Application of Image Processing and Different Types of Imaging Devices for Three Dimensional Imaging of Coal Grains 2015 Engineering Geology

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Application of image processing and different types of imaging devices for

three-dimensional imaging of coal grains

Krzysztof Oleszko, Mariusz Młynarczuk, Libor Sitek, Lubomı́r Staš

PII: S0013-7952(15)30020-X

DOI: doi: 10.1016/j.enggeo.2015.07.009

Reference: ENGEO 4101

To appear in: Engineering Geology

Received date: 7 May 2014

Revised date: 4 July 2015

Accepted date: 15 July 2015

Please cite this article as: Oleszko, Krzysztof, Mlynarczuk, Mariusz, Sitek, Libor,Stǎs, Luboḿır, Application of image processing and different types of imaging de-vices for three-dimensional imaging of coal grains, Engineering Geology (2015), doi:10.1016/j.enggeo.2015.07.009

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Application of image processing and different types of imaging devices

for three-dimensional imaging of coal grains

Krzysztof Oleszko*, Mariusz Młynarczuk*, Libor Sitek**, Lubomír Staš**

* AGH University of Science and Technology, Mickiewicza 30, 30-059 Krakow, Poland

**Institute of Geonics of the ASCR, Studentska 1768, Ostrava, Czech Republic

Abstract

Precise particle size measurements are important in many aspects of engineering geology, e.g. in

mineral processing and the study of methane hazard in coal mines. The volume of grains,

estimated exclusively on the basis of dimensions of the grains differs tens of percent from the

volume obtained from 3D digital measurements. This confirm that full three-dimensional

automatic imaging can be used in the measurements of the particles.

The paper discusses the technique of three-dimensional imaging performed with use of three

types of devices. Coal particles representing the 0.5 - 1.0 mm grain fraction were chosen as the

research material. The measurements were performed by means of: X-ray computed tomography,

confocal microscopy and optical profilometry. The last two techniques are less costly and more

easily available than computed tomography.

For the X-ray CT scanner, full three-dimensional imaging was performed. In the case of the

other two techniques, only those parts of the particles that were captured by the heads of the

relevant devices in question were measured. The invisible parts of the particle were reconstructed

with the assumption that the bottom part of the particle is similar (in some scale) to the top part of

the particle. The results obtained by means of X-ray CT scanner was used as the correct volume

and size values.The results indicate that measurements carried out carefully and with use of the more easily

available and less costly equipment, combined with careful data processing, can be used instead

of methods that are expensive and harder to employ. The percentage deviation between the

volume calculated with use of the data obtained with the X-ray CT scanner and the volume

calculated with use of the data obtained with the other two devices varies from 0.2 percent to ca.

5 percent.

Key words: 3D imaging, image processing, grain size, computed tomography, confocal

microscope, optical profilometery

1.

Introduction

These days, computers are ubiquitous, and the ways in which they can be used are manifold. One

of these applications is 3D imaging, which is very helpful as far as the study of the shape of

various types of grains – as well as their spatial description – are concerned (both on the “macro”

and the “micro” level). In particular, such studies are important in the context of geology and

mineral engineering. In the case of studies involving the analysis of the coal-methane system, and


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kinetics of methane diffusion through coal substance, the crucial factors are the shape and volume

of the particles. Specific grain parameters are used to determining methane release hazards as

well as methane and coal outburst in underground coal mines. The unipore diffusion model,

employed in the process of identifying methane threats in coal mines, is encumbered with

numerous assumptions, such as the one concerning the sphericity of grains - and the shape of the

grains is the most significant factor responsible for potential errors in determination of the value

of the diffusion coefficient. The study into the impact of changes and inaccuracies in the shape of

grains upon potential errors of the unipore model was presented in an article by Wierzbicki

(2011). Precise determination of the spatial parameters of grains, performed with use of 3D

imaging methods, may have a significant influence on methane diffusion models, and thereby on

improvement of safety in underground hard coal mines.

