IEEE Workshop on Nonlinear Circuit Networks
December 9-10, 2011

Research on Improvementof Two-Layer Cellular Neural Networks
Nurul Amirah binti Ramlan, Yoshihiro Kato, Yasuhiro Ueda,
Yoko Uwate and Yoshifumi Nishio
Dept. Electrical and Electronic Eng.,
Tokushima University
2-1 Minami-Josanjima, Tokushima, Japan
Email: { mira88, kkato, yasuhiro, uwate, nishio } @ee.tokushima-u.ac.jp
Abstract—In this paper, we research the combination of two
neurons in the Cellular Neural Networks (CNN). Our proposed
method is inspired from the two-layer CNN. Compare to twolayer CNN the data from each neurons are send using templates
A1 and B2 . We apply this method to image processing of grayscale image and binary image. From two examples in simulation,
we confirm proposed method have great potential in image
processing.

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 cellular automata [3][4] and neuralnetworks [5][6]. Unlike the conventional neural networks, theCNN has local connectivity property and since the structureof CNN resembles the structure of animals’ retina, they
have been successfully developed in various image processing
applications [7]. Wiring weights of the cells are established byparameters called a template. The template is used to decide
the performance of CNN.
In previous study of CNN, single-layer and two-layer CNNs
have been introduced with many kinds of templates. For highperformance processing, two-layer CNN have been proposed[8]. In this study we are not using parameter “template C” tocarry the data between both layers. As a new approach, wepropose a combination of two neurons for one cell in CNN. In
the propose method, two templates are used simultaneously. Inorder to investigate the process, we apply the method to binary
image. Frankly speaking, we also consider that the propose
method is the new characteristic to investigate the behavior ofCNN and the image feature when value is directly transferred
into the next neuron using templates A, B and I.
The list of this paper is structured as follows. In Sec.II,
we describe about two-layer CNN. In Sec.III, we explain thepropose method. In Sec.IV, we show example of simulation
result from the combination of two kinds of templates. Finallyin section V, we conclude the article.

to the neighbor cells. In the CNN, output value also depends
on parameters called a template. The CNN is contain withfeedback template A, control template B and constant bias I.
In previous paper, the two-layer CNN has been introduced.
The two-layer CNN have been confirmed to have more efficient structure for image processing. The two-layer CNN is acombination of two set of the single-layer CNN. The different
point from the single-layer CNN is that the two-layer CNN
has coupling templates C12 and C21 . The templates are used
to connect and transferred the data between first and secondlayers.
The state equations and the output equations for the twolayer CNN are given as follows.
State equation :dvx1ijdtj+1∑

A1 (i, j; k, l)vy1kl (t)k=i−1 l=j−1+i+1∑j+1∑

B1 (i, j; k, l)vu1kl (t)k=i−1 l=j−1+i+1∑j+1∑

C12 (i, j; k, l)vy2kl (t) + I1 ,k=i−1 l=j−1(|i − k| ≤ 1, |j − l| ≤ 1).

dvx2ijdti+1∑= −vx2ij +j+1∑

(1)

A2 (i, j; k, l)vy2kl (t)k=i−1 l=j−1+i+1
∑

j+1
∑

B2 (i, j; k, l)vu2kl (t)k=i−1 l=j−1+i+1
∑

j+1
∑

C21 (i, j; k, l)vy1kl (t) + I2 ,k=i−1 l=j−1

II. T WO -L AYER C ELLULAR N EURAL N ETWORKSIn this section, we explain about the structure of two-layer
CNN. The basic circuit unit in the CNN is called a cell. Eachcell in the CNN only take interaction communication with thecell in neighborhood. The values of each cell change accordingi+1∑= −vx1ij +(|i − k| ≤ 1, |j − l| ≤ 1).

