Fuzzy Region Merging Using Fuzzy Similarity Measurement on Image Segmentation

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 7, No. 6, December 2017, pp. 3402~3410
ISSN: 2088-8708, DOI: 10.11591/ijece.v7i6.pp3402-3410  3402
Journal homepage: http://iaesjournal.com/online/index.php/IJECE
Fuzzy Region Merging Using Fuzzy Similarity Measurement
on Image Segmentation
Wawan Gunawan1
, Agus Zainal Arifin2
, Rarasmaya Indraswari3
, Dini Adni Navastara4
1
Department of Science, Informatic Engineering, Institut Teknologi Sumatera, Bandar Lampung, Indonesia
2,3,4
Departement of Informatics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia
Article Info ABSTRACT
Article history:
Received Apr 8, 2017
Revised Sep 8, 2017
Accepted Sep 25, 2017
Some image’s regions have unbalance information, such as blurred contour,
shade, and uneven brightness. Those regions are called as ambiguous
regions. Ambiguous region cause problem during region merging process in
interactive image segmentation because that region has double information,
both as object and background. We proposed a new region merging strategy
using fuzzy similarity measurement for image segmentation. The proposed
method has four steps; the first step is initial segmentation using mean-shift
algorithm. The second step is giving markers manually to indicate the object
and background region. The third step is determining the fuzzy region or
ambiguous region in the images. The last step is fuzzy region merging using
fuzzy similarity measurement. The experimental results demonstrated that
the proposed method is able to segment natural images and dental panoramic
images successfully with the average value of misclassification error (ME)
1.96% and 5.47%, respectively.
Keyword:
Ambiguous region
Image segmentation
Fuzzy region merging
Copyright © 2017 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Wawan Gunawan,
Department of Science, Informatics Engineering,
Institut Teknologi Sumatera,
Bandar Lampung, Indonesia.
Email: wawan.gunawan@if.itera.ac.id
1. INTRODUCTION
Segmentation is a basic process in image processing. The purpose of segmentation is to divide the
image into regions that have homogenous features or have the same characteristics, e.g., contours, colors, and
contrast [1],[2]. In general, image segmentation methods can be divided among three categories, namely
automatic, semi-automatic, and manual [3]. Automatic image segmentation methods can be categorized into
several groups, namely the histogram-based, edge-based, region-based [4],[5], and hybrid technique [6].
Although automatic segmentation method is fast, optimization process needs to be done to get the optimal
parameters that greatly affect the accuracy of automatic segmentation results [7].
Automatic segmentation methods have drawbacks when the object and the background region of the
image did not have a clear dividing line, causing a difference in perception between the results of the
segmentation method and the user's wishes [8]. Semi-automatic segmentation method has been developed to
overcome that problem by providing additional information from the user to assist the system in the
segmentation process. Under these conditions, our study used a semi-automatic segmentation approach or
often referred to as the interactive image segmentation.
In interactive image segmentation, user can interact by providing input (user marking) that helps the
system in the determination of the object and the background area in the image. Several studies related to
semi-automatic segmentation have been proposed by [3],[9]-[12]. Based on those study, interactive image
segmentation consist of four main stages. The first stage is dividing the image into several small regions
(region splitting) to get the initial segmentation. The second stage is user marking manually some regions as

IJECE ISSN: 2088-8708 
Fuzzy Region Merging Using Fuzzy Similarity Measurement on Image Segmentation (Wawan Gunawan)
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object or background. The third stage is the extracting each region based on its features, such as color, shape,
membership function, texture, or size of the region. The last stage is merging all regions, to get two clusters
which are background and object.
Some regions have unbalance information values, such as blurred contour, shade, and uneven
brightness. In this study, we refer those regions as ambiguous regions. The ambiguous region is very
influential in the process of region splitting because they are very similar hence it is difficult to separate
them. The ambiguous region will be considered a single region even though the region has two values of
information, which are objects and background information. This can lead to error during the region merging
process for causing over segmentation. Figure 1(A) is an example of the ambiguous region, we can see that
the color in the region is very similar (fuzzy region) so it would be difficult to separate the region [13]-[14].
In Figure 1(B), although those two regions that have similar color, there is a clear line between those regions
hence it will be easy to separate them.
Figure 1. Different transition color in the region. (A) The ambiguous region, (B) Non -ambiguous region
The ambiguous region will affect the region merging process because the ambiguous region caused
over segmentation in the region splitting process. In binary region merging (BRM) [10],[15] each region has
only one probability (crisp fuzzy) to be in the object or background cluster. For images that have an
ambiguous region, binary region merging cannot be done because the region has two information values.
In this study, we propose a new strategy for region merging, namely fuzzy region merging, using
fuzzy similarity measurement in interactive image segmentation. Our contribution to this research is the
fuzzy region merging (FRM) process where each region will be merged using fuzzy similarity measurements,
so ambiguous regions within the image can be separated.
2. RESEARCH METHOD
Input images that are used for this study are natural images and dental panoramic images. The
natural images are obtained from real-world objects with different backgrounds and objects. Dental
panoramic images are obtained from Airlangga University Hospital [16]. Overall, we used grayscale images.
In this study, we focused just on the region merging strategy to overcome the ambiguous regions on the
image. We find the optimal similarity between regions using fuzzy similarity measurement. The steps of our
proposed method can be seen in Figure 2.
Figure 2. Stages of the proposed method
2.1. Initial Segmentation
Initial segmentation aims to divide the image into several small regions that share similar
characteristics. In this study, to get initial segmentation we use mean-shift segmentation software created by
A B