Three-dimensional imaging can be performed with various methods and different types of

devices, developed in recent years. The most common and widely used methods are described in

a paper by Pirard (2012). Unfortunately, many devices for 3D imaging are still very expensive

and hard to obtain. One solution to this problem is using less expensive equipment, with which

partial three-dimensional imaging can be performed. However these only measure the “upper”

part of the particles and not the entire particles - thus the “invisible under side” has to be

reconstructed in some way using some basic assumption, so that the measurement result is as

close as possible to the actual object. In their work, Lee et al. (2005, 2007) presented one possible

method of partial imaging without the restoration of the invisible part. They used laser

triangulation to obtain information about the shape of 3D objects, but did not find any

information about the bottom shape of the objects. A different approach to object-shape

digitization was presented by Maerz (2004). To obtain the 3D data, Maerz put the object on a

rotating table and produced its digital representation by means of a set of cameras. This methodresults in 3D images of the objects with the exception of the side on which it is resting on the

rotating table. Another approach (Giordano et al, 2006) employ an optical microscope for

imaging objects. They used obtained data in order to reconstruct a 3D image. Having

reconstructed the full spatial structure of the investigated object, they compared the results with

some more accurate techniques, such as optical tomography and X-ray CT. Estimation of the

particle-size distribution of particles was presented by Al-Thyabat et al. (2007). The subject of

the research was the material on a conveyor belt (granite and coal). In the process of imaging,

simple digital cameras were used, installed at the end of the conveyor belt. The material was

presented from different perspectives – the objects were imaged from above and as they were

falling. Unfortunately, the authors did not reconstruct the structure of grains in 3D. Full three-

dimensional imaging was presented by Lanaro et al. (2002), who employed a sophisticated laser

scanning technique. The method gives very good results as far as total 3D reconstruction is

concerned; however, it requires scanning both sides of objects, which might turn out to be

troublesome whenever it would be necessary to obtain data from a large quantity of particles

(given the precision with which the object must be rotated). Bujak and Bottlinger (2008) also

presented full 3D imaging. The system which they developed is based on analysis of free-falling


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objects. Free-falling particles are imaged from three orthogonal directions from which the 3D

dimensions of the particles can be determined. The idea itself is very clever, but there are a lot of

assumptions involved and that can introduce some error. Also, this method requires some special,

properly calibrated equipment. Another method of 3D imaging was presented by Fernlund (2004,

2005): here, the particles were photographed in two positions, lying and propped against a

luminous background. The method yields good results, but the pictures of the particles have to be

taken in a very careful manner, especially when it comes to setting the orientation of the object.

Some other techniques, such as scanning electron microscope analysis or a microscopy technique

with polarization optics and UV light, were presented by Persson (1998). Based on the

preliminary research by (Oleszko, Mlynarczuk 2012), the authors decided to use a confocal

microscope and an optical profilometer as the devices with which partial imaging would be

performed. Computed tomography (CT) scan, performing full three-dimensional imaging, was

used as a reference technique.

The above methods do provide information about the size and shape of particles but several of

the methods are very expensive and time consuming and some do not provide accurate enoughresults for accurate modelling of methane diffusion. Presently the models use the size and shape

results from the method based on substitute diameters; this is the most commonly used method.

However it is very time consuming and erratic. Thus there is a need for developing a fast,

inexpensive method that yields accurate enough results of the 3D size and shape of particles; that

yields accurate enough results for accurate modeling of the methane diffusion. We will test two

new methods and compare the results with those obtained from the X-ray CT based method. To

see if these less expensive and quicker methods can give accurately enough results that can

motivate their use instead of the X-ray CT which is expensive.

2.

Study area

Modern techniques of 3D imaging are very helpful when it comes to the process of spatial

description of grains, their size, shape, and surface texture. An important factor in selection of the

measuring method is their cost and availability and accuracy of the results. In most micro scale

cases, the best choice proves to be the X-ray CT scanner, which provides full representation of

the shape or structure of the investigated object in three-dimensional space. However, this

instrument is very expensive and not available to most researchers, thus we look for an

alternative that would still make it possible to preform sufficiently accurate size and shape

measurements. Such an alternative may be the confocal microscope or the optical/laser

profilometer. Unfortunately, none of these instruments provides us with a comprehensiverepresentation of an object in three-dimensional space, as the devices allow us to scan the grain

structure only from above (this is due to the fact that, in both cases, the head of the measuring

device cannot access a grain from any other side). An object, thus imaged, can be reconstructed

in such a way, that its recreated shape is close to the actual one.


