2011 International Workshop on Nonlinear Circuits,Communication and Signal Processing
NCSP'11, Tianjin, China, March 1-3, 2011

Application Using Checkered Arrangement of Cells in Two-Template CNN
Riichiro Yaname† , Yasuteru Hosokawa† and Yoshifumi Nishio‡‡Tokushima University
2-1 Minami-Josanjima, Tokushima, Japan
Phone:+81-88-656-7470
FAX:+81-88-656-7471
Email: nishio@ee.tokushima-u.ac.jp†Shikoku University
Furukawa, Ohjin, Tokushima, Japan
Phone:+81-88-665-1300
Email: s1937090@edu.shikoku-u.ac.jp

Abstract
In this study, three kinds of cloning templates of a discretetime Two-Template CNN are proposed. These cloning templates are designed by using some conventional cloning templates. Therefore, it is not difficult to design a new cloning
template for Two-Template CNN. Additionally, it is shownthat the image processing capability is higher than a conventional CNN.
1. Introduction
Cellular Neural Network (CNN) [1]-[3] is one of mutual
coupling neural networks. There are many studies. One ofadvantages is that cells are coupled only neighborhood cells.
Therefore, IC implementation is easily.
Some kinds of modified CNNs are proposed by individualresearchers. One of modified CNNs is Two-Template CNN[4]. Two kinds of cloning templates of Two-Template CNN
can be set up at once. Some interesting oscillatory phenomena are observed in this system. Furthermore, the architecture of Two-Template CNN is almost same as a conventional
CNN. Therefore, the advantage of IC implementation is notlost.
In our previous studies, there is not an investigation ofimage processing using Two-Template CNN in spite thatTwo-Template CNN is suitable for image processing. Additionally, there is not an investigation of discrete-time
Two-Template CNN in spite that some cloning templates
which have the same functions as continuous-time CNN areshown [5].
In this study, two kinds of cloning templates for discretetime Two-Template CNN are proposed. These templates are
based on some conventional cloning templates. Additionally,
the output function is set as a step function. It means thatbinary outputs are obtained in each iteration. Therefore, it is
not difficult to design these cloning templates.
By some computer simulations, it is shown that the image
processing capability is higher than a conventional CNN.

Figure 1: Architecture of Two-Template CNN.
2. Two-Template CNN
Figure 1 shows an architecture of Two-Template CNN.
Cells α and β are arranged as a checkered pattern. Basically,
the architecture is same as a conventional CNN. A difference
between cell α and β is only values of cloning templates. The
number of cells is set as M × N. The cell which is arranged at
ith row and the jth column is called as C(i, j). We investigate
1-neighborhood only in this study.
State equations of the discrete-time Two-Template CNN
are given as follows.
Cell α:xij (t + 1) =X

Aα (i, j; k, l)ykl (t)C(k,l)∈Nr (i,j)X(1)
Bα (i, j; k, l)ukl + Iα ,C(k,l)∈Nr (i,j)

where i and j are odd numbers, or i and j are even numbers.
Cell β:- 48 -xij (t + 1) =X

Aβ (i, j; k, l)ykl (t)C(k,l)∈Nr (i,j)

X

C(k,l)∈Nr (i,j)(2)
Bβ (i, j; k, l)ukl + Iβ ,

(a)

(b)

(c)
(a)

Figure 2: Simulation results (Dither). (a) Input image. (b)Simulation result of a conventional CNN. (c) Simulation result of Two-Template CNN.

(b)
(a)

(b)

Figure 3: Simulation results (Dither and noise reduction). (a)Input image. (b) Simulation result of Two-Template CNN.

(c)

Figure 4: Simulation results (Dither and noise reduction).
(a) Input image with noise. (b) Simulation result of TwoTemplate CNN. (c) Simulation result of a conventional CNN.

where i is an odd number and j is an even number, or i is an Two-template CNN:
even number and j is an odd number.
A{αβ} (i, j; k, l)ykl , B{αβ} (i, j; k, l)ukl , I{αβ} are called as
0 0 000.1
0
the feedback coefficient, the control coefficient and bias cur00.1 , B α = 0 4 0 , Iα = −3.7,Aα = 0.1
rent, respectively.
0 0 000.1
0
The output equation is given as follows.

−1 −1 −10 0 01
(xij (t) ≥ 0)
(3) Aβ = 0 0 0 , B β = −1 9 −1 , Iβ = 0.
yij (t) =−1(xij (t) < 0)0

By this function, output values are binarized.

00−1−1−1(5)where input state values are set as random numbers. Fig3. Simulations
ure 2(a) shows an input image. Figures 2(b) and (c) show simulation results of the conventional CNN and Two-Template
CNN, respectively. The cloning template of the conventional
3.1. System Set-up
CNN and cell β of Two-Template CNN means a dither. TheIn this section, computer simulations are carried out. All cloning template of cell α of Two-Template CNN means ainput images are gray scale images whose gradation is a 256 noise rejection. In the case of Two-Template CNN, we degradation. The size is 256 × 256. Boundary conditions are signed the cloning template by only coupling two cloning
set as 1.
templates for a conventional CNN. Therefore, the designing
method is a very simple. Additionally, the capability is higher
3.2. Dither
than a conventional CNN. In Fig. 2(c), a area which looks likegrayis confirmed. This area is a checkered pattern. This area
Figure 2 shows simulation results of a conventional CNNsizecanbe changed by changing Iα . Thus we consider that aand Two-Template CNN with following cloning templates.
better output image can be obtained. This template has an another capability. Figure 3 shows a simulation result of TwoConventional CNN:
Template CNN. Figures 3(a) and (b) show an input imageand a simulation result of Two-Template CNN, respectively.
0 0 0−1 −1 −1
In this case, some white dots are removed. Namely, a noise
9−1 , I = 0. (4) reduction is carried out. In order to realize these processing
A = 0 0 0 , B = −10 0 0−1 −1 −1on a conventional CNN, two cloning templates which are a- 49 -and Two-Template CNN on following cloning templates.
Conventional CNN:
0A = 10(a)

