社団法人 電子情報通信学会
THE INSTITUTE OF ELECTRONICS,
INFORMATION AND COMMUNICATION ENGINEERS

信学技報
TECHNICAL REPORT OF IEICE.

Apllications of Cellular Neural Networks
Using Mixture Template
Takashi INOUE† , Masaru NAKANO† , and Yoshifumi NISHIO†† Department of Electrical and Electronic Engineering, Tokushima University
2–1 Minami-Josanjima, Tokushima 770–8506, Japan
E-mail: †{takashi,nakano,nishio}@ee.tokushima-u.ac.jp
Abstract In this research, we propose cellular neural networks using mixture template as an example of space–varying cellular neural networks. As the ﬁrst step of the investigation of such complex nonlinear circuit networks,
we propose two mixing methods of the templates and investigate the output characteristics of the simple image
processing with a binary image and a grayscale image by computer simulations.
Key words Cellular Neural Network (CNN), image processing

1. Introduction

grayscale image.
In the Sec. 2, we review the basic of the standard CNN. In

Cellular Neural Networks (CNN) [1] were introduced by

the Sec. 3, we show how to mix the templates and show some

Chua and Yang in 1988. The idea of the CNN was inspired

computer simulated results. In the Sec. 4, noise removal per-from the architecture of the cellular automata and the neu-

formance of the proposed mixture templates is evaluated. In

ral networks. Unlike the conventional neural networks, thethe Sec. 5, simulation results for a grayscale image are shown.

CNN has local connectivity property. Since the structure ofSection 6 concludes the article.

the CNN resembles the structure of animals’ retina, the CNN
can be used for various image processing application [2]-[4]2. Cellular neural networks

including character extractions [5][6]. Further, the CNN can

In this section, we describe the basic structure of the CNN.

be utilized to produce some kinds of pattern generation [7][8].

The CNN has M by N processing unit circuits called cells

Wiring weights of the cells are established by parameters

as Fig. 1. Cells are arranged in a reticular pattern to M

called the template. The performance of the CNN is decided

line N row. We represent a cell C(i, j) using a variable iby the template. If the templates of all the cells in the CNN

which denotes vertical position and a variable j which de-are identical, the system is called space-invariant, while ifnotes horizontal position. The cell contains linear and non-the templates of all the cells in the CNN are not identical,

linear circuit elements. The CNN is an array of cells. Eachthe system is called space-varying. Typically, space-invariant

cell is connected to its neighboring cells according to a tem-system is mainly used in the studies of the CNN, because theplate. Usually, the template is the same for all cells except for

implementation cost is cheap. However, on the ﬂip side, theboundary cells. The CNN has the features of time continu-

performance of the system is considered to be limited.

ity, spatial discreteness, nonlinearity and parallel processing

In this research, we propose the CNN with mixture template as an example of space-varying CNN. By mixing two
diﬀerent templates, we expect that the proposed CNN possesses the both eﬀects of the two templates. It may be usefulto reduce the number of the successive precessing for somekinds of image processing tasks. Further, we are interested
in the complex behaviors of such a new class of nonlinear

capability.
The state equation and the output equation of the cell are
shown as follows.
State equation:
j+r
i+r
∑
∑
dvxij
A(i,j;k,l) vykl (t)= −vxij +dt
k=i−r l=j−r

j+r
∑ ∑
i+r

circuit networks. They can be utilized for future engineer+ing applications. As the ﬁrst step of the investigation of thisB(i,j;k,l) vukl (t) + I(1)

k=i−r l=j−r

concept, in this research, we propose two mixing methodsof the templates and investigate the output characteristicsof the simple image precessing with a binary image and a

Output equation:vyij (t) =1(|vxij (t) + 1| − |vxij (t) − 1|)
2

(2)
—1—

where vx , vy and vu represent a state, an output and an input

random in this article, the mixing method can be modiﬁedof cell, respectively. In the equation (1), A is the feedback

to some kinds of regular mixing method like alternate pat-

template and B is the control template. These and bias I

terns. Also the ratio of black cells and white cells is decided

are collectively called general template.

optionally.

The r − neighborhood of the cell C(i, j) in the CNN isdeﬁned by

We carry out computer simulations of the matrix mixing
using “Small Object Remover” template and “Patch Maker”
template.

N r(i, j) = {C(k, l) | max { |k − i| , |l − j| } <
= r,
1<
=k<
= M;

1<
=l<
= N}

(3)

Small Object Remover :

where r is a positive integer number. In our study, we ﬁx









1

1

0

0

0

A= 1

2

1 , B =  0

00  , I = −1. (4)

1

1

1

0

0



the value of r as 1.

