Image Anal Stereol 2016;35:29-37 doi:10.5566/ias.1333
Original Research Paper
ADAPTIVE PARAMETER SELECTION FOR GRAPH-CUT BASED
SEGMENTATION ON CELL IMAGES
KAZEEM O. OYEBODEB AND JULES R. TAPAMO
School of Engineering, Howard College Campus, University of KwaZulu-Natal, Durban, 4041, South Africa
e-mail: kazeemkz@gmail.com; tapamoj@ukzn.ac.za
(Received May 9, 2015; revised August 14, 2015; revised November 24, 2015; accepted December 15, 2015)
ABSTRACT
Graph cut segmentation approach provides a platform for segmenting images in a globally optimised fashion.
The graph cut energy function includes a parameter that adjusts its data term and smoothness term relative
to each other. However, one of the key challenges in graph cut segmentation is finding a suitable parameter
value that suits a given segmentation. A suitable parameter value is desirable in order to avoid image over-
segmentation or under-segmentation. To address the problem of trial and error in manual parameter selection,
we propose an intuitive and adaptive parameter selection for cell segmentation using graph cut. The greyscale
image of the cell is logarithmically transformed to shrink the dynamic range of foreground pixels in order
to extract the boundaries of cells. The extracted cell boundary dynamically adjusts and contextualises the
parameter value of the graph cut, countering its shrink bias. Experiments suggest that the proposed model
outperforms previous cell segmentation approaches.
Keywords: cell segmentation, energy function, graph cut, parameter selection.
INTRODUCTION
Cell segmentation provides an opportunity for
experts in the medical sciences to diagnose medical
conditions of cancer or tuberculosis with a clear
perspective. This suggests that to achieve a fast and
objective diagnosis, a reliable and robust segmentation
framework is essential. Graph cut provides this
platform leveraging a globally optimised segmentation
strategy. However, one of the key challenges of graph
cut is the selection of a suitable parameter value. The
parameter value plays a key role in the segmentation of
images by ensuring that important parts of cells such as
edges are revealed after segmentation. These parts are
often lost when segmenting elongated cells (Vicente
et al., 2008).
Segmentation of cell images provides a platform
to monitor closely cell mobility relative to the cells’
existence and interaction with other surrounding
bodies. This process provides the basis for medical
diagnoses through observation of shapes and forms
of segmented region. However, cells often suffer from
non-uniform illumination, with blurry cell boundaries
delineating them from their background. In addition,
live cells possess dynamic shapes and over selected
time frames, they take on different shapes like
oval, elongated or irregular. This makes segmentation
difficult when using techniques based on cell shapes.
Consider the highlighted cell in Fig. 1a at time 84.50
and its position in Fig. 1b at time 86:00; it is clear
that the shape of the cells has changed over the time
interval. Accurate monitoring or tracking of these cell
shapes over a given time frame is therefore crucial
for discovery of abnormalities such as cancerous cells
(Bengtsson, 1999).
(a) (b)
Fig. 1. Cell images. (a) Original position of
highlighted cell. (b) Final position of highlighted cell
from (a).
In order to deliver a robust graph cut segmentation,
a suitable parameter value must be realised. This is
imperative because an increase in parameter value will
invariably increase graph cut data term resulting in
noisy image output (Fig. 2). A decrease in parameter
value increases its smoothness term resulting in over-
segmentation. As demonstrated in Fig. 3, the graph cut
segmentation traverses a shorter route (red boundaries
in Fig. 3b) rather than the longer route in Fig. 3a.
This suggests that graph cut will by default preferably
traverse a shorter route for the segmentation of
elongated cells, unless constrained or informed by
some algorithm to take the route in Fig. 3a.
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OYEBODE KO ET AL: Adaptive Parameter Selection for Cell Segmentation
Based on the aforementioned facts, the objective
of this work is to develop a robust graph cut algorithm
that regularises graph cut data term as well as its
smoothness term by dynamically altering its parameter
value. Several cell segmentation approaches have
been proposed in literature leveraging graph cut. For
example, a two-stage cell segmentation approach is
proposed by Daněk et al. (2009). The first stage
segments isolated cells from their background, while
the second stage deals with touching cells or cell
clusters using shape priors.
