.


38 UHD Journal of Science and Technology | April 2017 | Vol 1 | Issue 1

1. INTRODUCTION

Biosensors can sense single molecule through using 
nanopores. They may sense unlabeled biopolymers such as 
DNA and RNA and single proteins. The sensing takes place 
when ion currents reduced largely due to blocking pores 
by passing molecules [1]. The nanopore diameter is very 
important for sensing molecules. The main step for finding 
that is through using segmenting of  them from scanning 
electron microscope (SEM) image.

Image segmentation defined as dividing images into 
multiple parts that have homogeneity in pixel intensity, 
color, or texture [2]. One of  the simple, sometimes useful, 

segmenting methods is threshold technique. However, it 
is time-consuming for its strategy based on trial and error 
method, and for sometimes, a single threshold value does not 
work well, especially, for a series of  image frames of  video 
data. Akhtaruzzaman et al. [3] used an automated threshold 
detection on a video which is a series of  image frames of  
human walking to segment human lower limbs. They applied 
automated threshold detection to convert the image frames 
into grayscale image, line fill algorithm to smoothing the edges 
of  object, and remove background to get out the object.

In general, image enhancing through denoising is an 
important previous step before segmenting objects. One 
of  the denoising filters is bilateral filter which reduces noise 
with remaining sharp edges of  the objects. Besides, Nguyen 
et al. [4] denoised specific artifacts and segmented the full 
body bone structure by employing 3D bilateral filter and 3D 
graph-cut, respectively. On the other hand, Sahadevan et al. [5] 
increased the accuracy of  super vector machine classifier 
using a bilateral filter which merges spatial contextual 
information to spectral domain.

Estimation of Nanopore Size Using Image 
Processing
Haidar Jalal Ismail, Azeez Abdullah Azeez Barzinjy, and Kadhim Qasim Jabbar
Department of Physics, College of Education, Salahaddin University-Erbil, Zanko, Erbil, Iraq

A B S T R A C T
Nanopores, which are nanometer-sized holes, have been utilized in apparatus that point toward sensing a range of molecules 
such as DNA and RNA and single proteins The important factor for sensing molecules is diameters of nanopores which can 
be found through a substantial process called segmenting for nanopores of scanning electron microscope (SEM) images. In 
this investigation, four segmentation methods, namely, threshold, bilateral filter, k-means, and expectation maximization-
Gaussian mixture model (EM-GMM) which has been utilized to segment three SEM images of nanopores efficiently. The 
quality of segmentation evaluated objectively through computing Rand index among them. Consequently, the nanopore size 
of Al

2
O

3
 films computed by means of SEM images. This study found that EM-GMM segmenting method gives promising 

results among other examined methods. It is for their high R-index, minimum adjustment parameters (just one variable 
which set usually 2), and low consuming time. Hence, it can be used efficiently for computing nanopore count and size.

Index Terms: Feature Extraction, Image Segmentation, Nanopore, Segmentation Evaluation

Corresponding author’s e-mail: haidar.ismail@su.edu.krd

Received: 10-03-2017 Accepted: 25-03-2017 Published: 12-04-2017

Access this article online

DOI: 10.21928/uhdjst.v1n1y2017.pp38-44 E-ISSN: 2521-4217
P-ISSN: 2521-4209

Copyright © 2017 Ismail, et al. This is an open access article distributed 
under the Creative Commons Attribution Non-Commercial No 
Derivatives License 4.0 (CC BY-NC-ND 4.0)

O R I G I N A L  RE SE A RC H  A RT I C L E UHD JOURNAL OF SCIENCE AND TECHNOLOGY



Haidar Jalal Ismail, et al.: Estimation of Nano-Pore Size

UHD Journal of Science and Technology | April 2017 | Vol 1 | Issue 1 39

Another method of  segmentation is K-means which put the 
image into multi cluster of  pixels according to factors such 
as their intensities. Chen et al. [6] propose a semiautomatic 
segmentation method, using K-means, to determine object’s 
mean temperature and variance through segmenting contours 
of  thermal images taken by the optical camera.

