BULLETIN OF THE TRANSILVANIA UNIVERSITY OF BRASOV VOL. 4 (53) No.1 – 2011 [629740]

BULLETIN OF THE TRANSILVANIA UNIVERSITY OF BRASOV • VOL. 4 (53) No.1 – 2011
SERIES I – ENGINEERING SCIENCES, ISSN 2065-2119 (Print), ISSN 2065- 2127 (CD -ROM)

ELECTRICAL ENGINEERING, ELECTRONICS AND AUTOMATICS

Bălan, T., Sandu, F., Cazacu, V.: Ontology Based Resource Management of Real and Emulated Telecom
Systems ………………………… ……………………………………………………………………………………………………… 85
Boldișor, C., Comnac, V., Coman, S.: A Practical Review of a Design Method for Fuzzy Controllers Based
On Self -Learning Algorithm ……………………………………………………………………………………………………….. 93
Cazacu, V., Székely, I., Sandu, F., Bălan, T.: Performance Metrics for the It Services Portfolio …………………. 99
Cociaș, T.T., Măcesanu, G., Moldoveanu, F.: On the Application of Voronoi Diagrams and Delaunay
Triangulation to 3D Reconstruction …………………………………………………………………………… …………………………….. …. 107
Fratu, A., Fratu, M.: Analytical Model of the Cutting Process with Scissors -Robot for Haptic Simulation …….. 113
Măceșanu, G., Grigorescu, S., Cociaș, T.T., Moldoveanu, F.: An Object Detection and 3D Reconstruction
Approach for Real -Time Scene Understanding ………………………………………………………………………………………. 121
Nedelcu, A.V., Stoianovici, V.C., Székely, I.: Energy -Efficient Integration of WSNs with Active RFID Systems …………… 127
Nicula, D.: Digital Electronics: A Modern Lab Approach …………………………………………………………… 135
Puiu, D., Floroian, D., Moldoveanu, F.: DASTS: Distributed Architecture for Sun Tracking System Mounted
On Mobile Platforms …………… ……… ……… ……………… ……… ……… ……………… ……… ……… ….. 143
Stoianovici, V.C., Nedelcu, A.V., Székely, I., Fadda, M.: A Software -Defined Radio Approach to Spectrum
Sensing Systems’ Architecture ………… ……… …………… ……… ……… ……………… ……… ……… …… 151
Suliman, C., Boldișor, C., Băzăvan, R., Moldoveanu, F.: A Fuz zy Logic Based Method for Edge Detection … 159

Bulletin of the Transilvania University of Bra șov
Series I: Engineering Sciences • Vol. 4 (53) No. 1 – 2011

A FUZZY LOGIC BASED METHOD FOR
EDGE DETECTION

C. SULIMAN1 C. BOLDI ȘOR1 R. BĂZĂVAN2
F. MOLDOVEANU1

Abstract: In this paper we present a method for detecting edges in grayscale
images. The method is based on the use of a fuzzy classifier. The difference
between our method and other similar methods is the use of a morphological operation to thin the obtained edges. Our entire algorithm was implemented in
the development/simulation environment called Matlab. The experiments have
shown promising results, we have obtained the desired thickness of the edges.
Key words: fuzzy logic, fuzzy classifier, computer vision, edge detection,
morphological skeleton.

1 Dept. of Automatics, Transilvania University of Bra șov.
2 Dept. of Telecommunications and Information Technology, Politehnica University of Bucure ști. 1. Introduction

In computer vision applications, the
difference between the objects from the scene and the rest of the scene is an extremely important task. Thus, in order to
extract the contour of an object we must
have full information on the edges of the
image. Therefore, edge detection is an
essential operation in image processing. An
extremely important property of any edge
detection method is its ability to extract
precise and good orient ed image edges. The
performance of edge detection methods has
always been subjective since each user
seeks to obtain certain results from an image.
In the literature there are numerous
methods used to detect edges, some of
them leading to the appearance of some of
the classical edge detectors like the
Roberts edge detector [6], the Sobel [6] or
the Prewitt edge detector [6]. More
recently, among conventional edge detection techniques emerged some new
methods based on fuzzy logic [1], [4], [5].
In the second chapter of the paper we
present the six classes to which an image pixel can belong to. In the third chapter we present the fuzzy classifier architecture that
we have used. In chapter four we mention
the fuzzy rules used to carry out the
competition between the pixels of a mask.
Also, we present here the results from the
fuzzy edge detection and the results after
applying the morphological skeleton [2], [3]
operation over the output image. The paper
ends with some conclusions.
2. Pixel Classification

As a first step before applying the fuzzy
logic based techniques for edge detection,
the image should be pre-processed. Since
images usually contain noise, this should
be removed. For the noise removal we
have chosen a 3 x 3 Gaussian filter.

