K. ZELI^, M. GODEC: A MODFIED MEAN-LINEAR-INTERCEPT METHOD FOR DISTINGUISHING ...
83–87
A MODIFIED MEAN-LINEAR-INTERCEPT METHOD FOR
DISTINGUISHING LAMELLAR AND GLOBULAR EUTECTIC
CARBIDES IN METALLOGRAPHIC SAMPLES
MODIFICIRANA "MEAN-LINEAR-INTERCEPT" METODA ZA
RAZLIKOVANJE LAMELARNIH IN GLOBULARNIH
EVTEKTI^NIH KARBIDOV V METALOGRAFSKIH VZORCIH
Klemen Zeli~1,2,3, Matja` Godec3
1Faculty of Mechanical Engineering, University of Ljubljana, A{ker~eva 4, 1000 Ljubljana, Slovenia
2Jo`ef Stefan International Postgraduate School, Jamova 39, 1000 Ljubljana, Slovenia
3Institute of Metals and Technology, Lepi pot 11, 1000 Ljubljana, Slovenia
klemen.zelic@fs.lj-uni.si
Prejem rokopisa – received: 2017-10-11; sprejem za objavo – accepted for publication: 2017-10-26
doi:10.17222/mit.2017.173
A new quantitative metallographic method to distinguish the morphology of lamellar from globular eutectic carbides in
micrographs of steel was developed. The analytical image-processing method uses a standard interception method to evaluate
the anisotropy of the analyzed surface features. On the basis of the degree of anisotropy the lamellar eutectic carbides the
morphology in steel samples can be distinguished from the globular morphology. In comparison to similar existing methods, our
method enables the user to uniquely specify the investigated image region. In this way it is especially useful for boundary cases,
where both morphological types of carbides are present on the same micrograph and different parts of the image need to be
analyzed separately.
Keywords: metallography, interception method, micrographs analysis, lamellar eutectic, globular eutectic
Opisana je nova kvantitativna metalografska metoda za razlikovanje lamelarne in globularne oblike evtekti~nih karbidov na
mikroskopskih posnetkih vzorcev jekla. Slikovno procesiranje mikroskopskih posnetkov, uporabljeno v analizni metodi, je
zasnovano na podlagi standardne prese~ne metode, s pomo~jo katere je ocenjena anizotropija vzorcev na povr{ini. Stopnja
anizotropnosti je dober parameter za razlikovanje evtekti~ne in lamelarne morfologije karbidov v jeklu. V primerjavi s
podobnimi obstoje~imi metodami, na{a metoda ponuja uporabniku edinstven na~in dolo~itve analiziranega podro~ja na sliki.
Zaradi tega je metoda uporabna predvsem za mejne primere, kjer se na eni sliki nahajata oba tipa karbidov in je zato izbira
obmo~ja analize zelo pomembna.
Klju~ne besede: metalografija, prese~na metoda, analiza mikroskopskih posnetkov, lamelarni evtektik, globularni evtektik
1 INTRODUCTION
Micrographic analyses are some of the basic forms of
investigation used in materials science. In metallurgy,
many properties can be explained by a metallographic
examination of the metal’s surface. However, the stan-
dard metallographic procedure for determining the sur-
face morphology from micrographs is usually only
qualitative. The techniques used to assess micrographs
are not analytical and sometimes only include looking at
the micrographs and forming an opinion. A clearer
insight into the system can only be obtained through a
quantitative characterization. Therefore, it is essential to
use analytical methods for the image processing and
feature recognition. Such methods usually provide us
with one or more parameters that analytically determine
the characteristics of surface features such as the average
feature size, feature density or anisotropy. A new,
quantitative metallographic method has been developed
to distinguish the morphology of lamellar from globular
eutectic carbides across a range of steel samples. The
distinction is based on the degree of anisotropy of the
surface features (referred to as the surface texture)
determined from micrographs of eutectic carbides. The
method is based on the mean-linear-intercept method1,2,
but modified for use with eutectic carbides. A small
feature is added to the method so as to enable the user to
uniquely specify the investigated image region. It was
used to distinguish a lamellar eutectic from a globular
eutectic. But it can also be used for many other appli-
cations where the degree of anisotropy needs to be deter-
mined from the surface features of the micrograph. The
method is based on the commonly used intercept me-
thod3 that is normally used for grain size determinations
in metallic materials.4 By obtaining the azimuthal
dependence of the intercept number we can estimate the
degree of surface texture. The Mean-Linear-Intercept
Method uses a principle that is similar to that used for
bone-tissue anisotropy determinations.5 The method was
applied to images of four different surfaces. Two of them
are computer-generated test images that prove the func-
tionality of the method. The other two images were
scanning electron micrographs of real samples of an
Materiali in tehnologije / Materials and technology 52 (2018) 1, 83–87 83
UDK 620.18:669.15-194.5 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 52(1)83(2018)
AISI D2 tool steel’s as-cast microstructure. These two
samples included two morphologically different types of
eutectic carbides: a lamellar and a globular eutectic. The
difference between the lamellar and globular eutectic
carbides can be seen from a picture by eye (Figure 1a
and 1b). With the developed method we can analytically
prove that a difference exists and estimate its extent by
monitoring the anisotropy parameter (AP).