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As it has already been mentioned, coal grains constituted the research material discussed in the

present paper. The coal was first subjected to the process of screening. As a result, particles

representing the 0.5 – 1.0mm grain fraction were obtained. The screening process was performed

‘in situ’, in an underground coal mine, and it involved employing screens that are regularly used

by miners for the purpose of desorption measurements. Subsequently, the separated sets of grains

were scanned with three different types of devices. The parameters measured by the three devices

were similar and consisted of: length, width, thickness and Ferret diameter. Results from the

XTH 225 ST X-ray CT scanner manufactured by Nikon were used as a reference data. The

second type of the measuring instrument used for obtaining data was the Olympus LEXT OLS

3100 confocal microscope, and the last one was the MicroProf optical profilometer utilizing

white light, equipped with the FRT CWL 3mm sensor. The profilometer was manufactured by

FRT.

3. Data acquisition

Each sample consisted of 55 randomly selected coal particles. Due to the particles fragility the

same set of particles could not be used for each of the different methods. Instead different

particles were measured for each method. Furthermore the results of some of the particles were

disregarded; they were clearly erratic results. In the end there were 44, 50 and 53 particle results,

respectively for the X-ray CT scan, confocal microscope and optical profilometer. The grains

measured by means of the confocal microscope and optical profilometer had not been prepared

for measurements in any way. In order to optimize and simplify the measurement procedure, the

particles measured by means of the X-ray CT scanner were embedded - before scanning - in a

special mass that had been molded into the cylindrical shape.

3.1 Confocal microscope

The confocal microscope, due to its specific nature, makes it possible to perform measurements

of the grain surface as seen from above. In this research, the measurements were performed

separately for every grain. Randomly chosen grains were scattered on the measuring table under

the microscope. Then, after setting the scanning head over the grain and selecting the desired

parameters of the study, the measurement procedure itself was carried out. Due to the fact that the

measurements were performed relatively fast, in order to improve the quality of the results and

minimize the number of potential errors, four scans were involved in each grain measurement.

The data obtained from the measurements was not pre-filtered - all of the filtering options

available in the microscope control software were turned off. The result of the measurement of

each particle was a CSV (Comma Separated Values) file containing a header with information

about the measurement parameters (the measuring point size, and the data concerning the

measured grain) and, in its subsequent lines, the height spatial distribution of the pixels on the

grain surface, with a resolution of 1024x768px (the measurements were performed with the same

fixed resolution for all particles). The size of each individual data point was 2.5x2.5m. Figure 1


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provides an example of a scanned grain. Lighter shades of gray mean that the grain points are

higher.

Figure 1. A sample grain of coal scanned with a confocal microscope

3.2 Optical profilometer

The optical profilometer, similarly to the confocal microscope, made it possible to measure grains

as viewed from above. Prior to the measurement, randomly selected particles were scattered on

the table of the measuring device. Then, the measurement parameters (the width and height of the

area to be scanned, as well as the size of the measuring point) were set individually for each

grain. After that, the grain was measured. The profilometer head remained stationary during the

process, while the table with the scattered samples was moving. Due to the fact that themeasuring table was moving relatively rapidly, causing some of the particles to relocate, a special

underlay was placed on the measuring table to prevent the movement of the particles. The

underlay placed on the measuring table did not affect the results of the measurements. Due to the

large amount of time needed to scan a grain, each grain was scanned only once. The obtained

data was not pre-filtered. As a result of the measurement process, for each particle, a text file

containing a header with information about the measurement (the size of the scanned area, the

measuring point size, and the data concerning the measured grain). Each measurement was

conducted with a different size of the scan area, matched to the measured grain size in order to

speed up the measurement process. After changing the size of the scan area, the software of the

profilometer automatically changed the size of the measuring point. Because of that, the size ofthe measuring point had to be adjusted to 10x10µm. As a result, the size of the measuring point

for all grains was identical, regardless of the different sizes of the scan areas and had no influence

on the result of imaging. An example of a view of a scanned particle is presented in Figure 2.


