2007 IEEE Workshop on Nonlinear Circuit Networks
NCN'07, Tokushima, Japan, Dec 7--8, 2007

Image Processing of Cellular Neural Networks withMixtured Template
Takashi INOUE and Masaru NAKANO and Yoshifumi NISHIO
Department of Electrical and Electronic Engineering,
Tokushima University,
2-1 Minami-Josanjima, Tokushima 770-8506, JAPAN
Email: {takashi, nakano, nishio}@ee.tokushima-u.ac.jp
Abstract— In this study, we propose mixtured template system
as a space-varying system for image processing. This system
has the structure that we assign one template to each cell frommultiple templates which are chosen optionally. If the proposedsystem can realize to make multiple kind processings at once, thenthe generalization processing time is reduced. In this research,
we show some interesting combination template by a simulation.

State equation:
dvxij
dt

=−vxij +j+ri+r∑∑A(i,j;k,l) vykl (t)k=i−r l=j−r

+j+r
i+r
∑
∑

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

k=i−r l=j−r

Output equation:

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. Wiring weights of the cells are established by parameters called the template. If the templates of the cells in theCNN are identical, the system is called space-invariant system,
or if the templates of the cells in the CNN are not identical,
the system is called space-varying system. The space-varying
system is not mainly used in the studies of CNN, and it
is difficult to predict the results to use multiple templates.
In the space-invariant system, the pattern extraction etc. canbe processed by repeating two or more processing. However,it takes time for this processing. If multiple processing are
made at once by the proposed system, processing time can bereduced. Also by mixing multiple templates, we hold up a hopethat new performance that characteristic of each template arefused is discovered. In this research, we propose a mixtured
template system of the CNN to rise performance of the CNN.
We test the combinations of various templates to discovereffective results using computer simulation. As a result, weobtain some interesting performance of two types of mixtured
template system.

1(|vxij (t) + 1| − |vxij (t) − 1|)(2)2vx , vy and vu represent a state, an output and an inputof cell, respectively. In the equation (1), A is the feedback
template and B is the control template. These and bias I arecollectively called general template.
vyij (t) =III. M IXTURED TEMPLATE SYSTEM
In this study, we propose two types of Mixtured Template
System (MTS). These systems are the CNN which haveinformations of multiple templates. In type 1 of MTS (MTS1), one kind of template is selected randomly per each cellfrom multiple templates which are chosen optionally.
Figure 1 shows structure examples of MTS-1 using twokinds of templates.

(a)II. C ELLULAR N EURAL N ETWORKSIn this section, we describe basic structure of the CNN. The
CNN has M by N processing unit circuits called cells as Fig.
1. Cells are arranged in a reticular pattern to M line N row.
We represent a cell C(i, j) using a variable i which denotes
vertical position and a variable j which denotes horizontal
position. Cell contains linear and nonlinear circuit elements.
The CNN is an array of cells. Each cells are connected toneighboring cells according to a template. The template is thesame for all cells expect for boundary cells.
The state equation and the output equation of the cell are
shown as follows.

-5-(b)(c)Fig. 1. Examples of mixtured template using two types of templates (Blackcells and white cells have different templates). (a) white : black = 75 : 25.
(b) white : black = 50 : 50. (c) white : black = 25 : 75.

In this figure, black cells and white cells have different
templates. In the system, mixture method is completely random. The ratio between black cells and white cells is decided
optionally.
On the other hand, in type 2 of MTS (MTS-2), we consider
that the template is resolved into the elements. Namely, intype 2 of MTS (MTS-2) each element of template is selectedrandomly each element from multiple templates which werechosen optionally. Templates (5), (6) show the examples thattwo kind templates (3), (4) is mixed at ratio of 5:5 by MTS-2.
Template 3:
a1 a2 a3
b1 b2 b3
A =  a4 a5 a6  , B =  b4 b5 b6  , I = I1 .
a7 a8 a9b7 b8 b9(3)Template 4:
α1 α2 α3β1 β2 β3A =  α4 α5 α6  , B =  β4 β5 β6  , I = I2 .
α7 α8 α9β7 β8 β9(4)Template 5:
α1 α2 a3β1 b2 β3
A =  α4 a5 α6  , B =  β4 β5 b6  , I = I2 .
α7 a8 a9b7 b8 β9(5)Template 6:
a1 α2 α3b1 β2 b3A =  a4 α5 a6  , B =  β4 β5 β6  , I = I2 .
α7 a8 α9b7 β8 b9(6)Object Remover. However, when the ratio of Patch Maker toSmall Object Remover is increasing, the strain of large objects
grew.