2 METHOD
Our new method uses a standard intercept method to
measure how many grain boundaries are intercepted if a
straight line is drawn on the image.3 The anisotropy is
estimated by performing numerous intercept methods on
the same image and then measuring the radial depen-
dency of the intercept number.1,2 In our case we chose a
point on the image (the intercept point) and then then a
family of lines was drawn to intercept the chosen point
so that the lines are rotated by a fixed angle relative to
each other (Figure 2). In this way the user has some
degree of freedom in comparison to the meanlinear-inter-
cept method as the intercept point can be chosen. The
intercept point should not be put outside the region of the
eutectic carbide or on the edge of an image, as could
easily occur if the method was fully automatic. For a
representative result the intercept point must be placed in
the middle of the eutectic carbide region of the micro-
graph. This is the main difference compared to the well-
known mean-linear-intercept method that is commonly
used for an anisotropy determination from micrographs.
A schematic demonstration of the method is shown in
Figure 2. There are 6 lines that cross the image in
different directions and meet at the intercept point. By
counting the intercept number for each line and then
plotting the radial dependence of the intercept number,
we would be able to estimate how anisotropic the image
is. The real algorithm includes many more intercept
lines. They are one angular degree apart so that every
image is processed by 360 lines. In this way the angular
dependence of the intercept number is suffciently
smooth. The intercept method was applied to processed
micrographs. The images were first binarized and then
processed by a mode filter. That is commonly used filter
for image characteristic enhancements6 that replaces the
value of each pixel with the most common pixel value
from its surroundings. This type of filtering turned out to
be the most effcient for revealing the phase boundaries
between the carbide and the austenite. Figure 3 shows
the images of the lamellar eutectic carbide before and
after the image processing.
The texture of the eutectic carbide is clearly seen on
the filtered image, as we obtained only the image of the
boundaries between the carbide and austenite phases.
The image was subsequently transformed into a
1280×1024 matrix of ones and zeros (depending on the
colors of the pixels). The intercept method was applied
for 360 different azimuthal angles by walking across the
matrix in two for loops. The outer loop determined the
angle, which was realized by turning the image counter-
clockwise around the interception point by Mathlab
K. ZELI^, M. GODEC: A MODFIED MEAN-LINEAR-INTERCEPT METHOD FOR DISTINGUISHING ...
84 Materiali in tehnologije / Materials and technology 52 (2018) 1, 83–87
Figure 1: Comparison between micrographs of: a) lamellar and
b) globular eutectic Cr7C3 carbides in as-cast AISI D2 tool steel, the
images were made on a scanning electron microscope (SEM) using a
backscattered-electron detector at a magnification of 4000×.
Figure 2: Shows the concept of our method, the intercept point is
placed on the desired spot in the image and the anisotropy of the
surroundings is evaluated
function imrotate. The inner for loop ran across the row
of the matrix that intercepts the interception point. The
value of pixel corresponding to the running increment
was subtracted from the value of its left neighbor. If the
difference between two neighboring pixel values was
non-zero the change from black to white was met. Every
change from black to white (from zero to one) was
stored as an intercept. At the end the density of the inter-
cepts in every direction was calculated by considering
the size of the carbide in different azimuthal directions.
This size was determined by saving the pixel coordinates
of first and the last intercepts for a given azimuthal
angle. The difference between both give us the size of
the carbide in terms of pixels. From the magnification of
micrographs we knew the exact scaling factor for the
transformation of distances measured in number of
pixels, to the micro meters. Interception densities for
every azimuthal angle were calculated as intercepts per
micro meter (units 1/micro meter) and averaged with a
moving average to reduce the noise. The moving-average
step size was set to 5 % of the whole range. After ave-
raging, the intercept density was plotted versus the
azimuthal angle. The image processing and the analysis
were made with the open-source GNU Octave program.
3 RESULTS
The results are obtained in the form of the angular
dependence of the intercept density . In order to prove
the functionality of our new algorithm, it was first tested
on two computer-generated images (Figure 4a and 4b).
Figure 4a shows a perfect lamellar structure (parallel
stripes). It is the most anisotropic texture that can exist.