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Figure 2. A sample grain of coal scanned with an optical profilometer

3.3 CT scanner

The CT scanner, in contrast to the previously mentioned devices, allows full three-dimensional

imaging of a single grain or a set of grains. All the particles in the set were scanned at the same

time - in contrast to the other two methods, which required each grain to be scanned individually.

The chosen grains were embedded in a cylindrical mass, designed specifically for this particular

purpose, and placed inside the scanner and measured. The parameters of the measurement, such

as the size of the scanning grid, the sampling distance and radiation dose, were set in such a way

as to adjust the result to the optimum scanning time without losing the acceptable quality. As a

result, a set of images saved in the TIF format was created. Each of the images presented a single

layer (a cross-section) of the scanned cylindrical sample with embedded coal grains in it. In total,

1628 files of the size of 1526x1070px were created. As a result, it yielded 1628x1526x1070px

resolution in three-dimensional space. The size of a single data point in 3D space (voxel) was

6.85x6.85x6.85m. A sample image of the whole sample is presented in Figure 3. Figure 4

provides an example of a cross section through the sample; it is the representation of a single

scanned layer.


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Figure 3. A sample image of the whole cylindrical - shaped sample

Figure 4. A sample cross section through the sample

4. Data processing

The processing of the collected data was carried out with custom software. The software was

written in Java without using the external libraries that provide the necessary image processing


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algorithms in both 2D and 3D. All the algorithms were newly implemented and thoroughly tested

(Oleszko, Mlynarczuk 2012).

4.1 Confocal microscope and optical profilometer

The processing of the data obtained with the confocal microscope and the optical profilometerwas carried out in an almost identical way. The only difference concerned setting the proper

resolution of the data set.

The measurement data contained information about the grain heights as seen from above. The

values included also the height of the measuring table on which the grains were spilled. All the

data was saved in the form of the 2D pixel array with the x and y dimensions. The information

concerning the bottom shape of the grains was missing. Additionally, during the measurement

process, some pixels were not measured due to the limitation of the measuring devices. Such a

situation occurs typically in this type of an analysis, where light plays an important role during

the measurement. It may be caused by the topography or the reflexive feature of the grainsurface. The pixels which were not properly measured were reconstructed by means of the

Kriging Method (Oliver et al., 1990). Next, the data was initially pre-filtered - simple

morphological opening and closing were applied in order to eliminate the unwanted noise. The

next step was to create a three-dimensional representation of the particles based on the data

obtained from the measuring devices. The 3D array was created in a typical way: each element of

the 2D pixel array contained information about the height of the grain at the measured point. The

x and y dimensions of the 3D array were the same as in the 2D array. In order to calculate the z

dimension, each point with the coordinates x and y has been extended into the z direction, with

the number of units equal to the value stored in the cell of the 2D height array. As a result, a 3D

XYZ voxel array was obtained, describing the top view of the spatial grain structure.

The data concerning the missing bottom shape, unavailable for the measuring head, was

reconstructed. The reconstruction algorithm was based on the assumption that bottom part of

every grain is similar, in some scale, to its top part. The information about the heights measured

on the analyzed grain including information about the height of the points on the outer

circumference of the grain, were used for calculations. The proposed reconstruction algorithm

was used in some previous studies (Oleszko, Mlynarczuk 2012).

Whole algorithm used a two-dimensional array containing information about height of points of

grain seen from above. Each element of array was described by the x and y coordinate and wascontaining value of measured height of single point of the top surface of the grain u(x, y). Value

of the u(x, y) was greater than zero. Points (of the two-dimensional array), which were

representing foundation on which the grain was resting, had value equal to zero. The result of the

algorithm, for every x and y coordinates, was value of bottom surface of the grain b(x, y) which

was defined as a scaled mirror reflection of the u(x, y) value. The value of reflection point r(x, y)

(point used to create the reflection) was determined in the following way (description refers to a


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single element of two-dimensional with coordinates x and y with value greater than zero, but it is

the same for the whole grain):

First part of the algorithm – initial reconstruction

- in the two-dimensional array of the measured values, the analyzed array element withcoordinates x and y u(x, y) was placed at the intersection of exact row and column

- for that exact row and column there were located points u(x, y) placed on the circumference of

the grain – row and column, were containing information of two pieces of circumference (for

row: left and right, and for column: top and bottom) so two pairs of points were found. In order to

eliminate potential error, the pairs of points were evaluated as median value of group of points on

the circumference.