Bulletin of the Transilvania University of Bra șov • Series I • Vol. 4 (53) No. 1 – 2011
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We consider the case in which we use a
3 x 3 mask, with the central pixel situated at coordinates ( i, j). Since the edge
detection method is applied to grayscale
images, the pixel position is represented as
a scalar p
i,j. The representation of such a
mask can be seen in the next figure:

Fig. 1. 3 x 3 mask with the central pixel at p i,j

An edge may appear in many directions.
In Figure 2 are presented the four cases in
which an edge may appear.

Fig. 2. The four directions in which an edge
may appear

For the four direction, denoted by d1, d2, d3,
d4, it is necessary to calculate the sum of the
differences of the bidirectional amplitudes between the p
5 pixel and its neighbours.
These will be computed as follows:

11 5 9 5 , dp pp p=−+−
22 58 5 , dp pp p=−+−
33 57 5 , dp pp p=−+−
44 56 5 . dp pp p=−+− For each pixel in the input image that is
not at the periphery, we must form a vector x = (d
1, d2, d3, d4) that contains the four
previously calculated distances.
The next step is to divide the input image
pixels into classes. For this purpose we
defined six classes: four classes for edges,
a background class and a class for noisy
edges. For the four classes that define the
edges we have used four typical situations
(see Figure 3).

Fig. 3. Typical situations for the four
classes of edges

Each of the four situations described
above corresponds to a single vector of amplitudes. The amplitudes will be related only to the minimum and maximum values
that they may have. The appropriate class
for the image background will correspond
to any pixel in whose neighbourhood the
amplitude difference in all four directions is
small. The last class, in which an edge is
regarded as containing noise, the amplitude
change in the vicinity of a pixel in all four directions is considered to be high.
Examples of cases where a pixel is part of the last class can be seen in Figure 4c and d.
At this point it is necessary to build six
prototype vectors, which will be noted with
c
0, c1,…,c5. These vectors are the centres
of the six classes defined previously. The

Suliman, C., et al.: A Fuzzy Logic Based Method for Edge Detection 161

a ) b )

c ) d )
Fig. 4. Typical situations for the four
classes of edges

vectors will contain the “min” and “max”
attributes. These attributes correspond to
the amplitude in the four directions. The
attributes “min ” and “max” will be defined
by the user depending on the degree of
sensitivity needed in the application. The
six vectors are given below:

( )0min, min, min, min c= – background,
( )1min, max, max, max c= – edge,
( )2 max, min, max, max c= – edge,
( )3max, max, min, max c= – edge,
( )4 max, max, max, min c= – edge,
( )5max, max, max, max c= – noisy edge.

The six vectors are central points for the
six sets of membership functions
corresponding to the six classes. The
membership functions are represented by
symmetrical triangular functions and are
determined by the central vector ci and a
parameter, w, with which you can change
the base of the surface. The parameter w is set by the user.
After reading the input image, each pixel
must be classified as belonging to one
class, otherwise it will be considered as
belonging to the background, and its
colour will be changed to black.

3. The Fuzzy Classifier Architecture

A fuzzy classifier is a system that
accepts as inputs vectors containing attributes or fuzzy truths that allow fuzzy
attributes to belong to different
membership functions. The output of the
classifier is represented by fuzzy truths for
the membership functions corresponding to
the input vector. The class attributed to an
input vector is the one whose truth value,
given by the membership functions, is the
greatest. For an input vector to belong to
only one class, the highest truth value must
beat by far the following truth value. The architecture of a fuzzy classifier for only two classes is presented in Figure 5. In this
type of architecture each node of the
hidden layer is represented by a triangular
type function centred on a prototype
ic.
These membership functions are presented
in the following relations:

0
0() m a x 0 , 1x
w−µ= −⎧ ⎫⎨ ⎬⎩⎭xc- for class 0,
1
1() m a x 0 , 1x
w−µ= −⎧ ⎫⎨ ⎬⎩⎭xc- for class 1,
2
2() m a x 0 , 1x
w−µ= −⎧ ⎫⎨ ⎬⎩⎭xc- for class 2,
3
3() m a x 0 , 1x
w−µ= −⎧ ⎫⎨ ⎬⎩⎭xc- for class 3,
4
4() m a x 0 , 1x
w−µ= −⎧ ⎫⎨ ⎬⎩⎭xc- for class 4,
5
5() m a x 0 , 1x
w−µ= −⎧ ⎫⎨ ⎬⎩⎭xc- for class 5,

Bulletin of the Transilvania University of Bra șov • Series I • Vol. 4 (53) No. 1 – 2011
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where x is the input vector for a pixel, c0…c5
are the five prototypes of classes defined above, and w is the parameter used to modify
the radius of the membership functions.