K. ZELI^, M. GODEC: A MODFIED MEAN-LINEAR-INTERCEPT METHOD FOR DISTINGUISHING ...
Materiali in tehnologije / Materials and technology 52 (2018) 1, 83–87 85
Figure 3: Comparison between: a) original SEM micrograph and b)
processed SEM micrograph. binarization and filtration were per-
formed on the micrograph
Figure 5: Results of algorithm performed on: a) test images "Stripes"
and b) test image "Random dots". Interception density is exceptionally
calculated as number of interceptions along the interception line per
kilo pixel since the test images do not have the real scale.Figure 4: a) test image "Stripes" and b) test image "Random dots"
We expect that there will be no intercepts in the direction
parallel to the lamellas (black stripes). The second figure
(Figure 4b) includes randomly distributed, approxima-
tely circular dots of random size. No anisotropy exists in
this image, so we expect no periodicity and high noise in
the dependence of the number of intercepts on the azi-
muthal angle. All our expectations were met when the
analysis was performed on Figure 4a and 4b, which
proves that the method works. Figure 5a shows the
results of the analysis of image Figure 4a, and the result
in Figure 5b corresponds to the Figure 4b.
After proving the functionality of the algorithm, it
was run on the real micrographs of the eutectic carbides
in Figure 1. Figure 6 shows the comparison between the
results for: a) the lamellar and b) globular eutectics.
The difference between the two graphs is obvious. In
Figure 6a we can see the drop in the intercept density at
an angle of 170°. This corresponds to the intersection
method performed in the direction parallel to the eutectic
lamellas. Also, the periodicity is very obvious. The two
peaks at approximately 80° and 260° correspond to the
large density of the phase boundaries in the direction
perpendicular to the eutectic lamellas. The anisotropy
clearly exists in the sample and we can also determine
the direction of the texture. Figure 6b, on the other hand,
shows no periodicity and the amplitude of the fluc-
tuations cannot be distinguished from the noise (note that
two maxima and two minima are always obtained in the
360-degree range if anisotropy is present - no more or
less than this is theoretically possible). The constant
density of the intercepts (inside the standard deviation)
in Figure 6b shows us that the analyzed features are iso-
tropic. For the full quantification we used the anisotropy
parameter (AP). The AP is a numerical value that tells us
how anisotropic the investigated surface features are. The
amplitude of the intercept density’s angular dependence
can be used as the AP, but due to the noise and non-sinu-
soidal shape it is hard to estimate without large devi-
ations. In analogy with the mean linear method we
plotted the inverse of the intercept density data para-
metrically and then fitted the parametric plot with an
ellipse. This procedure is an exact equivalent of fitting a
sinusoidal wave to the intercept density angular depen-
dence plot, but fitting the ellipse to a cloud of points of
parametric plot is much more elegant. Figure 7 shows
the comparison between two parametic plots for the
lamellar (a) and globular (b) eutectics.
K. ZELI^, M. GODEC: A MODFIED MEAN-LINEAR-INTERCEPT METHOD FOR DISTINGUISHING ...
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Figure 7: Parametric plots of inverse intercept density’s angular dependence for: a) a lamellar eutectic and b) a globular eutectic using an
elliptical fit; the plot axis corresponds to the directions of the vertical and horizontal edge of the processed image; coordinates of plotted values of
the inverse interception number density are calculated from angular dependence by parametric representation: x=cos/interception density and
y=sin/interception density.
Figure 6: Angular dependence of the intercept density for: a) a la-
mellar eutectic and b) a globular eutectic. Intercept density is defined
as number of interceptions along the interception line per length of the
interception line in micro meters.
The semi-major and semi-minor axes of the ellipse
indicate the direction of the largest and smallest intercept
densities. The quotient between the lengths of the
semi-major and semi-minor axis is used as the aniso-
tropy parameter. We calculated the AP for both cases.
For the lamellar eutectic APL = 3.00 and for the globular
eutectic APG = 1.39. In the case of the lamellar eutectic
the average feature in the direction of the semi-minor
axis is, on average, three times longer than the average
feature in the direction of the semi-major axis. In the
case of the globular eutectic this ratio is only 1.39.
4 CONCLUSIONS
Our new method for distinguishing lamellar from
globular eutectic carbides using micrographs offers a
fully quantitative approach. The distinguishing is based
on the anisotropy of the eutectic carbide. The software
output is an anisotropy parameter (AP). If the AP value
is 1 (inside the standard deviation) the analyzed features
are isotropic (globular eutectic). Any other value of the
AP between one and infinity shows that the investigated
surface features are anisotropic, i.e., a lamellar eutectic.
The method is very effcient for the boundary cases
where we have both types of carbides in the same image.
Sometimes one eutectic carbide can be divided into two
regions of different morphological carbide types. The
main feature of our method in comparison to existing
ones is the degree of freedom that the user has. By
selecting the intercept point the user can choose the
investigated area and in this way our algorithm becomes
useful for distinguishing between a lamellar and globular
eutectic morphology. The code of the software is open
source and can be obtained by contacting the author.
5 REFERENCES
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3 E. Heyn, Short reports from the metallurgical and metallographical
laboratory of the royal mechanical and technical testing institute of
charlottenburg, The Metallographis, 5 (1903), 3964
4 H. Abrams, Grain size measurements by the intercept method,
Metallography, 4 (1971), 59–78
5 W. J. Whitehouse, The quantitative morphology of anisotropic trabe-
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doi:10.1111/j.1365-2818.1974.tb03878.x
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