2012 International Workshop on Nonlinear Circuits,Communications and Signal Processing
NCSP'12, Honolulu, Hawaii, USA. March 4-6, 2012

Combination of Two Neurons for a Cell in Cellular Neural Networks
Nurul Amirah binti Ramlan, Yoshihiro Kato, Yasuhiro Ueda, Yoko Uwate and Yoshifumi Nishio
Tokushima University
2-1 Minami-Josanjima, Tokushima 770-8506, Japan
Phone/FAX:+81-88-656-7470/ +81-88-656-7471
Email: {mira88, kkato, yasuhiro, uwate, nishio}@ee.tokushima-u.ac.jp

Abstract

CNN and the characteristic of image processings achieved by
the new architecture which transfers the data to the other layer
directly.
The rest of this paper is structured as follows. In Sec.2, wedescribe about the basic CNN models which are single-layer
and two-layer. In Sec.3, we explain the proposed method. InSec.4, we show some examples of simulation results from thecombination of two kinds of templates. Finally in Sec.5, weconclude the paper.

In this paper, we propose a new structure of the Cellular Neural Networks (CNN) which combines two kinds of neurons
for one cell. The proposed structure is inspired from the twolayer CNN. Compared with the two-layer CNN, the data fromeach neuron are sent using templates A1 and B2 . We apply
this structure to image processing of gray scale image and binary image. From two examples in simulation, we confirm
that the proposed structure has a great potential in image pro2. Cellular Neural Networks
cessing.
1. Introduction
Cellular Neural networks (CNN) were introduced by Chuaand Yang in 1988 [1]. The idea of the CNN was inspired fromthe architecture of cellular automata and neural networks.
Unlike the conventional neural networks, the CNN has local connectivity property and since the structure of CNN resembles the structure of animals’ retina, they have been successfully developed in various image processing applications[2][3]. Wiring weights of the cells are established by parameters called a template. The template is used to decide theperformance of CNN. A template has its own characteristic
and the values do not change during the processing.
In previous studies of CNN, single-layer and two-layer
CNNs have been introduced with many kinds of templates.
In single-layer CNN, one set of templates are used. For using
two or more templates, a lot of processing is necessary andimplementation becomes difficult. For high performance processing, two-layer CNN has been proposed. The two-layer
CNN is a combination of two sets of single-layer CNNs andthe data from both layers are connected by coupling templates
C. In this study we are not using parameter “template C” tocarry the data between both layers. As a new approach, we
propose a combination of two neurons for one cell in CNN.
The proposed method is inspired from the two-layer CNN. In
the propose method, two templates are used simultaneously.
In order to investigate the process, we apply the method togray scale image and binary image. For the simulation, weused two sets of different templates. Also, we consider that
it is important to investigate the behavior of this new type ofIn this section, we explain about the structure of singlelayer CNN and two-layer CNN.
2.1. Single-layer CNN
The basic circuit unit in the CNN is called a cell. It contains linear and nonlinear circuit elements such capacitors,resistors, linear and nonlinear controlled sources. The circuit
size in the CNN is consider as M × N cells that arranged inM rows and N columns. Each cell in the CNN only takes interaction communication with the cell in neighborhood. Thevalues of each cell change according to the neighbor cells. In
the CNN, output value also depends on parameters called atemplate. The CNN contains with three templates which are
feedback template A, control template B and constant bias I.
The state equation and the output equation in the single-layer
CNN are described as follows.
State Equation :- 515 -dvxij
dt= −vxij +i+1
∑

j+1
∑

A(i,j;k,l) vykl (t)k=i−1 l=j−1+i+1
∑

j+1
∑

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

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

(1)

