how elliptical or circular the grain
shape is, is calculated using formula (8):
π΄ππ
πΈ= . (8)
ππ₯ β ππ¦
β’ The ratio of the inertia tensor to the grain area, which indicates the mass distribution
relative to the geometric properties of the grain, is calculated using formula (9):
πΌ
πΌππππ = . (9)
π΄ππ
During the research, an issue arose concerning the compatibility of existing image processing
algorithms, which were primarily tailored for analyzing two-dimensional images, with the three-
dimensional microstructures generated. To address this challenge, the approach involved
partitioning the three-dimensional microstructure into layers, each of a single voxel thickness, as
a preliminary step before the analysis of grain properties. This partitioning effectively transforms
the problem into a series of two-dimensional image sets, facilitating subsequent processing
procedures.
Figure 1: Arbitrary grain with labels for minor and major axes and orientation angle
The generated microstructure is depicted in Figure 2, while the experimental microstructure
is shown in Figure 3. These images will be utilized in the study for characterization and
comparison purposes.
Figure 2: Generated microstructure Figure 3: Experimental microstructure
3.2. Calculating and visualizing statistical characteristics
As part of the study, statistical characteristics were calculated for the results of the grain
characteristics analysis. For each of the characteristics obtained by software, the mean (10),
standard deviation (11), median (12), mode, range (13), and interquartile range (14) were
calculated.
β’ The average value is calculated as the arithmetic mean of the characteristic values for
each grain using the formula (10):
βππ=1 π₯π
π= , (10)
π
where π₯π - is the value of the characteristic for each grain, π - is the number of grains, and π -
belongs to the set of integers.
β’ The standard deviation is defined as the square root of the variance using formula (11):
βπ (π₯π β π)2
π = β π=1 , (11)
π
where π₯π - is the value of the characteristic for each grain, π - belongs to the set of integers, π - is
the average value, and π - is the number of grains.
β’ The median for a data set of the form (π₯1, π₯2, . . . , π₯β) is defined as (12):
π₯π+1 , ππ π ππ πππ
2
π = {π₯ π + π₯ π , (12)
2 2+1
, ππ π ππ ππ£ππ
2
where π₯π - are the values of the characteristic for each grain, ordered in ascending order, and π -
belongs to the set of integers.
β’ The mode (ππ) is the most frequent value in the data set.
β’ The range is the difference between the maximum and minimum values in the data set,
determined by formula (13):
π
ππππ = π₯πππ₯ β π₯πππ , (13)
where π₯πππ₯ - is the maximum value in the dataset, and π₯πππ - is the minimum value.
β’ The interquartile range is the difference between the third (75%) and first (25%)
quartiles in the dataset, determined by the formula (14):
πΌππ
= π3 β π1 , (14)
where π3 - is the third quartile, and π1 - is the first.
After these statistics were calculated, the data were visualized using violin plots. This method
made it possible to compare the distribution of grain property values in the generated and real
microstructures, providing an opportunity to conclude the interaction and characteristics of the
grains.
To build a violin chart, the data is first processed, including filtering by the selected
characteristic.
Then, the data is prepared for display, namely, it is combined into one DataFrame, where the
category (generated or real grains), the name of the property, and its value are indicated. The
next step is to build the graph itself using the Matplotlib and Seaborn libraries. In a scatterplot,
each grain property has its distribution of values for the generated and real grains. Adding
statistical information such as the mean, standard deviation, and median helps to better
understand the distribution of the data.
4. Testing
4.1. Testing image processing methods
One of the objectives of the study is to test the methods of processing images obtained from the
experiment and generated artificially. The testing process involves the experimental application
of various in-age processing and analysis algorithms to accurately determine the characteristics
of the microstructural elements of a material. It is primarily used to study the properties of
material grains.
The test results indicate the effectiveness of the chosen approach and the possibility of its
application in further research in this area. To achieve these goals, four images of different sizes
were generated (Fig. 2-5), containing the same grain. Each image includes one grain, which is the
same for all images. The first two samples consist of square grains of 50β¨―50 pixels each, with
sample sizes of 200β¨―200 and 250β¨―250 pixels, respectively (Fig. 2 and Fig. 3). The third and fourth
samples contain round grains with a radius of 50 pixels each. The overall dimensions of the
studied images are 200β¨―200 (Fig. 4) and 300β¨―300 pixels (Fig. 5).
For each image, the grain characteristics such as area, normalized area, shape factor,
equivalent circle radius, orientation angle, scale factor, and inertia tensor were calculated
according to (1)-(9). The calculated values of the characteristics were compared with the
analytically calculated values to verify the correctness of the image processing. The results of the
calculated characteristics are shown in Table 1.
Analyzing the results, it can be seen that the values of the characteristics do not depend on the
size of the age, so they can be compared for further study and matching the generated structures
to the experimental ones.