Fu and Wang [7] applied expectation maximization-
Gaussian mixture model (EM-GMM) on color images to 
segmenting them, and their results approve the power of  
it. The EM-GMM and fuzzy-C-means (FCM) methods are 
widely used in image segmentation. However, they have a 
major drawback for their sensitivity to the noise. Kalti and 
Mahjoub [8] proposed a variant of  these methods to resolve 
this problem. Their results showed improvement compare 
to standard version of  EM-GMM and FCM.

Several researches work to find geometrical structures 
of  nanopores. Alexander et al. [9] computed nanopore 
size, perimeter, and some other geometric features using 
histogram equalization, morphological, and statistical 
operations. In another work, that done by Phromsuwan 
et al. [10], size of  nanopores of  SEM images obtained through 
using morphological and Canny edge detector techniques. 
Parashuram and Vidyasagar [11] used morphological and 
global thresholding for obtaining nanopore diameter and 
statistical features. Same authors with Muralidhara [12] using 
same operations to obtain perimeter of  the nanopores. It can 
be realized that all above methods using methods that need 
trial and error parameters to give proper results.

This work aims to find semiautomatic algorithm to find 
diameter of  nanopores of  SEM images through examine four 
segmenting techniques. The performance will be evaluated 
objectively, and the average of  nanopore’s diameter will be 
computed.

2. MATERIALS AND METHODS

Three SEM images of  the nanopores anodic alumina 
film [13] used in this study for segmenting by our segmenting 
techniques and compute their diameters and number of  pores. 
They consist of  three SEM images with different widening 
times, namely, 0, 10, and 20 minutes as shown in Fig. 1.

The images segmented by four methods. The simple method 
is thresholding method that used here as ground truth images 
for objective evaluating of  other segmenting methods. The 
second and third segmenting methods utilize bilateral filter, 

k-means, as the first step and using region selector as the 
second step. The fourth one is segmenting images using 
EM-GMM (Fig. 2).

Thresholding is a technique of  selecting optimum gray level 
value which separates the region of  interest from other 
regions. Thresholding produced binary images from gray level 
by making pixels lower or greater than a gray level value to 
zero and other remaining pixels to one. If  g(x, y) is threshold 
output of  an input f(x, y) at specific input gray level value T, 
it can be described as [14] follows:

g x,y =
f x,y >T

otherwise
( ) ( )





1

0
 (1)

K-means method divides pixels into a number of  separate 
clusters. It’s algorithm consists of  two steps. First, it finds 
k centroid (k number of  clusters) for pixels of  the image, 
and second, relate each pixel to a centroid through using 
different methods of  computing distance between them. 
Euclidean distance may be used to measure distance, and it 
defined as follows:

d=||p (x,y)−c
k
|| (2)

Where p(x, y) is an input pixel to be cluster and c
k
 is the cluster 

centers. After grouping pixels into k sets (i.e. clusters), new 
Euclidean distance evaluated between each center and pixels, 
so pixels assigned to the minimum Euclidean distance [15].

The bilateral filtering is a technique for smoothing and 
sharpening edges of  an image. It obtained by applying one 
Gaussian filter for obtaining the spatial domain and another 
one for intensity domain. The filter output of  s pixel is given 
by following equation:

J s =
1
K(s)

(p s)(I I )Ip p s p( ) ∑ − −∈∅  (3)

Where K(s) is normalization expression:

K s = f(p s)g(I I )p p s( ) ∑ − −∈∅  (4)

Where f  and g are Gaussian, in the spatial domain and 
in the intensity domain, which represents the range filter, 
respectively [16].

Region selector method uses roicolor command in Matlab 
which select wanted region according to color or intensity 
levels in grayscale image.