Fig. 2. Illustration showing the compromise between
data term and smoothness term. (a) Original image.
(b) Segmentation with small parameter value, ensuring
a smoothened segmentation while, however, ignoring
cell details such as boundaries after segmentation. (c)
Segmentation with large parameter value, retaining
some cell edges after segmentation; however, image is
noisy. (d) Optimal segmentation with some edges still
missing.
(a) (b)
Fig. 3. (a) Ground truth. (b) Graph cut taking shorter
route (red boundaries) for segmentation in place of
longer route (green boundaries) as seen in (a).
Al-Kofahi et al. (2010) presented an automatic
cell segmentation where an image is segmented into
foreground and background using graph cut, then a
second graph cut segmentation follows to delineate
touching cells. Chen et al. (2008) adopted a graph
cut based active contour (GCBAC) where the active
contour constrains graph cut segmentation to areas of
interest. Qi (2014) proposed a method for segmenting
clustered cells through graph cut. The isolation of cell
clusters is carried out based on the knowledge that
cells are spherical in shape. In addition, a merging
algorithm for object segmentation is proposed by
Lin et al. (2003) where images are split into units,
then a merging algorithm assembles neighbouring
units together based on homogeneity criteria. The
merging algorithm is explored for cell segmentation by
Coelho et al. (2009) and also for object segmentation
by Roy and Biswas (2015). Lastly, a supervised
cell segmentation based on cell shape and texture
properties is proposed by Chen et al. (2013).
While the above approaches give good
segmentation results, some of them are not robust
in terms of cell over-segmentation. For example, the
method proposed by Al-Kofahi et al. (2010) may not
perform well when confronted with elongated cells
because their approach is based on blob shape priors.
Similarly, the GCBAC technique (Chen et al., 2008)
may result in under-segmentation, because cells have
varying intensity levels.
Our observation of the shrink bias of graph cut
and the poor segmentation results of non-uniform
illuminated cell images with unclear boundaries also
motivates this research. We therefore propose a cell
segmentation method that extracts cell boundaries
and can be used to adjust dynamically the relative
importance of graph cut data term to the smoothness
term. The main difference between the proposed
approach and the previous graph cut cell segmentation
is that instead of using a static regularisaation
parameter for graph cut segmentation, the proposed
approach uses knowledge about extracted cell
boundaries to adjust dynamically graph cut parameter
value. This model ensures that cell boundaries are
not reduced by graph cut during segmentation.
Furthermore, the proposed model saves segmentation
time since manual tuning of graph cut parameter value
is unnecessary.
RELATED WORKS
Boykov and Jolly (2001) proposed a graph cut
model where user selects sample foreground and
background pixels for an interactive segmentation. In
addition, a weight constraint is imposed on selected
sample pixels so as to minimise the graph cut shrink
bias. Peng and Veksler (2008) proposed a method
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Image Anal Stereol 2016;35:29-37
for graph cut parameter selection; they developed
an algorithm that selects a good segmentation based
on an array of graph cut parameter values. The
selection of best segmented image is based on texture
and homogeneity characteristics. Peng and Veksler
(2008) model uses a single parameter value throughout
the whole image for segmentation. However, over-
segmentation or under-segmentation may occur due to
the fact that some portions of the image may require
less smoothening than others (for example, object with
blurry boundary) (Candemir and Akgul, 2010).
Furthermore, in Candemir and Akgul (2010) an
adaptive parameter selection is introduced for object
segmentation. In this approach, the boundary of the
object of interest is carved by a canny edge detector
(Canny, 1986). Then the result is used to regularise
the parameter value of graph cut. However, for
non-homogeneous cell images, cell boundary may
not be extracted sufficiently, giving rise to over-
segmentation or under-segmentation. Vicente et al.
(2008) incorporated a connectivity prior in their graph
cut algorithm. Although their algorithm improves
graph cut segmentation, users are required to inscribe
additional scribbles during the process. This approach
is susceptible to time wasting.
Graph cut with shape prior has also been
researched in literature for object segmentation
(Freedman and Zhang, 2005). However, a limitation
of this method is the choice of an appropriate graph
cut parameter value (λ ; Lang et al., 2009; Wang et al.,
2013).