Additionally, the calculation of the relative error for the diverse grain characteristics acquired
from the analysis is presented in Table 1. The relative error is determined through the
comparison between the software-calculated value of the characteristic and the analytically
measured value. Elevated relative error values signify substantial deviations between
measurements, whereas lower values suggest relatively precise measurements.
In general, the analysis results show very good agreement between the values obtained
analytically and by software for most grain characteristics.
Figure 4: A 200β¨―200 pixel sample with Figure 6: A 200β¨―200 pixel sample with
50β¨―50 pixel square grains round grains of 50 pixels radius
Figure 5: A 250β¨―250 pixel sample with Figure 7: A 300β¨―300 pixel sample with
50β¨―50 pixel square grains round grains of 50 pixels radius
For example, for the characteristics π΄ππ and π΄π the discrepancy between analytical and
artificial values does not exceed 1%, which indicates the high accuracy of the analysis methods.
However, for the characteristics πΆπ , and πππ which reflect the shape and size of the grain, the
discrepancies between analytical and software values are much larger, reaching almost 15% for
πΆπ and 3.7% for πππ in some cases. These deviations, especially in the case of πΆπ characteristic,
may be the result of inaccurate calculation of the grain perimeter. This indicates the need to
improve image processing methods, in particular, to adapt algorithms to the peculiarities of grain
shape and size. Further research is aimed at improving the methods for calculating these
characteristics to provide more accurate results.
4.2 Analysis of the statistical characteristics of the distribution of grain
properties
One of the key tasks in materials science is to analyze the microstructures of materials to study
their mechanical properties and behavior. To do this, it is important to identify the relationship
between the characteristics of microstructure grains and material properties. A large number of
methods are used in modern science to analyze microstructures, among which one of the most
powerful tools is violin plots. Violin plots are an effective tool for comparing the distribution of
grain characteristics between generated and experimental microstructures. In each scatter plot,
the distribution of grain characteristics for the generated microstructures is shown on the left
and for the experimental microstructures on the right. In addition, the graph also provides
statistical information such as the mean, standard deviation, and median, according to (10)-(12),
which provides additional context for comparing the distributions.
In this paper, violin plots are used to compare the distribution of normalized grain area
(Fig. 6), grain scale factor (Fig. 7), grain shape factor (Fig. 8), equivalent grain circle radius (Fig. 9),
grain orientation angle (Fig. 10) and other characteristics (Fig.11-19).
This allows researchers to gain a deeper understanding of the microstructure of the material
and its impact on material properties.
Thus, the use of violin plots to compare the distribution of grain characteristics in generated
and experimental microstructures is a powerful tool in materials science and mechanics research.
Table 1
Comparison of characteristics
Figure 2 Figure 3 Figure 4 Figure 5
Error
Error
Error
Error
Analyti Prog Analyti Progr Analyti Progr Analytic Progr
cal ram cal am cal am al am
Size,
200 Γ 200 250 Γ 250 200 Γ 200 300 Γ 300
px
Agr
0.4%
0.4%
0%
0%
, 2500 2500 2500 2500 7854 7825 7854 7825
px
0.3%
0.2%
0%
0%
An 0.06 0.06 0.04 0.04 0.2 0.196 0.09 0.087
Pgr
0.5%
0.5%
8.2%
8.2%
, 200 199 200 199 314.2 340 314.2 340
px
0.79
1.1%
1.1%
15%
15%
Cs 0.785 0.785 0.793 1 0.851 1 0.851
3
0.14
0.2%
3.7%
0%
0%
ecr 0.141 0.113 0.113 0.25 0.249 0.16 0.166
1
π,
0%
0%
0%
0%
ra Β±0.79 -0.79 Β±0.79 -0.79 Β±0.79 -0.79 Β±0.79 -0.79
d
0% 0.02%
0% 0.02%
0%
0%
Sc 1 1 1 1 1 1 1 1
208.
3.7%
3.7%
πΌπ₯π₯ 208.3 208.3 208.2 625 622.7 625 622.7
2
1.5% 0.9%
1.5% 0.9%
0%
0%
AR 1 1 1 1 1.27 1.25 1.27 1.25
0%
0%
πΆπ 1 1 1 1 1.001 1.011 1.001 1.011
50%
50%
0%
0%
πΈ 0.5 0.75 0.5 0.75 0.79 0.785 0.79 0.785
πΌπ₯π₯ 0.08
1.3%
1.3%
0%
0%
0.083 0.083 0.083 0.079 0.08 0.079 0.08
π΄ππ 3
After constructing the violin plots, a comparative analysis of the statistical characteristics of
the distribution of grain properties in real and generated microstructures has been carried out.