Haidar Jalal Ismail, et al.: Estimation of Nano-Pore Size

40 UHD Journal of Science and Technology | April 2017 | Vol 1 | Issue 1

Fig. 1. Four segmentation methods for three scanning electron microscope images with pore widening times: (a) 0 min, (b) 10 min, and (c) 20 min 
(Scale bar = 500 nm) [13]

cba

The GMM consists of Gaussian distributions that defined 
as follows: f x = p N x |Qn k n kk=1

K
( ) ( )∑  (5)



Haidar Jalal Ismail, et al.: Estimation of Nano-Pore Size

UHD Journal of Science and Technology | April 2017 | Vol 1 | Issue 1 41

Where every component of  function N(x
n
|Θ

k
) is a Gaussian 

distribution which, for a D-dimensional vector x, defined 
as follows:

N x
1

(2p)
1
S

exp -
1
2
x-m (x-m)D/2 1/2

T -1|ΘΘ( ) = ( ) ∑{ } (6)
Where µ and Σ are a D-dimensional average vector and a 
D × D covariance matrix, respectively. The prior distribution 
π

k
 defines the probability of  noticing x

n
 that belongs to the 

kth class Ω
k
. It is unrelated to the observation x

n
. Moreover, 

π
k
 must possess these restrictions:

0 1, ; k=1, Kk kk=1
K

≤ ≤ ∑π π ....,  (7)
After finding the density function for an observation, the 
log-likelihood function of  N observations is as follows:

L N x |k n kk
K

n

N
Θ Θ( ) = ( )

== ∑∑ log( π11  (8)
According to Equations 5 and 8, the major feature of  the 
GMM is that its form is too simple and it needs few variables. 
Moreover, when GMM used in image segmentation, the 
correct results obtained if  they unrelated to each other. 
To find the variables (π

k
,
 
µ

k
,
 
and Σ

k
), the EM step is usually 

applied to get the upper limit of  the log-likelihood function 
in Equation 8. The last probability for expectation stage of  
EM obtained as follows:

p |x
N x

N x
t

k n
k n k

j=

K
j n j

Θ
Θ

Θ
( ) =

( )
( )∑

π |

|
1
ππ

 (9)

In the maximization step of  EM, the parameters (π
k
,
 
µ

k
,
 
and 

Σ
k
) are changed iteratively through the following formulas:

πk
t+1 n

N t
k n n

n

N t
k n

p x X

p |x
=

( )
( )

=

=

∑
∑

1

1

ΘΘ

ΘΘ

|
 (10)

ΣΣk
t n

N t
k n n k n k

T

n

N t
k n

p |x �(x -m )(x -m )

p x
+ =

=

=
( )

( )
∑

∑
1 1

1



 |
 (11)

πk
t+1 n

N t
k np x

N
=

( )
=∑ 1 ΘΘ |  (12)

Where t denotes the iteration value. The loop is stopped in 
the convergence condition. The value from Equation 9 for 
maximum posterior criterion used to get the class label for 
each pixel [17].

A. Rand Index
The Rand index, which founded by William Rand, used for 
the comparison of  two arbitrary segmentations using pair-
wise label relationships. It obtained by division of  the number 
of  pixel pairs that have the same label relationship in both 
segmentations. The n

uv
 is the number of  points labeled u in 

S and that labeled v in S’. The labeled points u in the first 
part of  S, and labeled points v in second part S’ are termed 
as n

u■
 and n

■v
, respectively. Afterward:

n
u■

=∑
v
n

uv
 n

■v
=∑

u
n

uv 
(13)

Clearly ∑
u
n

u■
=∑

v
n

u■
=N is the entire data points. Hence, the 

Rand index is as follows:

R S,S

n n n

N(N-1) /2

'
u u

2

v u

2

u,v uv

2

( ) = −
+( )−∑ ∑ ∑

1

1

2
� � �

 (14)

The R-index is 1 when both segmentations have total 
similarities and 0 for zero ones. This type of  similarity 
measurements takes small running time when unique labels 
in S and S’ are smaller than total data numbers N [18].