Fig. 5. The fuzzy classifier architecture for
two classes

In the fuzzy classifier architecture
presented in Figure 5 the output is
represented by a single node for each class.
This node summarizes all the values that
reach him from the hidden layer. When the
membership function of a node in the
hidden layer has a high value, the node in
the output layer, where the summing takes place, will also have a high value. This
way the class will be given by the output
node with the highest value. This type of architecture leads to
undesirable results in the case of an edge detector. By using this type of architecture
one can obtain thick edges, or in an image
processing application thin edges are needed.
To overcome the problems that may
appear in the case of using the above
architecture we will use a architecture in
which in the hidden layer is no longer
necessary to use multiple nodes for each
class, it is sufficient to use a single node. This way results a two level architecture
(see Figure 6).
The next step in edge detection is to
apply a set of rules to from image pixels
that have already been classified.
In the output image, pixels that have
already been classified as components of an
edge or those which are part of a noisy edge
will have the value 1. This value corresponds
to the colour white in the binary images.
The pixels that will be classified as belonging to the background will have in the output image the value 0 (black). As a result
of this process we will have a binary image.

4. The Fuzzy Rule Set

Before a pixel from the input image is to
be changed to white or black in the output
image, it must win the competition with all the pixels in its neighbourhood. The rules
that carry out the competition between pixels are presented below:

Fig. 6. The fuzzy classifier architecture used in the fuzzy edge detection process

Suliman, C., et al.: A Fuzzy Logic Based Method for Edge Detection 163

• IF x belongs to class 0 THEN change
pixel to black;
• IF x belongs to class 1 THEN carry out
the competition between d3 and the
neighbouring pixels in direction 3;
o If d3 wins the competition THEN
change pixel to white OTHERWISE change pixel to black;
• IF x belongs to class 2 THEN carry out
the competition between d4 and the
neighbouring pixels in direction 4;
o If d4 wins the competition THEN
change pixel to white OTHERWISE
change pixel to black;
• IF x belongs to class 3 THEN carry out
the competition between d1 and the
neighbouring pixels in direction 1;
o If d1 wins the competition THEN
change pixel to white OTHERWISE change pixel to black;
• IF x belongs to class 4 THEN carry out
the competition between d2 and the
neighbouring pixels in direction 2;
o If d2 wins the competition THEN
change pixel to white OTHERWISE
change pixel to black;
• IF x belongs to class 5 THEN change
pixel to white.
After applying the method presented so
far we have obtained edges close to the
desired thickness. The image used in our
experiments is a representative one for the
image processing domain. We used a
photo of a cameraman (see Figure 7a). The thickness of the obtained edges is of 2
pixels (see Figure 7b). However, for the
method to give the best results, the
obtained edges should have a thickness of
1 pixel.
To solve this problem and to be able to
obtain edges of the desired thickness we
have chosen to apply a morphological
operation, in particular the method of
morphological skeletonization. This
method reduces all objects in the image to simple lines without changing the essential structure of the image.

a)

b)
Fig. 7. Fuzzy edge detection: a) original
image; b) image containing detected edges

After applying the morphological skeleton
method, the problem with the thick edges
was removed. The result can be seen in
Figure 8.

Fig. 8. Edges after morphological
skeletonization

Bulletin of the Transilvania University of Bra șov • Series I • Vol. 4 (53) No. 1 – 2011
164
Edges now have a thickness of 1 pixel,
that is the desired thickness. The structure of the image after applying the skeleton
was not affected. 5. Conclusions

In this paper we have presented a fuzzy
based method for edge detection. The
method alone was not able to detect edges
of the desired thickness, but with the help of the morphological skeleton we were
able to extract edges with the thickness of
1 pixel.
Our entire algorithm was developed in
the environment called Matlab. One direct
improvement of this method is to
implement an edge linking algorithm so
that one can obtain continuous edges. This
method can also be combined with the
CPDA (C hord -to-Point A ccumulation
Technique ) and can be used in the process
on corner extraction.
Acknowledgement

This paper is supported by the Sectoral
Operational Programme Human Resources Development (SOP HRD), financed from the European Social Fund and by the
Romanian Government under the contract number POSDRU/6/1.5/S/6. References

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