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IJECE Vol. 7, No. 6, December 2017 : 3402 – 3410
3404
Edison System. The image is divided into several regions based upon the probability density gradient
functions. The result of the initial segmentation using the mean-shift algorithm is better than other methods
of low-level segmentation, because it is considering the spatial information and shape of the object image
[10].
2.2. Markers
Interactive image segmentation provides user interaction with the segmentation system in the form
of markers. Manual marking is one of the most major stages in the interactive segmentation because it will
affect the segmentation result. Interactive image segmentation is very sensitive to the quality of marking and
the number of marker [17]. Figure 3 illustrates the region marking process for natural and dental panoramic
images, the green line indicates the object region and the blue line indicates the background region. The
features of the regions that has been marked as object or background is carried out to determine its
characteristics.
Figure 3. Results of initial segmentation and user marking
2.3. Initialization of Fuzzy Region
Each member of the fuzzy set has a degree of membership value that determines the potential
members can enter a fuzzy. This stage is used to find the fuzzy region in the image, where the parameters of
each region that has been marked as the object 𝑀 𝑂 and background 𝑀 𝐵 will be calculated. Parameter
obtained by finding the highest gray level at each marker of region background 𝑀 𝑏
(𝑓)
and from the smallest
gray level at each marker of object region 𝑀𝑜
(𝑓)
. 𝑀 𝐵 value will always smaller than the value of 𝑀 𝑂. The
value of 𝑀 𝐵 and 𝑀 𝑂 is calculated using Eq. 1-3. Figure 4 shows the illustration of the determination of 𝑀 𝑏
(𝑓)
and 𝑀𝑜
(𝑓)
parameters to describe the value of 𝑀 𝐵 and 𝑀 𝑂. Fuzzy region is an ambiguous region of the image
which intensity is always between 𝑀 𝐵 and 𝑀 𝑂. Initial seed of background region 𝐶 𝐵 is the area between 𝑀 𝐵
and the minimal gray level in the histogram. Initial seed of object region 𝐶 𝑂 is the area between 𝑀 𝑂 and the
maximal gray level on the histogram.
𝑀 𝐵 = max⁡( 𝑔; 𝑀 𝑏
(𝑓)
) (1)
𝑀 𝑂 = min⁡( 𝑔; 𝑀𝑜
(𝑓)
) (2)
𝑓(𝑥) = {
𝑀 𝐵 =⁡ 𝑀 𝑂;⁡𝑀 𝑂 = 𝑀 𝐵, 𝑉𝐵 > 𝑉𝑂
𝑀 𝐵 = 𝑀 𝐵;⁡𝑀 𝑂 = 𝑀 𝑂, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(3)
After the fuzzy region was found, the next step is calculate the membership function in the gray
level histogram. S-function calculates the background membership function 𝜇 𝐵 and Z-function calculates the
object membership function 𝜇 𝑜. Each membership function is controlled by a point 𝑀 𝐶 = 127and is
calculated using Eq. 4 and Eq. 5. Figure 5 illustrates S-function that forms the letter S with a green line on the
histogram.

