IEEE Workshop on Nonlinear Circuit Networks
December 14-15, 2012

Research on a New Structure ofThree-Layer Cellular Neural Networks
Muhammad Izzat bin Mohd Idrus, Yoshihiro Kato,
Yoko Uwate and Yoshifumi Nishio
Dept. Electrical and Electronic Eng,
Tokushima University
2-1 Minami-Josanjima,
Tokushima, Japan
Email: izzat, kkato, uwate, nishio@ee.tokushima-u.ac.jp

Abstract— In this study, we research a new layer arrangementof three layer cellular neural network (CNN). In this paper, weinvestigate the output characteristics by using our proposed CNN
and also our designed templates to image processing of grayscale image and binary image. The simulation results show theeffectiveness with our proposed CNN.

I. I NTRODUCTION
Cellular Neural Networks (CNN) were introduced by Chuaand Yang in 1988 [1][2]. The idea of the CNN was inspired
from the architecture of the cellular automata and the neuralnetworks. The architecture of CNN is the combination of thesimple circuit which is called cell. Each cell only communicate
with each other directly in neighborhood. Each cell contain linear capacitors, linear resistors, linear and nonlinear controlled
sources and independent sources. The CNN has local connectivity property and they have been successfully developedin various image processing applications. In previous study ofCNN, single-layer CNN have been introduced with many kindof templates and after that, two-layer CNN have been proposed
for high performance processing [3]. Recently, to obtain highperformance in color image processing, three-layer CNN havebeen proposed [4].
In this study, we proposed a new structure of the threelayer CNN. We investigate the output characteristic between
the proposed CNN by apply to the gray-scale image which
has scenery in the background to remove noise and edge
detection simultaneously. Then, we analysis the effectivenessof simulation results of our proposed CNN.
In this paper, we describe about the proposed CNN in Sec.
II. In Sec. III, we show simulation results of the proposed
CNN respectively. Also, in Sec. III, we analysis the simulation
result. Finally, we conclude the our study in Sec. IV.

(C2 ) and (C3 ), respectively. Compare to the previous threelayer CNN [3], our proposed CNN do not have mutualconnection between layer. Furthermore, our proposed CNN
can be conventional CNN if all coupling templates (C1 ),(C2 ) and (C3 ) has removed. Also, our proposed CNN can beprevious structure of the two-layer CNN if coupling templates(C2 ) or (C3 ) has removed. From these characteristics, we cansay that our proposed CNN is the independent structure.

Fig. 1.

Block diagram of the proposed CNN.

The equations of the proposed CNN are described as below:(1) State equations of the proposed CNN:
State equation of CNN1 :j+ri+r
∑∑dvx1ij1Cdt=−R+vx1ij +A1 (i, j; k, l)vy1kl (t)k=i−r l=j−rj+ri+r∑∑B1 (i, j; k, l)vu1kl (t)k=i−r l=j−r+j+ri+r∑∑C2 (i, j; k, l)vy2kl (t)k=i−r l=j−r+j+ri+r∑∑C3 (i, j; k, l)vy3kl (t) + I1

k=i−r l=j−r(|i − k| ≤ 1 , |j − l| ≤ 1).

State equation of CNN2 :CII. P ROPOSED CNN
In this section, we introduce a new structure of the threelayer CNN. Figure 1 shows that the output of the first layer
CNN (CNN1) is delivered into the second layer CNN (CNN2)
and the third layer CNN (CNN3) by through coupling template(C1 ). In other way, the outputs of the CNN2 and the CNN3
are delivered into the CNN1 by through coupling templates- 109 -

dvx2ijdt=−j+ri+r∑∑
1
A2 (i, j; k, l)vy2kl (t)vx2ij +R
k=i−r l=j−r+j+ri+r∑∑B2 (i, j; k, l)vu2kl (t)k=i−r l=j−r+j+ri+r∑∑
k=i−r l=j−r

C1 (i, j; k, l)vy1kl (t) + I2(1)(|i − k| ≤ 1 , |j − l| ≤ 1).

