2006 RISP International Workshop
on Nonlinear Circuits and Signal Processing (NCSP'06)
Waikiki Beach Marriott, Honolulu,Hawaii, USA, March 3-5, 2006

Image Processing of Gray Scale Images by Fuzzy Cellular Neural Network
Koki Nishizono and Yoshifumi Nishio
Tokushima University
2-1 Minami-Josanjima, Tokushima, Japan
Phone:+81-88-656-7470, Fax:+81-88-656-7471
Email: {koki, nishio}@ee.tokushima-u.ac.jp

Abstract
In this study, we investigate the Fuzzy CNN proposed byT. Yang and L.B. Yang, and apply the Fuzzy CNN to threeimage processings of gray scale images. One can see that theintegration of fuzzy operations into the CNN results in nonlinear synaptic laws. These fuzzy synaptic laws have great
potential in image processing because of above three examples. We confirm its effectiveness.
1. Introduction
Cellular neural network (CNN) have been previously considered for many applications related to image processing.
And it is known that CNN is a very effective tool for image
processing. However, in every phase of image processing,
there exist many uncertainties.
Fuzzy set theory provides the mathematical strength to capture these uncertainties. In [1], fuzzy set theory is integrated
into the CNN paradigm to give birth to a new image processing paradigm, the Fuzzy CNN, which will become a powerful tool for image processing problems. From the beginningof the CNN, all structures and algorithms have been closelyconcerned with its realization by state-of-the-art VLSI technology. The design of Fuzzy CNNs should keep this tradition,e.g. local connectedness between neurons (cells) and simple
cell structures.
In [1], there are only a few application examples to the grayscale images, and detailed operation has not been clarified. In
this study, we research the Fuzzy CNN in more detail, andapply it to gray scale images by various fuzzy operations. We
present the effectiveness of the Fuzzy CNN.
2. Architectures of Fuzzy CNN [1]Fig. 1 Circuit of cell Cij in Fuzzy CNN.
The state equation of the cell Cij is defined by the following equation.

Cdvxij (t)dt= −+

1
vxij (t)RxA(i, j; k.l)vykl (t)Ckl ∈Nr (i.j)

+B(i, j; k.l)vukl (t) + I(1)

Ckl ∈Nr (i.j)+ FACkl ∈Nr (i.j) (Af (i, j; k, l)vykl (t))+ FBC ∈N (i.j) (Bf (i, j; k, l)vukl )klrOutput and input equations are the same as the original CNN.
Af (i, j; k, l) and Bf (i, j; k, l) are the synaptic weights usedby fuzzy operations FACkl ∈Nr (i.j) (·) and FBCkl ∈Nr (i.j) (·);
Af and Bf should be chosen in accordance with the application. FA (·) and FB (·) denote two fuzzy local operators defined in Nr (i, j), which may be any fuzzy logical expressions
 ’ and fuzzy AND ’∧
 ’.
combined by fuzzy OR ’∨
Therefore, equation (1) can be rewritten as follows.

CThe Fuzzy CNN has almost the same architecture as theoriginal CNN. We denote the cell in the i th row and j thcolumn as cell Cij . The circuit of Cij is shown in Fig. 1,where the suffixes u, x and y denote input, state and output,respectively.

dvxij (t)dt= −+

1
vxij (t)RxA(i, j; k.l)vykl (t)Ckl ∈Nr (i.j)+

Ckl ∈Nr (i.j)- 90 -B(i, j; k.l)vukl (t) + I

++++


Ckl ∈Nr (i.j)

Ckl ∈Nr (i.j)

Ckl ∈Nr (i.j)

Ckl ∈Nr (i.j)⎡0
Af min = Bf min = ⎣ 00

Af min vykl (t)Af max vykl (t)(2)

Bf min vukl (t)Bf max vukl (t)where Af min , Af max , Bf min , Bf max are the feedack MIN,
feedback MAX, feedforward MIN, feedforward MAX templates, respectively.
In this study, we use two fuzzy logical expressions, fuzzy
 ’ and fuzzy AND ’∧
 ’. Fuzzy OR means that the largest
OR ’∨value in fuzzy templates is chosen as fuzzy synaptic weights.
In order to use 1-neighborhood template here, Fuzzy ORchooses the largest value in 9 values. Fuzzy AND meansthat the smallest value in fuzzy templates is chosen as fuzzy
synaptic weights. In order to use 1-neighborhood template
here, Fuzzy AND chooses the smallest value in 9 values.