121



001 , B =  000040


00 , I = −0.5.
0(6)Two-template CNN:


00.1
00 0 000.1 , B α = 0 4 0 , Iα = −3.7,Aα = 0.1
00.1
00 0 0
1 0 10 0 0Aβ = 0 2 0 , B β = 0 4 0 , Iβ = −0.5.
1 0 10 0 0(b)

(c)

(a)

(b)

(7)
Figure 5(a) shows an input image. Figures 5(b) and (c)Figure 5: Simulation results (Hole filling). (a) Input image. show simulation results of a conventional CNN and Two(b) Simulation result of a conventional CNN. (c) Simulation Template CNN, respectively. The cloning template of theconventional CNN means hole filling. The cloning template
result of Two-Template CNN.
of cell α of Two-Template CNN means noise rejection. Thecloning template of cell β of Two-Template CNN is based onhole filling for a conventional CNN. The original matrix A ofthe cloning template is shown as follows.
0 1 0(8)A = 1 2 1 0 1 0Figure 6: Simulation results (Hole filling and noise reduction). (a) Simulation result of Two-Template CNN. (b) Simulation result of hole filling and noise reduction.
dither and a noise reduction are needed.
Here, the other results are shown. Figure 4(a) shows aninput image. Figure 4(b) shows a simulation result of TwoTemplate CNN with the cloning template (5). Figure 4(c)shows a simulation result of a conventional CNN. The cloningtemplate (4) and cell α of the cloning template (5) are continuously applied. In Fig. 4(b), some gray-scaled area are observed. For instance, a camera, buildings, cameraman’s pants
and so on looks like gray. These area are checkered patterns.
On the other hand, in the case of the conventional CNN, thesearea are blacked out. We consider that these results show theadvantage of Two-Template CNN.
3.3. Hole filling
Figure 5 shows simulation results of the conventional CNN

By rotating 45 degree, matrix Aβ are obtained. This modifying means that coupling of cell β is kept. Matrix Bβ andbias Iβ are same as the original cloning template. In this case,
we designed the cloning template by coupling and modifying
two cloning templates for a conventional CNN.
Advantages of Two-Template CNN are the transparency ofhole filling and noise reduction. In Fig. 5(b), we can not obeserve lines which pass though objects and all black dots arekept. In Fig. 5(c), hole filling is carried out as a checkered pattern which looks like gray. Therefore, we can see the lines.
Additionally, some black dots are removed. Therefore, weconsider that a Two-Template CNN is better than a conventional CNN.
Here, the other results are shown. Figure 6(a) shows a simulation result of Two-Template CNN with the cloning template (7). Figure 6(b) shows a simulation result of the conventional CNN. The cloning template (6) and cell α of thecloning template (7) are continuously applied. The input image of these two results is Fig. 4(a). In Fig. 6(b), some checkered pattern areas are observed. Especially, the shade of cameraman’s pants is processed effectively. On the other hand, inthe case of the conventional CNN, these area is blacked out.
In this case, we could not say that there is the advantage of
Two-Template CNN.

- 50 -

be confirmed as checkered patterns. Thus, we consider that abetter result can be obtained.
3.5. Discussion
We consider that common points of these results are follows three points. Initial state values are random numbers.
The cloning template A of cell α is noise rejection. The
cloning template A of cell β is not connected with cell α.
From these points, it is expected that cloning templates which
satisfy these points can be applied to Two-Template CNN. On
the other hand, investigating cloning templates which do notsatisfy these points is needed.

(a)4. Conclusions
In this study, we proposed three kinds of cloning templates
for Two-Template CNN. As a result, some common points
were shown.
In our future works, applying these cloning templates toFigure 7: Simulation results (Edge detection). (a) Input imsome
famous images for image processing studies, cloning
age. (b) Simulation result of conventional edge detection temtemplatevalues optimization, designing another cloning template. (c) Simulation result of edge detection and dither.
plates and so on are considered.
(b)

(c)

3.4. Edge detection

References

Figure 7 shows simulation results of a conventional CNNand Two-Template CNN on following cloning templates.
Conventional CNN:
0A = 00000−100 , B = −1−10−19−1
−1−1 , I = 2.
−1(9)Two-template CNN:
0Aα = 000Aβ = 00000000−100 , B α = −10−10−10 , B β = −1
0−1−1
9−1−19−1
−1−1 , Iα = 0,−1

−1−1 , Iβ = 2.
−1

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[4] J. Fujii, Y. Hosokawa and Y. Nishio, “Wave Phenomenain Cellular Neural Networks Using Two Kinds of Template Sets,” Proc. of NOLTA’ 07, pp. 23–26, 2007.

(10) [5] H. Saito, K. Jin’no and M. Tanaka, “Universality of DTCNN,” IEICE Technical Report, no. NLP96-72, pp. 65–
where input state values are set as random numbers. Fig72, 1996.
ure 7(a) shows an input image. Figures 7(b) and (c) show
simulation results of a conventional CNN and Two-Template
CNN, respectively. The cloning template of the conventional
CNN means edge detection. The cloning template of cell αof Two-Template CNN means dither. The cloning template ofcell β of Two-Template CNN means edge detection. Both ofthem, edge detection can be applied. However, in Fig. 7(b),we can not see white parts which is included in graphics of
the input image. By contrast, in Fig. 7(c), white parts can- 51 -