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Abstract: This paper proposed a Fuzzy monotonic
inclusion (FMI) approach in order to measure similarity
between images. Firstly, an image is segmented to several
regions, then each region is described by a fuzzy set.
Finally, extracted features from each region are mapped
into a fuzzy similarity model. FMI scheme makes relation
between regions and based on the relations, the regions are
selected for the comparison process. Thus, for every image
region, both parameters of fuzzy location and area is
extracted. We investigated FMI From the conceptual point
of view and Semantic relation among Objects. The
experimental results on Label Me database, a real world
image dataset including 163,000 images, show superiority
of the FMI in compared with UFM and Fuzzy Histogram.
Keywords: Fuzzy similarity, image retrieval,
monotonic fuzzy inclusion measure, similarity
measure.
1. Introduction
Since extremely powerful technologies are now
available to generate and process digital images,
there is a concomitant need for developing techniques
to compare the Query images with the image of
Dataset. Major Challenge in image comparison is
similarity. Because image retrieval system results
strongly depend on similarity, it is very important
how we define similarity measure. The similarity
concept is, in a general sense, an ambiguous and
relative concept for humans. This is due to the fact
that human have not got extrinsic similarity measures
[1]. From psychological and biological point of view,
similarity computation process is unknown for
scientists. There is a close relation between
perception and similarity in human beings. Main
problem during understanding image by machine is
the distance between high level semantic and low
level semantic [2]. During recent decade, region
based system is emerged. A region based retrieval
system segments images into regions (objects) and
retrieves images based on the similarity between
regions[3]. Objects play a key role to form regions.
Because every object is a great store of concepts,
human brain assigns a label to every object. Human
easily recognize objects even those seen only once. In
an unconscious process, human beings rank images
based on their objects[4]. Region based approaches
are very close to the human perception [5].Current
systems face great difficulties, due to the fact that
perceived image similarity is both subjective and task
dependent. We have performed experiments to
measure the agreement between human similarity and
machine similarity.
To approximate human perception of the shapes of
the objects in the images, Del Bimbo and Pale [6]
introduce a measure of shape similarity using elastic
matching. Most of best approaches in similarity
measure fall in a fuzzy Set. The theory of fuzzy sets,
proposed by Zadeh (1965), has gained successful
application in various fields[7]. Measure of similarity
between fuzzy sets, as an important content in fuzzy
mathematics, have gained attention from researchers
for their wide application in real world. Many
measures of similarity between fuzzy sets have been
proposed during the last decade. For example, Chen
(1994) proposed a similarity function. Wang (1997)
proposed new fuzzy similarity measures on fuzzy sets
and elements. After introducing Intuitionistic fuzzy
sets (IFS) by Attanassov, many similarity measures
are designed based on IFS[8]. An inclusion measure
A New Similarity Measure Based on Fuzzy Monotonic
Inclusion for Image Retrieval Systems
Jafar Emamipour
Sama technical and vocational training college, Islamic Azad University, Ilam Branch, Ilam, Iran
j.emamipour@gmail.com

2. 1834
is a pairwise relation between two fuzzy sets, which
indicate the degree to which one fuzzy set is
contained in another one and is generalized in
inclusion relation. There are many successful
applications of fuzzy inclusion measure, rough set
data analysis fuzzy relational database , fuzzy
concept lattice theory[9].
One of the major problems of current similarity
measure is weak ability to involve image semantic
concepts. During the last two decades, many
researchers have paid attention to it. Santini and Sain
[10] have carried out a study on the similarity
measures for selecting images based on
characteristics of human similarity measurement.
Even for this case, different results depend on the
perception of each person [11].
In this paper, we propose a novel fuzzy similarity
measure(FMI), which are based on monotonic
inclusion measure from Fuzzy Set Theory. This work
is carried out in two phases: First we segment image
to several regions and two feature vectors including
color ,texture, shape and location and area for each
region extract. Location and area of regions are
extracted from two ideas about objects; first, the
most important objects are always near the image
center. In a human visual system, objects play a main
role and human brain identifies pictures based on
objects. Second, important objects in an image tend
to occupy larger areas. Second, we define a novel
fuzzy similarity measure and feature vectors are
mapped in a mathematic fuzzy inclusion model in
order to make similarity vectors. We used a object
based dataset benchmark, Label Me, And Test
results on it. Label me is one of the great benchmark
to evaluate image retrieval systems.
The rest of this paper is organized as follows: In
section 2 we review fuzzy similarity measures. In
section3, we present a fuzzy inclusion algorithm to
calculate the similarity measure for two regions.
Section 4 describes the experiments we have
performed and provides the results. And, finally, we
talk about the conclusion in section5.
2. Fuzzy inclusion theory
Since the fuzzy set was introduced by Zadeh, many
new approaches and theories treating imprecision and
uncertainty have been proposed [10].The concept of
inclusion measure between two fuzzy sets is
proposed in gradual relations between objects which
have been studied in detail [13]. The similarity
measure, the inclusion measure, and the entropy of
fuzzy sets are three important topics in the fuzzy set
theory. The inclusion measure of fuzzy sets indicates
the degree to which a fuzzy set is contained in
another fuzzy set [14]. Sinha and Dougherty [15]
introduced an axiomatic definition of the inclusion
measure of fuzzy set. Inclusion measure and
similarity measure have been used widely to
knowledge processing[15].
3.Similarity measure using Fuzzy Inclusion
Measure
Our system use three major phase to retrieve. First:
blocking and feature extraction; second:
segmentation and formation of the regions. Third:
definition of fuzzy similarity vector and comparison
of vectors.First: to segment an image, the system
partitions the image into small blocks. A feature
vector is then extracted for image block. The block
size is chosen to compromise between texture
effectiveness and computation time. Smaller block
size may preserve more texture details but increase
the computation time as well [4]. In our system, each
block has 4×4 pixels. Feature extraction process has
been performed in two steps. First: we extract six
features for each block. Three of them are the average
color components in a LUV color space where L
encodes luminance and U and V encode color
information. The other three represent energy in the
high frequency bands of the wavelet transforms [4].
Second :The K-means algorithm is used to cluster the
feature vectors into several classes with every class
corresponding to one region in the segmented image.
For each region, we calculate properties of area and
location.
Third: In this section we define and propose a new
fuzzy similarity. First we use Unimodal membership
function, Cauchy. To simplify image is divided to ten
sections and we assign to every section a membership
value based on triangular membership function. We
use α-cut with α equal 2.0‫و‬2.0‫و‬2.0 to cut Fuzzy set.
If A, B, C, D are fuzzy sets and S is similarity then:
( ) ( )
( ) ( )
( ) ⇔
(1)
(2)
(3)
(4)