1(|vxij (t) + 1| − |vxij (t) − 1|).
2(2)Output Equation :vyij (t) =2.2. Two-layer CNN+In previous studies, the two-layer CNN has been introduced. The two-layer CNN has been confirmed to have moreefficient structure for image processing [4]. The two-layer
CNN is a combination of two sets of the single-layer CNNs.
The different point from the single-layer CNN is that the twolayer CNN has coupling templates C12 and C21 . The templates are used to connect and transfer the data between firstand second layers. The block diagram of the two-layer CNN
is shown in Fig. 1.

i+1
∑j+1
∑

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

(4)

Output equation :vy1ij (t) =1(|vx1ij (t) + 1| − |vx1ij (t) − 1|).
2(5)vy2ij (t) =1(|vx2ij (t) + 1| − |vx2ij (t) − 1|).
2(6)3. Proposed Method
In this section, we explain the algorithm of the proposed
structure. The proposed structure provides two neurons with
two types of templates for one cell in CNN. The proposed
structure is inspired from the two-layer CNN. In the proposed
structure, coupling templates are dismissed and the connection between two layers are accomplished by A1 and B2 . Thisis the different point between the proposed structure and thetwo-layer CNN. By not using coupling templates, the structure becomes simpler compared with the two-layer CNN.
Figure 2 shows the block diagram of the proposed structure. We define the input and the output values as vu1 , vu2 ,vy1 and vy2 . At first the initial states for the neuron α and theneuron β are the same. The input value vu1 is carried out withtemplate B1 in the neuron α. The output from the neuron α
is directly transfered into the neuron β as the input value vu2 .
Figure 1: Block diagram of the two-layer CNN.
In the neuron α, vy2 is carried out with template A1 , and inparallel vy2 is also carried out with template A2 in the neuron
The state equations and the output equations for the two- β. These processes continue until the output converges. Thelayer CNN are given as follows.
state equations and the output equations are given as follows.
State equation :dvx1ijdti+1∑= −vx1ij +j+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 ,Figure 2: Block diagram of the proposed structure.

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

(3)
State equation in the neuron α :dvx2ijdti+1∑= −vx2ij +j+1∑

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

j+1
∑

dvx1ijdt

k=i−1 l=j−1i+1∑j+1∑

k=i−1 l=j−1- 516 -j+1∑

A1 (i, j; k, l)vy2kl (t)k=i−1 l=j−1+B2 (i, j; k, l)vu2kl (t)i+1∑= −vx1ij +B1 (i, j; k, l)vu1kl (t) + I1 ,(|i − k| ≤ 1, |j − l| ≤ 1).

(7)

State equation in the neuron β :dvx2ijdti+1∑= −vx2ij +j+1∑

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).

(8)

(a)

(b)

(c)

(d)

Output equation :vu2ij (t) = vy1ij (t)1= (|vx1ij (t) + 1| − |vx1ij (t) − 1|).
2
vy2ij (t) =(9)1(|vx2ij (t) + 1| − |vx2ij (t) − 1|).
2(10)4. Simulation Results
In this section, we show two examples of the simulation
results using the proposed method.
4.1. Logic NOT operation
In single-layer CNN, when the “Logic NOT” template [5]in Eq. (11) is used to the Fig. 3(a), the output image becomesbinary image like Fig. 3(b).
Logic NOT template :0A1 =  00010

00  , B10I1==Figure 3: Simulation results of logic NOT operation. (a) Input
image (256×256). (b) Output result using the basic CNN.
(c) Output result using the fuzzy CNN. (d) Output of neuron
α using the proposed method.

Template in the neuron β :

0 0A2 =  0 20 00 0 0
 0 −2 0  ,0 0 00.
(11)

Also Fig. 3(c) shows the simulation result using the fuzzy
CNN (FCNN) [6]-[8]. By applying the logic NOT templateand fuzzy template to FCNN, the output image of the logic
NOT operation becomes gray scale image. However the feature of some parts in the input image with the similar grayscale value are lost. For example the texture of pants wornby the cameraman with the different color of gray scale isdisappeared.
For logic NOT operation using the proposed structure, weapply the template as follow.
Template in the neuron α :000000A1 =  0 −1.2 0  , B1 =  0 −0.4 0  ,000000
I1 = −1.
(12)

00  , B20I2

0=  00= −1.