PAPER ORGANISATION
The rest of the paper is organised as follows:
related works with respect to graph cut parameter
selection are reviewed, followed by the introduction
of proposed model. In the next section, proposed
model is evaluated on public and private datasets
with discussions put forward. Future improvements on
proposed model are discussed in the conclusion.
MATERIAL AND METHODS
The proposed model takes advantage of image
logarithmic transform. This is necessary because of
the high variability of foreground pixel values and
provides a way to shrink the range of foreground
pixel values. Foreground pixels having low values
are compressed logarithmically and transformed into
high values to enhance the distinctive categorisation
of foreground pixels into boundary pixels and non-
boundary pixels. This transformation is important
in order to adjust and contextualise graph cut
parameter value across the distinctive categorisation of
foreground pixels. Invariably, weights of pixels found
in cell boundary are adjusted. An image smoothening
processs begins the model.
IMAGE SMOOTHING
In order to reduce noise, cell image is smoothened
using the 2D Gaussian filter defined as follows:
F(a,b) =
1
2πσ2
exp
(
−a
2 +b2
2σ2
)
, (1)
where σ determines the smoothening degree. Given an
image I(x,y), an enhancement with the Gaussian filter
F(a,b) of size m× n is obtained by performing the
convolution of F(a,b) with I(x,y) defined by Eq. 2:
IG(x,y) =
m−1
∑
a=0
n−1
∑
b=0
F(a,b)I(x−a,y−b) . (2)
IG(x,y) is the smoothened version of image I(x,y).
CELL BOUNDARY EXTRACTION
Cell images have varying degrees of intensity
levels; hence they do not always have homogeneous
structure (Chen et al., 2008). Furthermore, cells
possess weak boundaries, which makes it difficult to
identify or isolate individual cells in an image frame by
visual analysis (Al-Kofahi et al., 2010). In this work,
cell boundaries are revealed by shrinking the dynamic
range of foreground pixel values in the image. The
reason for this is to ensure that the foreground pixel
values are compressed into a minimum value range.
Another justification for shrinking the dynamic range
of cell images is that they are of low quality and appear
to fade into the background. As a result, we transform
their foreground pixel values from a low pixel value to
a high pixel value. Hence it is important to reveal cells
at the point at which they begin to fade and blend with
the background. The logarithmic function is defined in
Eq. 3:
IL(x,y) = c∗ IG(x,y)α , (3)
where IG(x,y) is the intensity value of pixel at the
location (x,y) of the smoothened input image. IL(x,y)
indicates the intensity value of pixel at location (x,y) of
the output image. α (alpha) controls the level of pixel
shrinkage, and c is the scaling factor.
The cell boundary extraction process is detailed in
Algorithm 1 and in Fig. 4.
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OYEBODE KO ET AL: Adaptive Parameter Selection for Cell Segmentation
Algorithm 1 Cell Boundary Extraction
Require: I, . Original Image
Ensure: Ib . Extracted cell boundary image
1: I is Guassian-filtered using Eq. 2 and result saved in IG
2: Logarithmically enhance IG using Eq. 3, save result in IL
3: Binarise IL using Otsu thresholding, save result in Io
4: Define a structuring element B of ones, of size 7 by 7
5: Use B to erode Io, save result in IErode (IErode = (Io	B))
6: Subtract IErode from Io, save result in Ib (Ib = Io− IErode)
end
Fig. 4. Cell boundary extraction process. (a)
Smoothened images (IG). (b) Logarithmically
transformed images (IL). (c) Binarised cell images
using Otsu thresholding (Io). (d) Cell boundary
extraction (Ib).
GRAPH CUT ENERGY FUNCTION
DERIVATION
An image is represented using a graph G = (V,E),
where the graph nodes V correspond to image pixels
(a,b,d,e, f ,g in Fig. 5) and graph edges E are links
between nodes (examples of edges in Fig. 5 are O−
a,C−a,a−b,b−d, and a−e), corresponding to links
between pixels in the image context. Additionally,
nodes O and C are in the set V representing terminal
links. The objective is to assign a label L ∈ {0,1} to
pixels in the segmented image where 0 and 1 represent
background and foreground respectively. A Bayesian
framework is used to model image segmentation. Let
K be the segmentation of a given image while I is the
measured brightness function, then we have
P(K|I) = P(I|K)P(K)
P(I)
. (4)
Suppose pixel positions in a cell image i =
0,1, . . .n, then the intensity values of these pixels
which depend on K are given as I(0), I(1), . . . , I(n),
where each intensity value is independent of the other.