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( ) ( ) ( )
4. Fuzzy monotonic inclusion measure similarity
Scheme
4.1.Similarity measure equation
We called Equation (4),T, then similarity is:
( ) ( ) ( ) ( )
[( ( )) ( ( ))] ( )
The proposed similarity measure is computed in two
stages. First, area fuzzy location of each region is
computed. Second, the inner products among T(q,t)
and ( ) and ( ) is computed.
L(ri,j) represents region location of i and j for query
image (q) and target image (t) image, respectively
.A(ri,j) represents the region area i and j for query
image (q) and target image (t) image, respectively.
First part of above equation trends to compute shape
properties and second part mentioned to textured
images or images that their shape properties are not
important.
4.2 Region location computation
In order to compute regions location, a triangular
fuzzy membership function is used. By this way, for
regions that are near image center, a greater
membership value is assigned and regions that are
near image border, least amount membership value is
assigned. Highest membership value is 1 and is
assigned for exactly near image center. Lowest
membership value is 0.1 for regions that is located
near image border.
5. Experimental results
We implanted the FMI on Label me, a Real world
image data set with 163000 images. For each image,
the features, locations and area of all regions are
stored. We compared FMI with UFM[4] and Fuzzy
histogram[6] In section 5.1, we introduce the test
bed. Section 5.2 presents Precision of FMI. The
Precision Analysis is presented in section 5.3.
5.1. Test bed
The system is tested on a object based image
database (from Label Me), including 163,000
pictures which are stored in JPEG format. The
following is a list of qualities that distinguish Label
Me from previous work.
 Designed for recognition of a class of objects
instead of single instances of an object. For example,
a traditional dataset may have contained images of
dogs, each of the same size and orientation. In
contrast, Label Me contains images of dogs in
multiple angles, sizes, and orientations.
 Designed for recognizing objects embedded in
arbitrary scenes instead of images that are cropped,
Normalized, and/or resized to display a single object.
 Complex annotation: Instead of labeling an entire
image (which also limits each image to containing a
single object), Label Me allows annotation of
multiple objects within an image by specifying a
polygon bounding box that contains the object.
 Contains a large number of object classes and
allows the creation of new classes easily.
 provides non-copyright images and allows public
additions to the annotations. This creates a free
environment.
We used twenty two Semantic classes(See Table 1).
The results are compared with UFM (Unified Feature
Matching) scheme and Fuzzy Histogram.
Experimental results showed that proposed scheme
outperforms the UFM and Histogram approach.
Class
number
Class name Class
number
Class name
1 Night-
outdoor
12 Italy- Outdoor
2 animals 13 industry
3 Village 14 Organization-
indoor
4 House-
indoor
15 Dinner- indoor
5 sport 16 Bedroom-
6 Boston Park 17 Hotel room
7 Spanish
Roads
18 Harvard street
8 Forest park 19 Football field
9 airport 20 Mexico
10 New York
city
21 Italy
11 birds 22 Boston
5.2. The Precision of the proposed scheme
Table.1 Label me Classes
(5)

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For image categorization, good performance is
achieved. We illustrated the performance of proposed
scheme with UFM scheme and Fuzzy Histogram (see
Figure.1).As we can see the Precision of proposed
method for each class is higher than UFM method.
In classes that the concept of class is near to class
label High precision is achieved (animals and birds).
Least precision fall in classes that user understand
multi concept from that. Actually classes with more
than one objects, such as Village and Italy. In
general, Experimental results shows, with increase of
images semantic complexity the Precision of Three
method is decreased.
Behavior Comparison among three algorithms show
in many cases histogram demonstrated random
behavior and its average precision is very low.
5.3. Precision Analysis
For each of the twenty two image categories, the
average precision are plotted in Figure.2. The image
category identification number is indicated in Table
1. The Precision of proposed scheme is higher than
UFM scheme and Fuzzy Histogram.
6. Conclusion
In this paper, a new fuzzy inclusion measure for
measuring the similarity of images is introduced
which uses Fuzzy sets in order to make new
similarity measure. The results is tested on the
conceptual and objects based Dataset, Label Me,
Since, we paid more attention to objects, accuracy of
retrieval system is increased and so entropy rate of
retrieved images in comparison with UFM and
Fuzzy Histogram is decreased. FMI make strong
conceptual relation among objects, so the nearest
image to query image retrieve. Two new features
includes fuzzy location and area of regions are
extracted and involve in fuzzy similarity model. Also
this approach is close to human perception. FMI
computational overhead and time consuming is very
low and is useful for real time computations.
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Figure 1. Comparing The Precision of FMI with UFM and
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Figure 2. Comparing the FMI method with UFM and
Fuzzy histogram on Precision for each class.
Figure3. Label Me Image samples

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