(2)

State equation of CNN3 :dvx3ijCdtj+ri+r∑∑
1
A3 (i, j; k, l)vy3kl (t)− vx3ij +R=

k=i−r l=j−r∑ ∑j+ri+r+B3 (i, j; k, l)vu3kl (t)k=i−r l=j−r+j+ri+r∑∑

C1 (i, j; k, l)vy1kl (t) + I3

k=i−r l=j−r(|i − k| ≤ 1 , |j − l| ≤ 1).

(3)(2) Output equations of the proposed CNN:
Output equation of CNN1 :vy1ij (t)1(|vx1ij (t) + 1| − |vx1ij (t) − 1|).
2=To get the good result, the template for the CNN1 is very
important to design because CNN1 is the main operation.
For this simulation, we put “Edge detection” in CNN1by through the coupling templates (C2 ) and (C3 ). We put“Small object remover”’s template into the CNN2 andCNN3 by through (C1 ). Then, we put “Heat dif f usion” and“Smoothing” in CNN2 and CNN3 respectively. The designed
templates is obtain by experienced and at this moment, wecannot explain it in details. From this result, we can say thatour proposed CNN can detect the edge of image and remove
noises simultaneously. Even there have some noises remain in
the simulation results, we still can say that our proposed CNN
is effective.
Remark: For Fig. 4 of simulation, we did not show the simulation results of conventional CNN and the two-layer CNN.
For the conventional CNN, the results show less effective. For
the two-layer CNN, the results show almost same effective as
our proposed CNN.

(4)

Output equation of CNN2 :vy2ij (t)1(|vx2ij (t) + 1| − |vx2ij (t) − 1|).
2=(5)Output equation of CNN3 :vy3ij (t)1(|vx3ij (t) + 1| − |vx3ij (t) − 1|).
2=

(6)

III. S IMULATION R ESULTS(a)

In this section, we show simulation results for the the proposed CNN. For simulations, we use four types of templates
which are “Small object remover”, “Edge detection”,“Smoothing” and “Heat dif f usion”. All of these originaltemplates can be found in [5]. The designed templates andsimulation results are shown as follow:
T emplate]1 :[ of CN N000A1 =010000[, B1 =000

T emplateof CN N 2 : ][0.10.15
0.1

A2 =0.15
00.15

0.10.150.1[, B2 =T emplate[ of CN N]3 :A3 =010121010[, B3 =

Coupling[ T emplates] :C1 =[C3 =111121111−1−1−1−18−1[, C2 =−1−1−1000].

000−1−1−1000000000], I1 = −1.

000000−18−1000(7)], I2 = 0.

(8)

(b)

Fig. 2. Simulation results for gray-scale image with scenery. (a) Initial

image. (b) Output image.

IV. C ONCLUSION
In this study, we have proposed a new structure of threelayer CNN. From the computer simulations of gray-scale
image which has scenery in background, we investigated theoutput characteristics of the proposed CNN. We can saythat the proposed CNN have potential in image processing.
However, at the moment, we do not say that our proposed
CNN show excellent performance that conventional CNN andtwo-layer CNN. In future works, we would like to use anothertype of images like color image. We also would like to try
other tasks in our proposed CNN.
R EFERENCES[1] L. O. Chua and L. Yang, “Cellular Neural Networks: Theory,” IEEE
Trans. Circuits Syst., vol. 32, pp. 1257-1272, Oct. 1988.

], I3 = −0.5.

−1−1−1(9)[2] L. O. Chua and L. Yang, “Cellular Neural Networks: Applications,” IEEE
Trans. Circuits Syst., vol. 32, pp. 1257-1272, Oct. 1988.
[3] Z. Yang, Y. Nishio and A. Ushida, “Image Processing of Two-Layer
CNNs:Applications and Their Stability,” IEICE Trans. Fundamentals,
vol. E85-A, No. 9, pp. 2052-2060, Sept. 2002.

],(10)[4] T. Inoue and Y. Nishio, “Research of Three-Layer Cellular Neural Networks Processing Color Images,” IEICE Technical Report, NLP2008-25,
pp. 33-36, Jul. 2008.
[5] Cellular Sensory Wave Computers Laboratory Computer and Automation
Research Institute Hungarian Academy of Sciences, “Cellular wave
Computing Library (Template, Algorithm, and Programs) Version 2.1”

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