- based on evaluated pairs of point, two straight-line equations were determined: for the row (f row)

and for the column (f col).

- using lines equations, there was established value of point which was used to create the

reflection of the top value:

Second part of the algorithm – scaling of evaluated values

In order to enhance created bottom part of grain, evaluated values b(x, y) were scaled. As a base

for scaling there was adopted value of center of the gravity of the grain.

- for the point of center of gravity with exact coordinates: xc, yc, there was establish value of point

used to create the reflection (identically as described in the first part of the algorithm

) r(xc, yc). In case, when the value of point of center of gravity u(xc, yc) was less than r(xc, yc)

value then, instead of the center of gravity, whole scaling was based on max height value of the

grain.

- based on evaluated r(xc, yc) value, there was established a scale factor:

- using established scale factor, the b(x, y) value was evaluated in following way:

- in case, when evaluated value b(x, y) was less than zero, then the b(x, y) was adopted as zero

value.


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Third part of the algorithm – reconstruction of grain bottom structure

Having the b(x, y) value, the bottom part of the grain saved in 3D XYZ voxel array (mentioned

before) was reconstructed. From the perspective of image analysis, the value of the voxels

representing the grain were marked as “1”, and the value of the voxels representing the grain

surroundings were marked as “0”.

To the spatial image obtained in that way, a 3D algorithm of morphological filtering was applied

in order to eliminate possible noise (Serra 1988). On the basis of objects prepared in 3D space,

additional calculations were performed, which are presented further in the article.

4.2 X-Ray CT scanner

The data obtained with the CT scanner differed significantly from the data obtained with the

microscope and the profilometer. The CT scan data contained complete information about the

three-dimensional shape of the studied grains. Therefore, the processing algorithm of the CT data

was entirely different. Each of the data files, 1628 tif images, containing 2D data concerning the

cross sections, was processed separately so that a coherent picture in three-dimensional space

could be obtained. Every two-dimensional image was pre-filtered in order to eliminate the

unnecessary noise connected with measurement specification. In this case, the measurement was

carried out on the objects embedded in a special mass which generates some noise. The 2D

involved employing the median filter, then the opening by reconstruction followed. The

algorithm removed all the noise and errors without detriment to the data describing the particles.

As a result of the filtering process, the images containing the two-dimensional view of the grains

and uniform background allowing unambiguous identification of the tested objects were created.

Thus prepared images were used to reproduce the three-dimensional shape of the particles. Thealgorithm for creating a 3D image (in a loop over all the two-dimensional images) recognized the

grains, if necessary, separated them with a watershed algorithm (when it was necessary), labeled

them and then created 3D objects. In order to eliminate possible noise, the 3D algorithm of

morphological filtering was applied to obtain the three-dimensional image. On the basis of the

objects created in 3D space, the dimensions and volume of the grains were calculated.

5.

Measuring methods

In order to compare the results obtained in the course of the measurements of the data established

with the microscope, the profilometer and the X-ray CT scanner, the exact parameters werecalculated. For each particle, the following parameters were determined: volume, height, width,

and length. ‘Length’ is understood as the x dimension, ‘width’ as the y dimension and

“thickness” as the z dimension. The volume was calculated as the sum of three-dimensional

voxels and as the product of the calibration factors determining the dimensions of a single voxel,

respectively. The single voxel size was the same with respect to all directions, which was

essential for the sake of keeping the proportions (e.g. processing filtration in 3D space). For the


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microscope and profilometer data, the thickness was calculated directly, and no additional

transformation was applied. For the CT data, the thickness was calculated in two different ways,

without and with extra processing, which is described further in text. The x and y dimensions

were calculated by means of the Feret diameter - one of them was determined as the exact Feret

diameter and the other - as the shortest perpendicular diameter. A similar method was presented

by Wang (2006). Additionally, the surface area of each grain's top-view projection was calculated

so that further calculations could be processed.

