IEEE Workshop on Nonlinear Circuit Networks
December 13-14, 2013

Possibility of Image Processing by CNN Using Two
Kinds of Cloning Templates
Yoshio Nakayama

Yasuteru Hosokawa

Yoshifumi Nishio

Dept. Media and Information Syst.,
Shikoku University
Email: ny.h.s.t.g@gmail.com

Dept. Media and Information Syst.,
Shikoku University
Email: hosokawa@keiei.shikoku-u.ac.jp

Dept. Electrical and Electronic Eng.,
Tokushima University
Email: nishio@ee.tokushima-u.ac.jpjAbstract—Many modified CNN have been proposed. However,most of modified CNN are lost the simplicity of the system.
In this study, new cloning template of CNN using two kindof cloning templates is proposed. By some computer simulations,
possibility of image processing by CNN using two kinds of cloningtemplates is revealed.

I. I NTRODUCTION
Cellular Neural Networks (CNN) proposed by Chua andYang [1][2] can be carried out many kinds of image processing. The characteristic of CNN depend on a cloning template.
A combination of processing using some cloning templates
has ability of enable processing that conventional systems arenot done. However, an ability of one processing is limited.
Thus, many modified CNN have been proposed.
Most of modified CNN obtained higher ability, lost the simplicity of the system. The simplicity is important for integrated
circuit implementation of CNN. As one of modified systems
which is not lost the simplicity, cellular neural network using
two kinds of cloning templates was proposed by Fujii et al[6].
The system was investigated as coupled oscillatory system
mainly. Active pattern formations, clustering and so on areobserved. On the other hand, application of the systems is notinvestigated.
In this study, new cloning template of CNN using twokind of cloning templates is proposed. By some computer
simulations, possibility of image processing by CNN using
two kinds of cloning templates is revealed.

iCell αFig. 1.

+∑Structure of Two Template CNN.

dxij= − xij + Iβ
dt∑+Aβ (i, j; k, l)ykl

Figure 1 shows a structure of CNN using two kind ofcloning templates. Cell α and Cell β have different cloning
templates. Two kinds of cells are placed as a checkered.
The state equations are shown as follows,
1: Cell α (i + j is even number)c(k,l)

Cell β2: Cell β (i + j is odd number)

II. CNN USING TWO KIND OF CLONING TEMPLATES

dxij= − xij + Iαdt∑
+Aα (i, j; k, l)ykl

c(i,j)c(k,l)+∑(2)Bβ (i, j; k, l)ukl

c(k,l)(1)

A{αβ} (i, j; k, l)ykl , B{αβ} (i, j; k, l)ukl , I{αβ} show feedback
value, input value, bias value, respectively. The output function
is shown as follows.

Bα (i, j; k, l)ukl
yij = f (xij ).

c(k,l)- 81 -(3)(a)Fig. 2.

Computer Simulation Result.

wheref (x) = 0.5(|x + 1| − |x − 1|).

(4)

The boundary is set as fixed boundary condition. The value
is set as 1.

(b)

(c)

Fig. 3. Computer Simulation Result (square.) (a) Original image, (b) Caseof left upper cell is cell α, (c) Case of left upper cell is cell β.

III. I MAGE PROCESSING BY CNN USING TWO CLONINGTEMPLATES

A. Proposed Cloning Templates
Proposed cloning template is shown as follows.

2 1 22 0 2
Aα = 0 2 0 , Aβ = 1 2 1
2 1 22 0 2
0 1 0−1 −1 −1
B α = 1 0 1 , B β = −1 2 −1 ,0 1 0−1 −1 −1Iα = 2,(5)Iβ = −2.