1

3. Mixture template0Usually, it is desirable that all of the templates at all cells
are identical, namely, space-invariant. However, we are interested in what kind of phenomena can be observed fromspace-varying CNN, because such systems are new class ofnonlinear circuit networks and they may have a possibility
for novel engineering applications.
In this research, we propose the CNN with two kinds of
mixture templates, matrix mixing and element mixing, as an(a)example of space-varying CNN,
3. 1 Matrix mixing(b)Fig. 2 The performance of Small Object Remover. (a) Input
image. (b) Output image.

In the ﬁrst method of the mixing, we prepare two diﬀerent CNN templates and choose one of them for each cell at

Figure 2 shows how the Small Object Remover template

random.

works. By using this template, large objects remain andsmall objects are removed from input binary images.
P atch M aker:



(b)









1

0

0

0

0

A= 1

2

1 , B =  0

1

0  , I = 4.5. (5)

0

1

0

0

0



(a)



0

0



Figure 3 shows how the Patch Maker template works.
By using this template, black objects are expanded without
limit.
Figure 4 shows the simulation results using only Small Object Remover template for an input image with relatively
large spot noises. We can see that the Small Object Remover cannot remove such noises at all.
Figure 5 shows the simulation results for the same input(c)Fig. 1 Examples of matrix mixing. Black and white cells correspond to two diﬀerent CNN templates. (a) white : black =75 : 25. (b) white : black = 50 : 50. (c) white : black =25 : 75.

image using the mixture template with the matrix mixing.
From the output images, we can say that the CNN with the
mixture templates possesses the both eﬀects of the two templates, namely black regions are expanded by the eﬀect of
the Patch Maker template and the shrinking spot noises are

Figure 1 shows structure examples of the matrix mixing.
In this ﬁgure, black cells and white cells have diﬀerent templates. Though we assume that the mixing is completely

removed by the eﬀect of the Small Noise Remover template.
Although the eﬀect of the noise removal is enhanced by increasing the ratio of the Patch Maker template to the Small

—2—

(a)

(b)

(c)
Fig. 3 The performance of Patch Maker.

(a)

(b)

(c)

(d)

(a) Input image.

(b) Transitional image. (c) Output image.

(e)
Fig. 5 Simulation results for the same input image in Fig. 4(a)(a)

using mixture template with matrix mixing. (a) small(b)Fig. 4 Simulation results using only Small Object Remover tem-object remover : patch maker= 80:20. (b) small object
remover : patch maker= 70:30. (c) small object removerplate. (a) Input image. (b) Output image.

: patch maker= 60:40. (d) small object remover : patchmaker= 50:50. (e) small object remover : patch maker=

Object Remover template, it makes the shape of the large
objects broken and the output becomes completely black for
Figs. 5(d) and (e).

40:60.

element of them for each element of the matrices and theSome examples of the mixture templates obtained fromthe Small Object Remover template and the Patch Maker
template using the element mixing are as follows.

0

0

A= 1

2

1 , B =  0

00  , I = −1.

0

1

1

0

0

0

0

1

1

0

0

0

A= 1

2

1 , B =  0

00  , I = 4.5.

0

1

1

0

0

0









1

0

0

0

0

A= 1

2

1 , B =  0

1

0  , I = 4.5.

0

1

1

0

0

0

Example 2:(7)

Example 3:














(8)

with even ratio. Figure 8 shows the simulation results for



1





The above templates are obtained by mixing the elements

Example 1:





0



threshold I at random as shown in Figs. 6 and 7.





1

In the second method of the mixing, we prepare two different CNN templates as the matrix mixing, but choose the



1



3. 2 Element mixing



0



the same input image as in the previous subsection using the(6)

mixture template with the element mixing of diﬀerent mixing ratios. From the output images, we can say that thiselement mixing method has similar eﬀect to the previous
matrix mixing method.

—3—

Table 1 Noise removal performance of mixture templates.

Matrix mixing
template (4) : (5) number of denoising= 80:20

distortion level

template (4) : (5) number of denoising= 70:30

distortion level

template (4) : (5) number of denoising= 60:40

distortion level

template (4) : (5) number of denoising= 50:50

distortion level

template (4) : (5) number of denoising= 40:60

distortion level

Element mixing
15

number of denoising

4783

distortion level

663

26

number of denoising

10

1015

distortion level

808

33

number of denoising

20

1438

distortion level

1033

40

number of denoising

26

11514

distortion level

1394

40

number of denoising

30

11514

distortion level2116

ing spot noises. While the distortion level of the large objects
are evaluated by the number of the cells in the inputted large
objects whose colors change from white to black, namely thediﬀerence in pixels between the original object images andthe output object images. The results are summarized inTable 1 for various mixing ratios. The both mixing methods
remove the noise as the ratio of the Patch Maker increases.
Fig. 6 Wiring weights of two templates.