In order to conform the CT data to the data obtained by means of the other devices, the grains

were rotated in three directions so that the orientations similar to the grains from the profilometer

and microscope could be established. The grains measured with these two devices were lying

freely. To simulate this type of arrangement, the grains were rotated so that the smallest thickness

could be determined. Then, using the repositioned grains, width and length were calculated by

means of the Ferret diameter.

To compare the results obtained due to the application of the 3D image analysis methods and thewidely used manual methods for estimating the volume of grains, the volumes of grains were

calculated with four different substitute diameters. Usually, with this type of measurements, there

is a rough assumption that the grain is spherical, and its volume is calculated according to the

standard formula of a sphere (Drzymala 2007). In this case, the substitute diameters were defined

as:

• the diameter of the sphere, which has the same surface area of projection as the analyzed

grain (projection diameter);

• the arithmetic mean of length, width and height of the analyzed grain (arithmetic

diameter);

•

the geometric mean of the three dimensions of the analyzed grain (geometric diameter);

• the harmonic mean of the three dimensions of the analyzed grain (harmonic diameter).

6.

Results

Table 1 presents the calculated average volume for all the types of measurement instruments

involved, as well as the standard deviation for each value.

Table 1. The volume results, calculated and compared

CT scanner Confocal microscope Optical profilometerVolume [mm

3] 0.508 0.509 0.533

Standard deviation 0.421 0.234 0.284

Table 2 presents the percent deviation between the volumes calculated with the CT data and the

data obtained with the other devices.


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Table 2. The percent deviation of the calculated volumes as compared to the CT scanner volumes

Confocal microscope Optical profilometer

Percentage deviation 0.197 4.921

The calculated average dimensions of grains, based on the measurement data, are presented in

Table 3. The values for the X-ray CT scanner presented in column ‘CT scanner’ were obtained

without additional transformations. The column ‘CT scanner after transformations’ presents the

average grain dimensions calculated on the basis of the X-ray CT data after performing additional

grain transformations.

Table 3. The average grain size results, calculated and compared

CT scannerCT scanner after

transformations

Confocal

microscope

Optical

profilometer

Length [mm] 1.582 1.741 1.805 1.804

Width [mm] 0.923 1.107 1.295 1.338

Thickness [mm] 1.109 0.790 0.716 0.711

For the calculations based on grains scanned by means of X-ray CT, the parameters of the rotated

grains simulating the free lying arrangement, were adopted. The average volumes calculated with

substitute diameters as well as the volumes obtained from the 3D analysis, are presented and

compared in Table 4. The values from the 3D analysis were treated as a reference. Figure 6 presents percentage differences between the volumes obtained with use of the popular methods

and the volumes obtained by means of the data from the 3D imaging methods.

Table 4. The average grain volumes obtained with the 3D analysis and the commonly used methods,

calculated and compared

Volume evaluated as:

3D

analysis

Projection

diameter

Arithmetic

diameter

Geometric

diameter

Harmonic

diameter

3D method V[mm3] V[mm3] V[mm3] V[mm3] V[mm3]

CT scanner 0.508 1.001 0.933 0.796 0.684

Confocal

microscope0.509 1.348 1.078 0.877 0.701

Optical

profilometer0.533 1.417 1.110 0.899 0.712


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0

20

40

60

80

100

120

140

160

180

D i f f e r e n c e [ % ]

The percentage deviation between 3D volume and volume evaluate

using described methods

Proj

Arit

Geo

Har

Figure 6. The percentage deviation between the 3D volume and the volume evaluated by means of the described

standard methods

7.

Discussion

Given that the X-ray CT method allows total reconstruction of the particles we assume the resultsare most accurate and thus they are used as reference values for comparison of the results from

the other two methods (Table 2). For each measuring method there were used about 50 grains,

which yield a fairly representative group of test objects. The average volume calculated on the

basis of the confocal microscope data, differs from the reference volume by about 0.2 percent.