This cloning template is based upon hole filling and noise deOne of the computer simulation result is shown Fig. 2. Figure 2(a) shows the original image. Figure 2 (b) shows the result.
Dark area becomes black and bright area becomes white. Gray
area becomes checkered pattern. It means that intermediatearea of brightness can be extract in one processing. This
template can adjust the intermediate area by changing I,
However, details of the original image is disappeared. In orderto reveal the characteristics of CNN using two kinds of cloning
templates, computer simulations are carried out about someimages.
B. the case that image width is even number
In this system, the result is influenced by height or widthof an image. For instance, when image width is even number,
left upper cell and right upper cell become different cell types(Cell α and Cell β.) On the other hand, when image widthis odd number, left upper cell and right upper cell become
same types (Cell α or Cell β.) In this subsection, the case thatimage width is even number is shown.
Figure 3 shows a computer simulation result. Figure 3 (a)shows a original image which is drawn square, (b) showsin case that left upper cell is cell α, (c) shows in case thatleft upper cell is cell β. Namely, a difference of two cases
is positions of cell alpha and cell beta. In all simulation
results, (a), (b) and (c) show same meaning, respectively. In
Figure 3 (b), black dots are observed in a left upper cell anda right lower cell. Excepting two dots, this result is same as
the original image. In Figure 3 (c), black dots are observed ina right upper cell and a left lower cell. Additionally, cornerdots of the square become white.
In the case of Fig 4, black dots appear two corners of theimage. A edge of the circle changes a little.
In the case of Fig 5, black dots appear corners of theimage. Additionally, a edge of the hypotenuse of a right
triangle is expand in the case of Fig. 5 (b). The reason is theboundary condition which is set as black. On right top andleft bottom side, some pixels are surrounded by black pixels.
Therefore, these pixels become black. Then these changes
propagate to center along the edge of the hypotenuse. Finally,
the hypotenuse is expand.
In the case of Fig 6, lower, middle and upper area become
black, checkered and white, respectively. The result shows thatthe image is divided into three areas by brightness. White area
is surrounded by black dots because boundary condition isblack. Figure 6 (b) is same as inverted Fig. 6 (c) horizontally.
The difference is that checkered dots are inverted.
C. the case that image width is odd number
In this subsection, image size is set as 33 × 33. Namely,
two corner of top of images is set as Cell α and Cell α or
Cell β and Cell β.
Figure 7 shows a computer simulation result in the case ofa square. Figure 7 (a) shows a original image. Figure 7 (b)and (c) show in case that four corners are set as cell α or cellβ, respectively. In Figure 7 (b), four dots observed on fourcorners and the square is not change. In Figure 7 (c), four- 82 -

(a)

(b)

(a)

(c)

(b)

(c)

Fig. 4. Computer Simulation Result (circle.) (a) Original image, (b) Case ofleft upper cell is cell α, (c) Case of left upper cell is cell β.

Fig. 6. Computer Simulation Result (gradation.) (a) Original image, (b) Caseof left upper cell is cell α, (c) Case of left upper cell is cell β

(a)

(a)

(b)

(b)

(c)

(c)

Fig. 5. Computer Simulation Result (triangle.) (a) Original image, (b) Caseof left upper cell is cell α, (c) Case of left upper cell is cell β.

Fig. 7. Computer Simulation Result. (a) Original image, (b) Case of fourcorners are cell α, (c) Case of four corners are cell β

dots did not observe on four corners and corners of the squareis lacked.
Figure 8 shows a computer simulation result in the case ofa circle. Figure 8 (a) shows a original image. Figure 8 (b)and (c) show in case that four corners are set as cell α orcell β, respectively. In Figure 8 (b), four dots observed onfour corners appear and the circle is changed some pixels onedges. In Figure 8 (c), there is no changes.
Figure 9 shows a computer simulation result in the case ofa triangle. Figure 9 (a) shows a original image. Figure 9 (b)and (c) show in case that four corners are set as cell α or cellβ, respectively. In Figure 9 (b), three dots observed on corners
appear and the triangle is no changes. In Figure 9 (c), a edgeof the hypotenuse is expand and right top and left bottom areas

become black.
Figure 9 shows a computer simulation result in the case ofa gradation. Figure 9 (a) shows a original image. Figure 9 (b)and (c) show in case that four corners are set as cell α or cellβ, respectively. Figure 10 (b) and (c) are symmetric in thecenter line.
D. Consideration
In the case of even numbers, images become asymmetry.
It is not suitable for image processing. In the case of odd
numbers, two results are obtained by depending on cell arrangement. The boundary condition is set as black. Therefore,
dots of corners appeared. It is not important. However, anobject which have a slant changes by depending on cell- 83 -(a)

(a)

(b)

(b)

(c)

Fig. 8. Computer Simulation Result. (a) Original image, (b) Case of fourcorners are cell α, (c) Case of four corners are cell β(c)Fig. 10. Computer Simulation Result. (a) Original image, (b) Case of fourcorners are cell α, (c) Case of four corners are cell β

R EFERENCES

(a)

(b)

(c)

Fig. 9. Computer Simulation Result. (a) Original image, (b) Case of fourcorners are cell α, (c) Case of four corners are cell β[1] L. O. Chua and L. Yang, “Cellular Neural Networks: Theory,” IEEE
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[6] J. Fujii, Y. Hosokawa and Y. Nishio, “Wave Phenomena in Cellular NeuralNetworks Using Two Kinds of Template Sets,” Proc. of NOLTA’07,
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[7] M. Oda, Z. Yang, Y. Nishio and A. Ushida,k “Analysis of TwoDimensional Conductive Plates Based on CNNs,” Proc. of NCSP’05,pp. 447–450, 2005.
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arrangement. By paying attention to this point, we can obtainthe image divided into three areas by brightness.
IV. C ONCLUSIONSIn this study, new cloning template of CNN using two kindsof cloning templates has been proposed. By some computer
simulation results, following characteristics are shown. This
template is suitable for images which have odd number widthand height. In CNN using two kinds of cloning templates, cellarrangement is influence to the result of image processing.
This template can be obtained the image divided into threeareas by brightness.

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