However, the distortion level becomes large. We can see thatthe eﬀect of the matrix mixing seems to be larger than thatof the element mixing.

5. Simulation results for grayscale image
In this section, we apply CNN with mixture template of
the matrix mixing to a grayscale image in Fig. 9. In thissimulation. we use the Smoothing Operation template andthe Diﬀusion template.
Fig. 7 Wiring weights of element mixing.

Smoothing Operation:

4. Noise removal performance
In order to compare the two mixing methods quantita-level of the large objects of the input image. The input image have 40 noises. The Large objects of input image consistof 11514 pixels.
The denoising level of the small objects are evaluated by
the number of denoising, namely, the number of the vanish-









1

0

0

0

0

A= 1

2

1 , B =  0

00  , I = 0.

0

1

0

0

0

0



tively, we examine the noise removal performance investigating the denoising level of the small objects and the distortion



0



(9)

Dif f usion:




0.1

A =  0.15
0.1











0.15

0.1

0

0

0

0

0.15  , B =  0

00  , I = 0.

0.15

0.1

0

0

0



(10)

—4—

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

(e)

(f)

(e)
Fig. 8 Simulation results for the same input image in Fig. 4(a)using mixture template with element mixing. (a) small
object remover : patch maker= 80:20. (b) small object

Fig. 10 Variation of output when mixing ratio of (9) and (10)remover : patch maker= 70:30. (c) small object removeris 20 : 80. (a) t =1. (b) t =5. (c) t =15. (d) t =20.

: patch maker= 60:40. (d) small object remover : patch(e) t =35. (f) t =50.

maker= 50:50. (e) small object remover : patch maker=
40:60.

6. Conclusions
In this research, we have proposed the CNN using mixture template with two kinds of mixing methods, the matrix
mixing and the element mixing. By computer simulationsof simple image processing tasks for a binary image and agrayscale image, we investigated the basic output characteristics of the proposed systems. As we expected, we could
conﬁrm the eﬀects of the both templates by mixing them to
one mixture template. At the moment, we do not say that
Fig. 9 Grayscale input image.

the proposed method exhibited a superior performance thanthe original CNN at the moment. However, we feel that weFigure 10 shows the transient variation of the output images when the mixing ratio of (9) and (10) is ﬁxed as 20 : 80.

obtained some results to open a new direction of the researchon the CNN.

Figure 11 shows the converged output images with changing

References

the mixing ratio of (9) and (10). As a result, if we can choose[1] L.O. Chua and L. Yang, “Cellular Neural Networks:Theory,”
IEEE Trans. Circuits Syst., vol. 32, pp. 1257-1272, Oct.
1988.
[2] F. Dirk and T. Ronald, “Coding of Binary Image Data using
Cellular Neural Networks and Iterative Annealing,” Proc. of
ECCTD’03, vol. 1, pp. 229-232, Sep. 2003.
[3] M. Namba and Z. Zhang, “Cellular Neural Network forsuitable combination of multiple templates, then the image
processing with both characteristics, namely smoothing anddiﬀusion, can be realized,

—5—

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 11 Converged output images with changing mixing ratio of(9) and (10). (a) (9) : (10) = 0 : 100. (b) 5 : 95.
(c) 20 : 80. (d) 50 : 50. (e) 70 : 30. (f) 100 : 0.

[4]

[5]

[6]

[7]

[8]

Associative Memory and Its Application to Braille Image
Recognition,” Proc. of IJCNN’06, pp. 4716-4721, Jul. 2006.
H. Koeppl and L.O. Chua, “An Adaptive Cellular Nonlinear
Network and its Application,” Proc. of NOLTA’07, pp. 1518, Sep. 2007.
T. Kozek, K.R. Crounse, T. Roska and L.O. Chua, “Smart
Image Scanning Algorithms for the CNN Universal Machine,” Proc. of NOLTA’95, vol. 2, pp. 707-712, 1995.
J. Kishida, C. Rekeczky, Y. Nishio and A. Ushida, “Feature Extraction of Postage Stamps Using an Iterative Approach of CNN,” IEICE Trans. on Fundamentals, vol. E79A, no. 10, pp. 1741-1746, Oct. 1996.
K.R. Crounse and L.O. Chua, “Methods for Image Processing and Pattern Formation in Cellular Neural Networks:
A Tutorial,” IEEE Trans. Circuits Syst., vol. 42, no. 10,
pp. 583-601, Oct. 1995.
K.R. Crounse, L.O. Chua, P. Thiran and G. Setti, “Characterization and Dynamics of Pattern Formation in Cellular
Neural Networks,” International Journal of Bifurcation and
Chaos, vol. 6, no. 9, pp. 1703-1724, 1996.

—6—