A joint probability of their intensity values is given as
Fig. 5. Representation of an image in graph context.
P(I|K) = P(I(1)|K) P(I(2)|K) . . .P(I(n)|K)
=
n
∏
i=0
P(I(i)|K) . (5)
In Eq. 5, P(I|K) gives the likelihood function.
It emphasises the cell image creation process, that
is, the probability of quantifying I(i) when K is
given. In Eq. 4, P(K),P(I) are the prior probabilities;
P(K) describes the partitioning of grey values of
image pixels into ones and zeros while P(I) describes
their intensity distribution. The maximum a posteriori
(MAP) estimation (Boykov and Jolly, 2001) for image
segmentation is defined as in Eq. 6:
KMAP = argmax
K
P(I|K)P(K)
P(I)
. (6)
P(I) is a constant and the estimation can then be
rewritten as
KMAP = argmax
K
P(I|K)P(K) . (7)
The negative logarithm of the posterior probability
can be minimised yielding Eq. 8:
E(K) =− log
n
∏
i=1
P(I(i)|K)− logP(K) . (8)
The negative logarithm of the probability gives
the energy function E(K). Since the logarithm of a
product is equal to the sum of logarithms of terms of
the product, hence the energy function is rewritten in
Eq. 9:
E(K) =
n
∑
i=1
− log(P(I(i)|K))− logP(K) . (9)
In Eq. 9, n is the total number of pixels in a given
image. The prior probability (second term in Eq. 9)
is modelled as a markov random field (MRF) pair-
wise interaction between neighbouring pixels (i and j)
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Image Anal Stereol 2016;35:29-37
(Greig et al., 1989; Boykov and Jolly, 2001), which is
given as
B(K) =− logP(K), (10)
= ∑
(i, j)∈N
exp
(
−|I(i)− I( j)|
2
2σ2
)
· 1
ed(i, j)
.
In the right-hand-side of Eq. 10, N is the set of
neighbouring pixels (i and j) in a given image. ed(i, j)
provides the Euclidean distance between i and j
(Boykov and Jolly, 2001). B(K) favours neighbouring
pixels (i and j) having similar greyscale intensities.
B(K) has a low value when neighbouring pixels (i
and j) have different greyscale intensities. Hence the
behaviour of B(K) suggests a cut when neighbouring
pixels have different intensity values. σ describes how
much we are concerned about pixel similarity. Then,
Eq. 11 becomes the energy function,
E(K) = λ R(K)+B(K) , (11)
where
R(K) =−
n
∑
i=1
log(P(I(i)|K)) .
Within the context of a graph (Fig. 5) the data
term R(K) gives weight to each of the graph edges, for
example, edges O− a,C− a,O− b,O− e,O− f ,O−
g,C − e,C − f and C − b in Fig. 5. The weight of
these edges is determined by the negative logarithm
of the probability of a pixel being a foreground or
background pixel, considering sample pixels selected
by user. B(K) provides weight to node edges, for
example, edges a− b,b− d and a− e in Fig. 5. The
energy function in Eq. 11 is similar to the graph
cut energy function introduced by Boykov and Jolly
(2001); the first term gives the data term while the
second term gives the smoothness term. λ regulates
the relative importance of the data term versus the
smoothness term.
GRAPH CUTS ENERGY FUNCTION
MODIFICATION
We seek to adjust the parameter value λ
dynamically in the graph cut energy function. This
dynamic adjustment is motivated by Ib as discussed
earlier. Ib increases the weights of pixels at cell
boundaries in order to survive a cut. Thus, the graph
cut energy function may be rewritten as follows:
E(K) = λ̂ R(K)+B(K) . (12)
where λ̂ = λ (β Ib + Inb), Ib is boundary pixel, and Inb
is non-boundary pixel.