0 0
1.2 0  ,0 0(13)Figure 3(d) shows the simulation result using the proposedstructure. The result using the proposed structure shows someparts with the similar gray value are performed the logic NOT
operation well. For the neuron β, the output becomes wholewhite. From the result, we can say that the proposed structure performs the Logic NOT operation more finely than theFCNN.

4.2. Combination of “Hole filling” and “White propagation”
For second simulation example, “Hole filling” template [5]is used in the neuron α and a new “White propagation” template is used in the neuron β.

- 517 -5. Conclusions(a)

In this study, we have proposed a combination method of
two neurons for a cell in CNN. We can say that the data fromeach neuron still can be sent to each other by only using templates A1 and B2 . In our proposed structure, two types oftemplates can be confirmed to effect in one output value. The
proposed structure was also approved to have a great ability
in image processing.
In the future works, we would like to change the size oftemplate and circuit implementation to investigate the effects
for output feature. Besides gray scale and binary images, wealso would like to try to use the proposed structure for motion
pictures.

(b)

References[1] L. O. Chua and L. Yang, “Cellular Neural Networks: Theory,” IEEE Trans. Circuits Syst., vol. 32, no. 10, pp. 12571272, Oct. 1988.

(c)[2] H. Koeppl and L. O. Chua, “An Adaptive Cellular Nonlinear Network and its Application,” Proc. of NOLTA’07,
pp. 15-18, Sep. 2007.

(d)Figure 4: Simulation results. (a) Input image (256×256).
(b) Initial state. (c) Output image of neuron α. (d) Output
image of neuron β.

“Hole filling” template :0 1 0
A1 =  1 3 1  , B10 1 0I1

0=  00
= −1.

040

00 ,0New “White propagation” template :
0 0.5 00 0A2 =  0.5 3 0.5  , B2 =  0 10 0.5 00 0
I2 = −2.75.

[3] L. O. Chua and L. Yang, “Cellular Neural Networks: Applications,” IEEE Trans. Circuits Syst., vol. 35, no. 10,pp.1273-1290, Oct. 1988.
[4] Z. Yang, Y. Nishio and A. Ushida, “Templates and Algorithms for Two-Layer Cellular Neural Networks,” Proc.
of IJCNN’02, vol. 3, pp. 1946-1951, May 2002.

[5] L. Kek, K. Karacs and T.Roska, “Cellular Wave Computing Library (Templates, Algorithms, and Programs),
Version 2.1,” Cellular Sensory Wave Computers labora(14)tory, Hungarian Academy of Sciences, Budapest, Hungary, 2007.

[6] T. Yang and L.B. Yang, “Fuzzy Cellular Neural Network:
0Theory, Proc. of CNNA’96, pp. 181-186, 1996.
0 ,[7] T. Yang and L.B. Yang, “Fuzzy Cellular Neural Network:
0Applications, Proc. of CNNA’96, pp. 225-230, 1996.
(15)

The results are shown in Fig. 4. The output of the neu- [8] K. Nishizono and Y. Nishio, “Image Processing of Gray
Scale Image by Fuzzy Cellular Neural Network” Proc. ofron α is obtained as Fig. 4(c). It is the same as the case ofNCSP‘06, pp.90-93, Mar. 2006.
the basic CNN with“Hole filling” template. The connection
between vy1 and vu2 , enable the value from the neuron α directly process to the neuron β in the same loop. Figure 4(d)is the output of the neuron β. Only enclosed shape that exists
in a black area of the initial state in Fig. 4(b) is detected as theoutput of neuron β. From these results, we can say that both
templates can be used simultaneously.
From both simulation results, we can say that the proposed
structure has the distinctive output feature.

- 518 -