(2)

1(|vx1ij (t) + 1| − |vx1ij (t) − 1|).
2

(3)

Output equation :- 137 -

vy1ij (t)=Output equation :1vy2ij (t) =(|vx2ij (t) + 1| − |vx2ij (t) − 1|).
2III. P ROPOSED M ETHOD(4)
vu2ij (t) = vy1ij (t) =In this section, we explain the algorithm of the proposed
method. The proposed method is inspired from the two-layer
CNN. In the proposed method, coupling templates are dismiss
and the connection between two layers are accomplished by
A1 and B2 . It is the different point between the proposed
method and the two-layer CNN. By not using coupling templates, the structure becomes simple compare to the two-layerCNN.

vy2ij (t)=1(|vx1ij (t) + 1| − |vx1ij (t) − 1|). (7)21(|vx2ij (t) + 1| − |vx2ij (t) − 1|).
2IV. S IMULATION R ESULTS
In this section, we show the simulation result using ourproposed method. Figure 2(a)(b) are set as the input images
in both neurons α and β. The “Hole filling” template [9] isused in the neuron α, and a new “White propagation” templateis used in the neuron β.
“Hole filling” template :A1

B1
Fig. 1.

Block diagram of the proposed method.

Figure 1 shows the block diagram for the proposed method.
In Fig. 1, we can see how the connection is taken between
neuron α and neuron β. We define the input and the output
values as vu1 , vu2 , vy1 and vy2 . At first the initial state for theneuron α and the neuron β are same. The input value vu1 iscarried out with template B1 in the neuron α. The output fromthe neuron α is directly transfer into the neuron β as the input
value vu2 . In the neuron α, vy2 is carried out with template
A1 , and in parallel vy2 is also carried out with template A2
in the neuron β. These processes continue until the output
converges. The state equations and the output equations are
given as follows.
State equation in the neuron α :dvx1ijdt=i+1∑−vx1ij +j+1∑

A1 (i, j; k, l)vy2kl (t)k=i−1 l=j−1+i+1
∑

j+1
∑

=i+1
∑

−vx2ij +j+1∑

(5)

A2 (i, j; k, l)vy2kl (t)k=i−1 l=j−1+i+1
∑

j+1
∑

B2 (i, j; k, l)vy1kl (t) + I2 ,k=i−1 l=j−1(|i − k| ≤ 1, |j − l| ≤ 1).

131040
01 ,0
00  , I1 = −1.
0(9)

(10)

The simulation results are shown as Fig. 2. The output ofthe neuron α is obtained as Fig. 2(c). It is the same as thecase of the single layer CNN with“Hole filling” template.
The connection between vy1 and vu2 let the value from theneuron α directly process to the neuron β in the same loop.
Figure 2(d) is the output of the neuron β when the input
value vu2 is processed with the initial state in Fig. 2(b). Only
enclosed shape that exists in a black area of the initial statein Fig. 2(b) is detected as the output of neuron β. Fromthese results, we can say that both templates can be usedsimultaneously.
V. C ONCLUSIONSState equation in the neuron β :dvx2ijdt

0=  10
0=  00

New “White propagation” template :
0 0.5 0A2 =  0.5 3 0.5  ,0 0.5 0


0 0 0
B2 =  0 1 0  , I2 = −2.75.
0 0 0

B1 (i, j; k, l)vu1kl (t) + I1 ,k=i−1 l=j−1(|i − k| ≤ 1, |j − l| ≤ 1).

(8)

(6)

In this study, we have proposed combination of two neurons
for a cell in CNN. In our proposed method, two types oftemplates can be confirmed to effect in one output value. We
can say that the data from each neurons still can be send toeach other by only using template A1 and template B2 . Fromthese simulation results, we could be said our proposed method
have potential in image processing.
In the future works, we like to change the size of templateand circuit to investigate the effects for output feature. Besides
binary images, we also would like to try to use the proposed
method for gray scale image and motion picture.

- 138 -(a)

(b)

(c)

(d)

Fig. 2. Simulation results. (a) Input image (256×256). (b) Initial state.
(c) Output image of neuron α. (d) Output of neuron β.

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