2008 IEEE Workshop on
Nonlinear Circuit Networks, Tokushima, Dec 5-6, 2008

A Design Method of 5 × 5 Templates
for Cellular Neural Networks
Takashi INOUE and Yoshifumi NISHIO
Department of Electrical and Electronic Engineering,
Tokushima University
2-1 Minami-Josanjima, Tokushima 770-8506, JAPAN
Email: {takashi, nishio}@ee.tokushima-u.ac.jp
Abstract— In this study, we propose a simple template design
method of cellular neural networks by combining two existing
templates. In this article, we investigate the output characteristicsof simple image processings using the proposed template design
method and show its effectiveness with simulation results.

I. I NTRODUCTION
Cellular Neural Networks (CNN) [1] were introduced byChua and Yang in 1988. The idea of the CNN was inspired
from the architecture of the cellular automata and the neuralnetworks. Unlike the conventional neural networks, the CNN
has local connectivity property. Since the structure of the CNN
resembles the structure of animals’ retina, the CNN can beused for various image processing application.
Wiring weights of the cells are established by parameters
called the template. The performance of the CNN is decided by
the template. There are some major template design methods
such as template learning [2]. However, the template leaning
takes a long time to find desired template.
In this study, we propose a simple template design methodof cellular neural networks by combining two existing templates. We investigate the output characteristics of image
processing using the proposed template design method andshow its effectiveness with simulation results.

Finally, we create a new 5 × 5 combination templatefrom the two 3 × 3 templates with the mixing rate;
Combination T emplate:
 1
11
pa11

 0
1A=
 pa21
 0


0

pa120

pa13

(1−p)a211(1−p)a212(1−p)a2130(1−p)a221(1−p)a231(1−p)a223(1−p)a233

pa123

0

pa133

pa131

0

pa122 +(1−p)a222(1−p)a232
pa132

pb111

0

pb112

0

pb113

(1−p)b211(1−p)b212(1−p)b2130(1−p)b221(1−p)b231

pb122 +(1−p)b222(1−p)b232pb132(1−p)b223pb123(1−p)b233

00

pb133

 0

1B=
 pb21
 0pb13200

I = pI1 + (1 − p)I2 .

,


,


(4)

The schematic picture of the procedure is shown in Fig. 1.
In Fig. 1(c), the white elements are 0.

II. T EMPLATE D ESIGN M ETHOD
In this section, we propose a template design method of theCNN. In our template design method, we simply prepare twokinds of 3 × 3 different templates;
T emplate 1 :
 1
 1
11
11
A1 =  a121

a11a12

a13a122a123

 , B1 =  b121

b11a131a132a133b131b12b13b122b123b132b133(a) , I1 .
(c)(1)
T emplate 2 : 2a11A2 =  a221
a231

a212
a222
a232

a213
a223
a233





 , B2 = 

b211
b221
b231

b212
b222
b232

b213
b223
b233

Fig. 1. Combining two templates. (a) Template 1 (3×3). (b) Template 2 (3×3). (c) Combination template (5 × 5).

 , I2 .
(2)

Next, we choose the mixing rate;
M ixing Rate:p(0 ≤ p ≤ 1.0)

(b)

(3)

- 35 -The following is an example of the procedure.
T emplate 1 :



1 1 1
1 2 1
A1 =  1 2 1  , B1 =  2 0 2  , I1 = 0.
1 1 1
1 2 1(5)T emplate 2:
0 0.5 00.2 0 0.2
A2 =  0.5 4 0.5  , B2 =  0 1 0  ,0 0.5 0
0.2 0 0.2
I2 = 4.5.

(6)

M ixing Rate:p = 0.8.
Combination T emplate:0.8 0 00
0.80.1A= 000.8 0
0.80 0 0.04
0B=
 1.6
 0 0.04
0.80(7)
0.8 0 0.8
0.1 00 
2.4 0.1 0.8 ,
0.1 00 
0.8 0 0.8
1.600.8
0 0.04 0 0.201.6 ,
0 0.04 0 
1.6
00.8

I = 0.9.

(a) Input image(b) p = 1.0.

(c) p = 0.8.

(d) p = 0.7.

(e) p = 0.6.

(f) p = 0.5.

(8)

III. S IMULATION R ESULTS FOR N OISE R EDUCTION
In this section, we show the simulation results for noise
reduction. All the original templates in this section are foundin [3]. We set the “Small Object Remover” template asTemplate 1 and the “Patch Maker” template as Template 2.
Small Object Remover (T emplate 1) :

1 1 10 0 0
A1 =  1 2 1  , B1 =  0 0 0  , I1 = −1. (9)1 1 10 0 0
By using this template, large objects remain and smallobjects are removed from input binary images.
P atch M aker (T emplate 2):
0 1 00 0 0A2 =  1 2 1  , B2 =  0 1 0  , I2 = 4.5.
0 1 00 0 0(10)By using this template, black objects are expanded withoutlimit.
Figure 2 shows the simulation results using combination
template. Figure 2(b) shows the simulation results using only
“Small Object Remover” template for an input image withvarious size of spot noises. We can see that the “SmallObject Remover” template cannot remove relatively large spot
noises at all. Figures 2(c), (d), (e) and (f) show simulation
results using combination template with different mixing rates.
In Fig. 2(c), all noises removed and the two large objects
are little distorted. However, when the ratio of the “PatchMaker” template is larger than 30%, the output image becomescompletely black.
Remark: In this simulation, the mixing rate p=1.0 gives
almost similar identical output image to the case that theFig. 2.
Simulation results using combination template of Small Object
Remover Template (Template 1) and Patch Maker Template (Template 2)
with different mixing rates.

standard CNN with the “Small Object Remover” template isused. However, the output is not always the same even if wechoose p=1.0. Because the template 1 is expanded to 5x5 size
and this can cause a different effect to the image. This meansthat the choice of template 1 or 2 is important in our template
design method. In this noise reduction, we consider that thelarge noises can be removed by setting the “Small ObjectRemover” template outside of the combination template.
IV. C ONCLUSIONSIn this study, we have proposed the template design methodof the CNN by combining existing templates. By computer
simulations of simple image processing for binary images, weinvestigated the basic output characteristics of the proposedsystems. As we expected, we could confirm the effects of both
templates by combining them. At the moment, we do not saythat the proposed method exhibited a superior performance
than the original CNN. However, we feel that we obtainedsome results to broaden the research on the CNN design.
R EFERENCES[1] L.O. Chua and L. Yang, “Cellular Neural Networks:Theory,” IEEE Trans.
Circuits Syst., vol. 32, pp. 1257-1272, Oct. 1988.
[2] Á. Zarándy, “The Art of CNN Template Design,” Int. J. Circ. Theor.
Appl., vol. 27, no. 1, pp. 5-23, Jan.-Feb. 1999.
[3] Cellular Sensory Wave Computers Laboratory Computer and Automation
Research Institute Hungarian Academy of Sciences, “Cellular wave
Computing Library (Template, Algorithms, and Programs) Version 2.1”

- 36 -