The analysis conducted facilitated the identification of similarities and differences between both
types of microstructures, enabling an assessment of the compliance of the generated
microstructures with real conditions. The data obtained will be used to further improve the image
processing algorithms and virtual reconstruction of grain microstructures. Information on the
analysis of statistical characteristics is presented in Table 2.
Conclusions
Throughout this study, the objectives have been attained, yielding significant results
conducive to the advancement of image processing methodologies and the analysis of material
microstructures.
Figure 8: Comparison of normalized grain Figure 9: Comparison of grain-scale factor
area distributions distributions
Figure 10: Comparison of grain shape factor Figure 11: Comparison of the distributions of
distributions the grain equivalent circle radius
Figure 12: Comparison of grain orientation Figure 13: Comparison of grain moment of
angle distributions inertia distributions
Figure 14: Comparison of grain moment of Figure 15: Comparison of grain aspect ratio
inertia distributions between grain axes distributions
Figure 16: Comparison of grain compactness Figure 17: Comparison of the distribution of
ratio distributions the ratio of the area to the grain axes
Figure 18: Comparison of distributions of the Figure 19: Comparison of distributions of the
ratio of the main moment of inertia to the ratio of the moment of inertia between the
grain area axes to the grain area
corresponding to individual grains in the material microstructure. The successful testing of these
First, image processing algorithms were developed to automatically detect regions
algorithms on test images enabled the accurate determination of various characteristics of each
Generated 0.005 0.179 0.018 0.766 0.38 3.705 1.864 0.276 0.114 0.061 0.025 0.036
IQR
Real 0.004 0.091 0.022 1.855 0.744 90.32 42.49 0.23 0.091 0.051 0.028 0.047
Generated 0.011 0.981 0.048 2.047 1.556 10.47 5.869 1.116 0.386 0.236 0.123 0.113
Range
Real 0.008 0.384 0.045 3.135 2.168 184 207.9 0.755 0.243 0.113 0.063 0.103
grain, including area, shape factor, orientation angle, and so forth.
Generated 0.005 0.785 0.04 0 2.45 0.188 0 1.5 1.25 0.817 0.047 0
Mode
Real 0 0.354 0.007 -1.566 1.133 3.151 -156.4 1.331 1.084 0.652 0.031 -0.069
Generated 0.006 0.574 0.044 -0.114 1.425 4.584 0.194 1.597 1.185 0.72 0.075 0.005
Median
Real 0.004 0.617 0.034 -1.199 1.788 87.17 -15.45 1.699 1.155 0.719 0.056 -0.02
Generated 0.003 0.151 0.012 0.533 0.307 2.454 1.339 0.206 0.08 0.044 0.019 0.024
deviation
Standard
Real 0.002 0.102 0.013 1.138 0.52 50.94 47.31 0.187 0.064 0.032 0.019 0.028
Statistical summary table
Generated 0.006 0.561 0.042 -0.109 1.488 4.537 0.229 1.614 1.195 0.713 0.076 0.004
Mean
Real 0.003 0.579 0.030 -0.574 1.95 82.61 -26.06 1.708 1.165 0.718 0.061 -0.022
Table 2
π΄ππ
π΄ππ
πΌπ₯π¦
πΌπ₯π₯
ecr
πΌπ₯π¦
πΌπ₯π₯
AR
πΆπ
An
Cs
Sc
π
πΈ
The resulting grain characteristics were further analyzed and it has been found that
dimensionless characteristics, such as normalized area, equivalent to the radius of a grain circle,
which is determined based on the normalized area, are most suitable for more efficient
comparison of microstructures. The study also showed that other dimensionless quantities, such
as the ratio of the inertia tensor to the grain area, the grain wrapping ratio, the ratio of the area
to the principal grain axes, and the grain scale factor, are very useful for comparing
microstructures, as they will not depend on the size of the image itself. Also, when comparing the
characteristics calculated analytically and software, it has been found that grain properties
calculated using the perimeter have a larger error, so it is recommended to avoid characteristics
such as the grain shape coefficient and use characteristics defined as a ratio to the area, such as
the ratio of the inertia tensor to the grain area.
Our study also included the development of an algorithm for comparing grain characteristic
distributions based on the analysis of violin plots and the comparison of statistical properties of
the distributions. This algorithm will be used to further tune the generation of microstructures
using the MatViz3D software package.
The results obtained are an important step towards the further development of image
processing methods and virtual reconstruction of grain microstructures. They can be used in
further research in the field of materials science and mechanics to gain new knowledge and
develop new materials with improved properties.
Acknowledgments
This work has been supported by the Ministry of Education and Science of Ukraine in the
framework of the realization of the research project βAlgorithms, models, and tools of artificial
intelligence for two-level modeling of complex materials behavior for dual-use technologiesβ
(State Reg. Num. 0124U000450).
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