3. RESULTS AND DISCUSSION

All three SEM images segmented using threshold technique 
obtained after a large number of  trial and error for optimize 
threshold intensity pixel value, morphological operation, and 
removing small objects. They considered as ground truth 
images through visual perception to objective evaluating 
other segmenting methods (Fig. 1). The results of  other 
segmenting methods are shown in same figure too.

Fig. 1a shows SEM that suffers from some noise effect. 
The Wiener filter and adaptive histogram equalization used 

Fig. 2. Image processing steps for different segmentation methods



Haidar Jalal Ismail, et al.: Estimation of Nano-Pore Size

42 UHD Journal of Science and Technology | April 2017 | Vol 1 | Issue 1

Fig. 3. (a-c) Total counting nanopores and distribution of nanopore sizes for threshold segmenting (ground truth image) and expectation 
maximization-Gaussian mixture model (higher R index) for all three scanning electron microscope types

a cb



Haidar Jalal Ismail, et al.: Estimation of Nano-Pore Size

UHD Journal of Science and Technology | April 2017 | Vol 1 | Issue 1 43

for denoising and contrast enhancement before segmenting 
by threshold technique. Nevertheless, it still effects on 
segmenting by other methods.

Fig. 1b and c show good segmenting for all segmenting 
methods. Fig. 3 presents all three images that segment by 
threshold, ground truth image, and EM-GMM, higher R 
index, that number labeled each pore. Furthermore, the 
distribution of  pore size which mentioned showed in same 
figure. They can be fitted mainly as Gaussian distribution as 
appear charts of  Fig. 3 and that in agreement with what in 
results of  Macias et al. [13].

The time consuming for running code, Rand index, number, 
and diameter of  nanopores for segmenting methods and for 
all three SEM images presented in Table I. The obtained 
results for diameter of  nanopores are in a good agreement 
with Macias et al. [13] results for threshold segmenting and 
smaller for EM-GMM segmenting. The method of  analysis 
SEM images in mentioned reference is unknown. The 
EM-GMM is semiautomatic method, with high R index, 
and relatively smaller time consuming is better than other 
segmenting methods studied here.

4. CONCLUSION

Four different segmenting methods are applied on three 
SEM images with various time widening pores 0, 10, and 
20 minutes. It can be noticed that the threshold segmenting 
possesses good results, but perhaps, it needs a large number 

of  trial and error for choosing optimum threshold pixel 
intensity and needs also morphological operation and 
removing small objects. The authors also concluded that 
the EM-GMM is superior than bilateral filter and K-means 
with region selector, since it has higher R index than them. 
Consequently, their segmenting results used for pore counting 
and computing their diameters. Likewise, it has relatively small 
time consuming of  running. Accordingly, EM-GMM can be 
used professionally for segmenting SEM images and finding 
number of  pores and their diameters.

5. ACKNOWLEDGMENT

The authors would like to express their acknowledgment to 
the Salahaddin University for supporting him with available 
tools.

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TABLE I
Time Consuming, Rand Index, Nanopore Diameter and Nanopore Counts for all SEM Images Segmented by 

the Four Techniques
Nanopore Threshold segment Bilateral filter, region selector K*means, region selector EM-GMM
a

Time (s) 1.31 29.21 15.51 19.96
Rand index - 0.781 0.757 0.91
Diameter (nm) 36.7±10.4 - - 39.3±19.5
Pore count 51 - - 60

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Rand index - 0.599 0.592 0.870
Diameter (nm) 54.2±11.9 - - 46.6±9.1
Pore count 81 - - 83

c
Time (s) 1.36 30.35 14.79 13.68
Rand index - 0.503 0.503 0.755
Diameter (nm) 71.8±15.9 - - 59.8±12.7
Pore count 83 - - 84

SEM: Scanning electron microscope, EM‑GMM: Expectation maximization‑Gaussian mixture model



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