In Eq. 12, β (β = 2,3,4, . . .) defines the weighting
factor around cell boundaries. Eq. 12 shows that
the weights on cell boundary pixels via the data
term are increased. This development makes the
parameter value adaptive. Putting the boundary pixel
weights above other foreground pixel weights gives an
assurance that cell boundaries can survive the graph
cut shrink bias. The Max-Flow Min-Cut algorithm
proposed by Boykov and Kolmogorov (2004) has been
used for segmentation. Algorithm 2 summarises the
cell segmentation process.
Algorithm 2 Segmentation of cell image using
logarithmic transform and graph cut
Require: I, . Greyscale image
Ensure: IS . Segmented image
1: I is Gaussian-filtered using Eq. 2 and the result is saved in
IG
2: Find Ib for I using Algorithm 1
3: Construct the graph G from IG
4: for each pixel (x,y) of IG for the data term do
5: if IG(x,y) == Ib(x,y) then
6: Ib = 1, Inb = 0, λ̂ = βλ
7: Add weight λ̂R(K) to IG(x,y) in G to form a weight
link with terminal node O
8: Add weight 0 to IG(x,y) in G to form a weight link
with terminal node C
9: else
10: Ib = 0, Inb = 1, λ̂ = λ
11: Add weight λ̂R(K) to IG(x,y) in G to form weight
links with terminal nodes O and C
12: end if
13: end for
14: for each pixel (x,y) of IG for smoothness term do
15: Add weight B(K) to the link that connects (x,y) to its
adjacent neighbours
16: end for
17: Store the Minimum Cut Maximum flow of G in IS
end
RESULTS
DATASET
Experiment is conducted on fluorescence
microscopy images of human cells. These are cells
taken from different parts of the human body at the
research centre for HIV and Tuberculosis, University
of KwaZulu-Natal. The image dataset contains 30
images each having a size of 1201 by 901 pixels. Each
image has an average of 27 cells. The cell images
are captured within an interval of 10 minutes using a
time-lapse microscope. Ground truths to these images
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OYEBODE KO ET AL: Adaptive Parameter Selection for Cell Segmentation
are manually constructed. In order to strengthen the
evaluation process further, public available dataset
U2OS (Coelho et al., 2009) containing 48 images
was also used to test the performance of the proposed
model. Each image has an average of 40 cells.
EVALUATION
The performance of the proposed model is
measured using the Rand Index (RI), Hausdorff
distance (H) and Sensitivity (ST ) metrics (Coelho
et al., 2009). High values of RI and ST and a low value
of H are indicative of good segmentation. The Rand
Index (RI) is defined in Eq. 13:
RI(%) =
(TP+TN)
(TP+TN+FP+FN)
, (13)
where true positive (TP) defines the total number of
foreground pixels in the segmented image S (binary)
that overlap foreground pixels in the ground truth G
(binary). True negative (TN) gives the total number
of background pixels in the segmented image S that
overlap background pixels in the ground truth G. False
positive (FP) defines the total number of foreground
pixels in the segmented image S that are referenced
as background pixels in the ground truth G. False
negative (FN) defines the total number of background
pixels in the segmented image S that are referenced
as foreground pixels in the ground truth G. Hausdorff
distance (H) is defined in Eq. 14 as
H(G,S) = max{V (l) : Sl 6= Gl} , (14)
where l indicate co-ordinates of considered pixel pair
in S and G. V (l) gives the distance between the
considered pixel pair in S and G. The sensitivity (ST)
formula is obtained by:
ST(%) =
TP
TP+FN
. (15)
PARAMETER SELECTION
In this experiment, the weight factor β as well as
λ , the graph cut parameter, are both set to 20. For
optimal image enhancement (Eq. 3), the value of c
is set to two. This value is used for both public and
private dataset. However, α is set to 0.45 for public
dataset and 0.50 for the private dataset. For parameters
with respect to Gaussian smoothening indicated in
Eq. 2, we reflect on all potential combinations of σ and
the Gaussian kernel size m× n {σ ,m,n} = {2,3,3},
{2,5,5}, {2,10,10}, {3,3,3}, {3,5,5}, {3,5,5} and
{2,10,10}. The parameter {2,10,10}minimises noise
better than other combinations, hence it is adopted for
proposed model.