(a)

(b)

(c)

(d)

Fig. 3. Simulation results using MTS-2. (a) small object remover : patchmaker= 70:30. (b) small object remover : patch maker= 60:40. (c) small object
remover : patch maker= 50:50. (d) small object remover : patch maker= 40:60.

Figure 3 shows simulation results using MTS-2 which
mixed Small Object Remover and Patch Maker. As a result,the noise decreased with increasing the ratio of Patch Maker.
However, when the ratio of Patch Maker was got over 60%,
the output image becomes completely black. A large object in
the input image warps with increasing the ratio.
We examine about two kind results like denoising level ofsmall object and distortion level of large object. The results
are as follows.

IV. S IMULATIONTABLE I

In this section, we show the simulation results of MTS-1
and MTS-2 for image processing using below two kind oftemplates.

PERFORMANCE OF NOISE REDUCTION

Small Object Remover :1
A= 1
1

121



0 0 0
11 ,B =  0 0 0 ,
10 0 0I = −1.

(7)

Mixtured system 1
template(4):(5)=80:20
template(4):(5)=70:30
template(4):(5)=60:40
template(4):(5)=50:50
template(4):(5)=40:60

number of denoising
distortion level
number of denoisingdistortion level
number of denoising
distortion level
number of denoising
distortion level
number of denoising
distortion level

Mixtured system 2

15783
l26
1015
331438————-

number of denoising
distortion level
number of denoising
distortion level
number of denoising
distortion level
number of denoising
distortion level
number of denoising
distortion level

4663
10808
201033261394
302116

P atch M aker:
0
A= 10121
00 0 0
1 ,B =  0 1 0 ,
00 0 0I = 4.5.

(8)

The distortion level denotes difference of the original image
and output image. By Table 1, MTS-1 decreased the noise
well as against MTS-2 when ratio of Patch Maker was small.
However, the distortion level is large. The MTS-2 did notdecrease the noise if there are not big mixing ratio of PatchMaker. However, distortion level is small.

V. S IMULATION RESULTS FOR GRAYSCALE IMAGE(a)

(b)

(c)

(d)

Fig. 2. Simulation Results of MTS-1 using Small Object Remover and PatchMaker. (a) Input image. (b) small object remover : patch maker= 80:20. (c)small object remover : patch maker= 70:30. (d) small object remover : patchmaker= 60:40.

Figure 2 shows the simulation results of MTS-1. As a result,the performance is risen with mixing Patch Maker to Small-6-

In this section, we use the grayscale image (Fig. 9) as input
image. In this simulation. we use MTS-1 with Smoothing
Operation and Diffusion.
Smoothing Operation:
0 1 00A =  1 2 1 ,B =  00 1 00000


00 ,0I = 0.

(9)

Diffusion:
0.1 0.15 0.100.15  , B =  0
A =  0.15 0
0.1 0.15 0.10000


00 ,0I = 0.
(10)(a)(b)(c)(d)

Fig. 4. Convergent output images with changing the ratio of (9) and (10).
(a) Input image. (b) (9) : (10) = 0 : 100. (c) 5 : 95. (d) 20 : 80.

Figure 4(a) is an input image. Figures 4(b)(c)(d) are theconvergent output images with changing the ratio of (9) and(10). As a result, if we can discover suitable combination ofmultiple templates then the processing with both characteristics would be realized.
VI. C ONCLUSIONSIn this study, we proposed the mixtured templates systems 1and 2 as the space-varying templates systems. We investigatedcharacteristics of the proposed system by simulation. As aresult, we clarified that characteristic of CNN can be improvedby the proposed system.

Acknowledgments
This research is supported by the fund of Open ResearchCenter Project from MEXT of Japanese Government (20072011).
R EFERENCES[1] L. O. Chua and L. Yang, ”Cellular Neural Networks:Theory,” IEEE Trans.
Circuits & Syst., vol. 32, pp. 1257-1272, Oct. 1988.

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