However, the average volume calculated on the basis of the data obtained with the optical

profilometer differs from the reference value by about 5 percent. During the measurements

performed with these two devices, only the data from the part of the grain visible to the

measuring head could be collected. Reconstruction of the underside of the grain was modeled.

Taking this fact into account, it can be concluded that the results are more than satisfactory.

The dimensions calculated on the basis of the data obtained with the microscope and the

profilometer (Table 3), are very similar to the results of the specification of the measurement. In

both cases, the grains - placed on the measuring table - were measured as seen from above, and

they were resting in a natural stable position on the measuring table. Therefore, in both cases, the

height of the particles is the lowest value, and, what follows, the shortest axial dimension. The X-

ray CT results (without grain transformations) differ from the results obtained with use of the


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other methods. This is due to differences in processing the measurement and arrangement of

particles. The grains measured in this manner were immersed in the mass. They did not turn

naturally; instead, they were “frozen” in the position in which they were placed within the

hardening mass. This circumstance proved critical in this context. That is why the difference

between the average height, width, and length is not as substantial as in the previous cases.

Analyzing the data from Table 3 it can be seen, that the results obtained by means of the X-ray

CT data (after performing grain transformations) are more similar to the values obtained for the

samples investigated with the profilometer and the microscope. The dimensions correspond to

each other, and the thickness is the smallest one. When the percentage differences presented in

Figure 6 are taken into account, one can notice that, in general, the smallest differences occur

with the volumes calculated on the basis of the data from the X-ray CT scanner. It should be

regarded as natural, as these values are the most accurate ones and they represent the full 3D

grain structure. On the other hand, the percentage differences in the case of the data obtained by

means of the confocal microscope and the profilometer are quite similar, but they differ a lot

from the values obtained by means of the CT scanner. The biggest differences concern the

volumes calculated with the projection diameter. Here, a difference is expected, since the height

of grains is not taken into consideration while calculating the projection diameter. In this case,

height is significant, since it is the smallest value among the x, y and z dimensions.

8.

Summary

The present paper provided a description of measurements of coal grains performed with the X-

ray CT scanner, the confocal microscope and the optical profilometer. The measurements carried

out with the X-ray CT scanner were based on the full three-dimensional shape of the measured

grains. The other measurements were based on the top view of the grains. The obtained data was processed and prepared for further calculations. In the case of the measurements based only on

the top view shape, the bottom parts of the particle that were not visible, were reconstructed with

the assumption that the bottom part of the particle is similar to the top part of the particle. This

reconstruction algorithm, proposed by the authors, was the most important part of the processing

stage. The comparison of the measured data proves that the results obtained on the basis of the

data from the microscope and the profilometer differ slightly from the results obtained with

tomographic measurements. Therefore the measurements performed with the confocal

microscope or profilometer, can be used instead of measurements conducted with the help of the

X-ray CT scanner. It is very important, since the tomographic measurements are still poorly

accessible and relatively expensive. However, it must be remembered that some X-ray CT

measurements cannot be replaced. This concerns instances where obtaining a full spatial image is

crucial.

Acknowledgments


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This work was supported by the Research Tasks 11.11.140.032 and 15.11.140.338 of the AGH

University of Science and Technology, Faculty of Geology, Geophysics and Environmental

Protection, and by the project for the support of the long-term strategic development of the

research organization RVO: 68145535. The article was also written in connection with the

project “Institute of clean technologies for mining and utilization of raw materials for energy

use”; reg. no. CZ.1.05/2.1.00/03.0082, which is supported by the Research and Development for

Innovations Operational Program financed by the Structural Funds of the European Union and

the State budget of the Czech Republic. The authors are thankful for the support.

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Highlights

Coal grains were measured in 3D using three types of devices.

X-ray CT scanner, confocal microscope and optical profilometer were used.

An algorithm for 3D reconstruction was proposed.

There were compared results from all types of devices used.

Results obtained from 3D and evaluated by standard 2D methods were compared.

Documents

Application of Image Processing and Different Types of Imaging Devices for Three Dimensional Imaging of Coal Grains 2015 Engineering Geology