RESULTS DESCRIPTION
Some results of the application of proposed model
on cell images are presented. The proposed model
shows improved performance over other models while
considering metrics H,ST and RI as seen in Tables 1
and 2 and Figs. 6 and 7. These results (Fig. 6 and Table
1) demonstrate that elongated cells are segmented
to a reasonable degree. However, in extreme cases,
where cell boundaries are not visible, poor results are
obtained. Table 1 also indicates that the shrink bias of
graph cut is reasonably minimised by proposed model;
this is evident in the metrics ST and RI. In these
metrics, the contribution of FN is reduced as compared
to the traditional graph cut.
This analysis (shrink bias) also holds for the public
dataset as seen in Table 2, in terms of metrics H and
RI; proposed model performs better as compared to
other cell segmentation models. However, in terms
of the RI, proposed model is the second best. This
can be attributed to the fact that some extracted
boundaries via Algorithm 1 may not be actual cell
boundaries, but noise. Since boundaries of noise may
have been extracted, the FP component in the RI
metric is invariably increased. This obviously degrades
the performance of the proposed model. This shows
that a more sophisticated filtering method should be
adopted in order to reduce noise significantly. The
merging algorithm (Table 2) performs better with
respect to minimising its FP component of the RI
metric. The template-matching algorithm also shows
good performance with respect to RI; however, its H
value is the highest.
Table 1. RI, H and ST evaluation of proposed model
and traditional graph cut on private dataset.
Model RI(%) H ST(%)
Traditional graph cut
(Boykov and Jolly,
2001)
92.00 8.52 45
Proposed model 94.00 7.78 60
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Image Anal Stereol 2016;35:29-37
Fig. 6. Visual results of segmentation of four samples of cell images from private dataset. (a) Original images.
(b) Ground truth. (c) Traditional graph cut. (d) Proposed model.
Fig. 7. Visual results of segmentation of four samples of cell images from public dataset. (a) Original images. (b)
Ground truth. (c) Traditional graph cut. (d) Proposed model.
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OYEBODE KO ET AL: Adaptive Parameter Selection for Cell Segmentation
Table 2. RI, H and ST evaluation of proposed model
and traditional graph cut on public dataset.
Model RI(%) H ST(%)
Otsu threshholding
(Coelho et al., 2009) 92 34.9
Template-matching
(Chen et al., 2013) 95 77.8
Merging algorithm
(Coelho et al., 2009) 96 12.9
Traditional graph cut
(Boykov and Jolly,
2001)
92.4 15.11 83.58
Proposed model 95.30 12.69 88.63
DISCUSSION
One contributing factor to the improved
performance of proposed model is the incorporation of
cell boundary into graph cut. By giving more weight
to pixels at cell boundaries, the shrink bias of graph
cut is mitigated. The contributing factor to the poor
performance of traditional graph cut which is obvious
in Fig. 6 is the inability to adjust its parameter (λ )
value adaptively; hence the shrink bias of graph cut
comes into play.
However, when images contain touching cells or
dense cells, there is a reduction in the performance
of the model. For example, the model cannot draw
boundary lines to separate touching cells. The model
sees touching cells as a single cell. For future work,
one may investigate the possibility of incorporating
the segmentation of cell clusters. Our approach is
an interactive cell segmentation process where user
selects sample foreground and background pixels. The
automation of foreground and background sample
pixel selection may further improve the performance of
proposed model. In addition, a more robust approach
that is immune to noise for boundary extraction is
suggested for better performance.
CONCLUSION
This work has explored adaptive graph cut
parameter selection. This is achieved by cell boundary
extraction and fusing this into the graph cut
parameter value, thereby providing an avenue to alter
dynamically pixel weights in the graph formulation.
This development reasonably counters the shrink bias
of graph cut. The proposed model has been tested on
78 cell images with an average running time of 19
seconds per image on a Windows 7, Core i5 processor,
and experiment results indicate a better segmented
output. This model provides a basis for objective
diagnosis of diseases such as tuberculosis or cancer by
medical experts.
ACKNOWLEDGMENT
The authors would like to thank Dr Alex Sigal of
the KwaZulu-Natal Research Institute for Tuberculosis
and HIV (K-RITH), for providing the private dataset
used in this research.
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