⎤0 0
1 0 ⎦.
0 0

The results are shown in Fig. 3. Because a part of gray scaleis black and becomes binary image in (a), the NOT operation
can not be performed well. However, in (b), a part of grayscale is not black and does not becomes binary image. So theFuzzy CNN performs the Logic NOT operation of grey scale
image.

3. Image processing examples(a) using original CNN.

Now, we apply the fuzzy CNN to a gray scale image shownin Fig. 2.

(b) using Fuzzy CNN.
Fig. 3 Logic NOT operations.
Fig. 2 Original image.

3.2. Edge detection

The second image processing is Edge detection. The original template for binary image is⎡⎤⎡⎤The first image processing is Logic NOT. The original tem0 0 0−1 −1 −1plate for binary image isA = ⎣ 0 1 0 ⎦ , B = ⎣ −1 8 −1 ⎦ , I = −0.5.
0 0 0−1 −1 −1⎡⎤⎡⎤
0 0 00 0 0
We apply the following fuzzy template with the fuzzy AND
A = ⎣ 0 1 0 ⎦ , B = ⎣ 0 −2 0 ⎦ , I = 0.
logic.
0 0 00 0 0
Af max = Bf max = 0 ,⎡⎤We apply the following fuzzy template with the fuzzy AND
0 1 0logic.
Af min = Bf min = ⎣ 0 1 0 ⎦ .
Af max = Bf max = 0 ,0 1 03.1. Logic NOT operation- 91 -The results are shown in Fig. 4. We can see that the Fuzzy Fig. 6. Though Fuzzy CNN can remove the noise well inCNN extract the edges in the gray scale image very well. comparison with the original CNN, there are a lot of places
However, in the original CNN, there exists many noises. where the edges disappear.
Therefore, the original CNN cannot perform well.

(a) using original CNN.

(a) using original CNN.

(b) using Fuzzy CNN.
Fig. 4 Edge detection.
Next, we try to detect edges of a gray scale image shown inFig. 5 by using two fuzzy logical expressions, fuzzy OR andfuzzy AND, simultaneously.

(b) using Fuzzy CNN.
Fig. 6 Edge detection.
We try to add a fuzzy OR template in addition to a fuzzy
AND templates. The fuzzy templates are shown in the folowing.
⎡⎤⎡
0 0.1 00Af max = ⎣ 0.1 0.3 0.1 ⎦ , Bf max = ⎣ 00 0.1 00⎡0Af min = Bf min = ⎣ 00⎤
0 00.1 0 ⎦ ,0 0⎤
1 01 0 ⎦.
1 0The result is shown in Fig. 7. By using both fuzzy OR temFig. 5 Original image.
plates and fuzzy AND templates, the Fuzzy CNN extract theWe apply the above templates, and the results are shown in edges and remove noise well.

- 92 -Fig. 7 using Fuzzy AND and OR templates.
4. Conclusions
In this study, we have investigated the Fuzzy CNN proposed by T. Yang and L.B. Yang, and applied the Fuzzy CNN
to three image processings of gray scale images. One can seethat the integration of fuzzy operations into the CNN results
in non-linear synaptic laws. These fuzzy synaptic laws havegreat potential in image processing because of above threeexamples. We have confirmed its effectiveness.
References[1] T. Yang and L.B. Yang, “Fuzzy cellular neural network: anew paradigm for image processing,” Int. Journal of Circuit Theory and Applications, vol.25, pp.469-481, 1997.
[2] T. Yang and L.B. Yang, “Fuzzy cellular neural network:
theory,” Proc. Int. Workshop on Cellular Neural Networkand Their Applications (CNNA‘96), pp.181-186, 1996
[3] T. Yang and L.B. Yang, “Fuzzy cellular neural network:
applications,” Proc. Int. Workshop on Cellular Neural
Network and Their Applications (CNNA‘96), pp.225230, 1996.
[4] L. O. Chua and L. Yang, “Cellular neural networks: theory and applications,” IEEE Trans. Circuits and Systems,
CAS-35, pp.1257-1290, 1988.

- 93 -