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Figure 4. Initializes the fuzzy region in the histogram
Figure 5. Determination of S-function and Z-function in the gray level histogram
The smaller the value of gray level in the histogram, the greater the membership function of
background in the histogram. Z-function forms the letter Z with red line on the histogram. The larger the
value of gray level in the histogram, the greater the gray level membership function of object in the
histogram. We use S-function and Z-function because these functions consider the membership function of
the object and the background object also against a contradictory background.
𝜇 𝐵(𝑔) = 𝑆(𝑔; 𝑀 𝐵, 𝑀 𝐶, 𝑀 𝑂) =
{
0,⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝑔<𝑀 𝐵⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡
2{
𝑔−𝑀 𝐵
𝑀 𝑂−𝑀 𝐵
}
2
,⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝑀 𝐵≤𝑔≤𝑀 𝐶⁡⁡
1−⁡2{
𝑔−𝑀 𝑂
𝑀 𝑂−𝑀 𝐵
}
2
,⁡⁡⁡⁡⁡⁡𝑀 𝐶<𝑔≤𝑀 𝑂
1,⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝑔>𝑀 𝑂⁡⁡⁡⁡⁡⁡⁡⁡
⁡⁡
(4)
𝜇 𝑂(𝑔) = 1 − 𝑆(𝑔; 𝑀 𝐵, 𝑀 𝐶, 𝑀 𝑂) (5)
2.4. Fuzzy Region Merging
The last stage is fuzzy region merging for each fuzzy region⁡fi….rϵ⁡F. We use fuzzy similarity
measurement on initial seed of background region CB and initial seed of object region CO. Fuzzy similarity
calculated based on the similarity between the gray level and the intensity, membership functions, and the
difference of membership function with the ordinal set. Fuzzy similarity measurement δ calculates the initial
subset of global information CB and CO to local information on each fuzzy region fi⁡ in the image as
illustrated in Figure 6. Similarity value δ for set (CX ∪ {fig⁡}), initial seed of an area CX, membership of all g
gray level in the fuzzy region fi⁡, and gray level intensity h(g), can be calculated using Eq. 6.
(Cx ∪ {fij⁡}) =
∑g=1
n (g−fm(Cx∪{fig⁡})2
∑z=1
n ⁡h(g)
, (6)

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Figure 6. Fuzzy region merging using fuzzy similarity measurement
Fuzzy mean value 𝑓𝑚(𝐴) of the merged area 𝐴, that is considering the gray level intensity ℎ(𝑔),
membership functions 𝜇 𝐴(𝑔), and the difference of membership function with the ordinal set |(μA(g) −
μA
′
(g)|, can be calculated using Eq. 7. Based on the results of fuzzy similarity measurement, each fuzzy
region 𝑓𝑖𝑔⁡ can be merged to background or object cluster based on the greatest similarity of the fuzzy region.
Determining the similarity value 𝑔 in fuzzy region 𝛿𝑖𝑔 can be calculated using Eq. 8 by finding the largest
index.
𝑃(𝐴) =⁡∑ 𝑧=1
𝑛
⁡ℎ(𝑔)⁡× 𝜇 𝐴(𝑔) × |(𝜇 𝐴(𝑔) −⁡ 𝜇 𝐴
′
(𝑔))|. (7)
𝛿𝑖𝑔 = 𝑎𝑟𝑔𝑚𝑎𝑥(𝛿(𝐶 𝐵 ∪ {𝑓𝑖𝑗⁡}) ∗ 𝛿(𝐶 𝑂 ∪ {𝑓𝑖𝑗⁡})) (8)
3. EXPERIMENTAL RESULT
The proposed method is implemented on the 15 dental panoramic images (that have been used in
[12] and [16]) and 10 natural images. Figure 7 show several of the test images after initial segmentation and
user marking process. Figure 8 shows the ground truth images that are created manually. Figure 9 shows the
segmentation results of the proposed method. We also compared our proposed method with binary region
merging approach proposed by Ning et.al. [10], named maximal similarity based region merging (MSRM).
(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 7. Sample of input images

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(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 8. Ground truth images
(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 9. Segmentation results of the proposed method
Segmentation results of MSRM are shown in Figure 10. Each segmented image will be compared
with ground truth images to determine the performance of segmentation results. In this study, the evaluation
was conducted by using misclassification error (ME) that is calculated based on the Eq. 9.
𝑀𝐸 = 1 −
|𝐵 𝑂∩𝐵 𝑇|+|𝐹 𝑂∩𝐹 𝑇|
|𝐵 𝑂|+|𝐹 𝑂|
, (9)
where 𝐵 𝑂 and 𝐹𝑂 are the background and the object of the ground truth image, while 𝐵 𝑇 and 𝐹𝑇 are the
background and the object of the segmentation result. The smaller value of ME shows the segmentation
results method is getting better and closer to ground truth images.
The implementation results based on the value of ME for several of the test images is shown in
Table 1. The proposed method provides better performance than MSRM with an average ME value 4.55%
for natural images and 5.46% for dental panoramic images. It was concluded that the proposed method is
more resistant to the interference of ambiguous region.

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(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 10. Segmentation results of the MSRM method
Table 1. Comparison result of the proposed method and MSRM on several test images
No Images
Misclassification Error (%)
MSRM Proposed method
a Dental 1 1.97 2.38
b Dental 2 15.64 9.42
c Dental 3 33.47 14.38
d Dental 4 17.37 7.70
e Natural 1 7.60 7.52
f Natural 2 1.11 0.77
g Natural 3 0.91 0.98
h Natural 4 2.48 3.16
4. DISCUSSION
Based on the experimental results, the discussion of this study is divided into 3 sections. Section 4.1
will discuss about the initial segmentation process using the mean-shift algorithm. Section 4.2 analyzes user
marking process. And Section 4.3 will analyze the fuzzy region merging.
4.1. Experiment Analysis of Region Splitting
Region Splitting using mean-shift software from Edison system has been successfully implemented
to get the initial segmentation. The image can be divided into several homogeneous regions. Some studies
also used the mean-shift software to get the initial segmentation as proposed by [3],[9]-[12]. There are two
parameters that must be entered for this application is spatial bandwidth (sb) and the color bandwidth (cb). In
this study, we test the spatial bandwidth values between 7-20 for natural images and 20-50 for dental
panoramic images. For color bandwidth, we use value of 3.5-6.5 for natural images and 4.5-5.5 for dental
panoramic images.
On image that has an ambiguous region, it is very difficult to get the right parameters to obtain the
initial segmentation. Figure 11 shows the example of initial segmentation with different parameters. The
images in the first row on Figure 11 shows that there will be different initial segmentation result using
different parameters. However, over segmentation is happened on those results because there is ambiguous
elapsed areas within the region. This is unlike the initial segmentation results for the images in the second
row on Figure 11. It can be concluded that the ambiguous region will be very influential at the time of the
initial segmentation and will certainly affect the results of segmentation.

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(sb = 7 and cb = 3.5) (sb = 7 and cb = 6.5) (sb = 20 and cb = 4.5) (sb = 40 and cb = 6.5)
(sb = 7 and cb = 3.5) (sb = 7 and cb = 6.5) (sb = 20 and cb = 4.5 (sb = 40 and cb = 6.5)
Figure 11. Test initial segmentation with different parameter
4.2. Experiment Analysis of Markers Process
Interactive segmentation approach is very sensitive to the quality of marking and the number of user
marker. This phenomenon has become a major concern in determining the number of given markers that will
be used as a parameter [17]. Table 2 shows the number of markers based on the average value of ME on the
natural and dental panoramic images. Number of marker 1, means that there is one marker for object and one
marker for background show the smallest value of ME compared with two and three markers.
Table 2. Determination of Marker Number
Images
Number of Markers & Misclassification Error (%)
1 2 3
Natural 2.04 5.03 5.07
Dental Panoramic 5.47 8.82 10.31
4.3. Experiment Analysis of Fuzzy Region Merging
Binary region merging (BRM) approach, as proposed [10] is not so effective for images that have a lot
of ambiguous regions. The ambiguous region will lead to over-segmentation because there are some regions
that have two values of information, both as background and object. To overcome this problem, this study
propose fuzzy similarity measurements to find the greatest similarity value for the ambiguous region. Figure
12 illustrates the differences of segmentation result in the binary region merging (BRM) and the proposed
fuzzy region merging (FRM). In Figure 12(b), we can see that each region has only a probability value of 0
and 1, in contrast to proposed method in Figure 12(c) where the value of each region ranged between 0 and 1.
(a) (b) (c)
Figure 12. (a) Initial segmentation (b) Binary Region Merging, (c) Fuzzy Region Merging
5. CONCLUSIONS

 ISSN: 2088-8708
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In this study, we propose a new strategy for region merging process using fuzzy similarity
measurement for image segmentation. Mean-shift algorithm was implemented to get initial segmentation. In
the marking process, user give marker for the appropriate object and background region. Our contribution of
this research is to separate ambiguous regions in the image using fuzzy similarity measurement. Based on the
experimental results on the natural and dental panoramic images, the proposed method has successfully
segmented the images with an average value of misclassification error (ME) 5.47% and 1.96%, respectively.
The proposed method only measures information from the gray level features and membership function.
Therefore, combining information from other features such as spatial information, texture, and shape for
region merging process can be developed further in order to obtain more accurate segmentation results.
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