Cellular Neural Networks with Eﬀect from Friend
Having Most Diﬀerent Values and Its Friends
Yoshihiro Kato, Yoko Uwate and Yoshifumi Nishio
Department of Electrical and Electronic Engineering, Tokushima University,
2-1 Minami Josanjima, Tokushima 770-8506, Japan
Email: {kkato, uwate, nishio}@ee.tokushima-u.ac.jp

Abstract— Generally, in the conventional CNN, each cell isconnected to only its neighboring cells according to a template.
In this case, the information that a cell can obtain from its
neighboring cells is limited. In actual association, we possible
to gain diﬀerent perspectives and grow up by involving diﬀerent
types of friends. Therefore, in this study, we focus on the conceptof human relationship in the real world. Then, we propose
cellular neural networks with eﬀect from friend having mostdiﬀerent values and its friends. The proposed method is the
new approach in consideration of the phenomena in such actual
society.

I. Introduction
In recent years, our life teems with information by growth ofhigh information society. Generally, sequential digital circuits
are used for many information processing. However, sequential
digital circuits cannot perform real time processing. Therefore,
the neural networks were devised based on the human’s nervous system. The neural networks can design of analog circuit.
Additionally, the neural networks can perform expression of
nonlinear operating characteristics. Hence, the neural networks
can express complicated processing easily. In fact, neuralnetworks are used in every direction, such as an associative
memory, pattern recognition, image processing, and so on.
Then in 1988, Cellular Neural Networks (CNN) [1] wereintroduced by L. O. Chua and L. Yang. The idea of the CNN
was inspired from the architecture of the cellular automata andthe neural networks. A diﬀerent point from the conventional
neural networks is that CNN has local connectivity property.
The local connectivity property makes the CNN tailor made for
VLSI implementation. Therefore, the CNN has the features oftime continuity, spatial discreteness, nonlinearity and parallel
processing capability. Furthermore, the structure of CNN resembles that of animals’ retina. Therefore, CNN can be usedfor various image processing applications [2]-[4]. In CNN,
each cell is connected to its neighboring cells according to atemplate. Then, each cell is influenced by neighboring cells
and its value is updated.
Generally in the conventional CNN, each cell is connected
to only its neighboring cells according to a template. In
this case, the information that a cell can obtain from its
neighboring cells is limited. Then, in order to increase theinformation that a cell can obtain from its neighboring cells,
there is also an approach of extending size of template.
However, this approach has the potential to collapse the local
connectivity property of CNN. Additionally, there is not so

978-1-4577-1729-1/12/$26.00 ©2012 IEEE.

much template of large than the size of 3×3 matrix. In previous
times, method of changing connection of among cells without
extending size of template has been proposed. Especially, amethod of introduced the concept of small-world network isinteresting [5]. Therefore, we focus on the concept of humanrelationship in the real world. In the previous study, we haveadapted the concept of eﬀect from best friend and its friends
to network of CNN and proposed new method. As the proverb“Evil communications corrupt good manners” says, we receive
a great amount of influence from connected friends. In the caseof that we make friends of foreign country, we possible to learn
foreign country’s values and foreign language. Furthermore
in the case of that we make friends of the opposite sex, we
possible to re-evaluate one’s own greatness from viewpoint of
opposite sex. In this way, we grow up by involving diﬀerent
types of friends.
In this study, we adapt the concept of eﬀect from friend
with most diﬀerent value and its friends to network of CNN.
Then, we propose the new method in consideration of thephenomena in such actual society, and investigate the eﬀect
in image processing. In the proposed method, connections ofamong cells are decided by the value of each cell. In each cell,a cell with the most diﬀerent value of center cell is defined as“Diﬀerent cell” in eight neighboring cells. Hence, the valueof each cell is updated receive influences from the diﬀerent
cell and its neighboring cells. Then, we show some simulation
results and confirm its eﬀectiveness.
The list of this paper is structured as follows. In Sec. 2, we
review the conventional of the standard CNN. In Sec. 3, we
propose the new method of CNN. In Sec. 4, some simulation
results of the proposed method are shown. The section 5
concludes the article.
II. Cellular Neural Networks
In this section, we explain the conventional structure of
the CNN. The CNN has M by N processing unit circuits
called cells. The cell contains linear and nonlinear circuit
elements which are typically linear capacitors, linear resistors,
linear and nonlinear controlled sources. Cells are arranged
in a reticular pattern to M line N row. We represent a cellC(i, j) using a variable i which denotes vertical position anda variable j which denotes horizontal position. The CNN isan array of cells. Each cell is connected to its neighboring
cells according to a template. Usually, the template is the495same for all cells except for boundary cells. The CNN has thefeatures of time continuity, spatial discreteness, nonlinearityand parallel processing capability. The state equation and theoutput equation of the CNN are shown as follows.
State equation :dv xi jdt

= −v xi j +

j+r
i+r 


A(i, j;k,l) vykl (t)(a)

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 :1(|v xi j (t) + 1| − |v xi j (t) − 1|),(2)
2where v x , vy and vu represent a state, an output and an inputof cell, respectively. In the Eq. (1), A is the feedback templateand B is the control template. These and the constant bias I
are collectively called general template. The output equation
is a piece-wise linear function. In fact, the output value of
CNN is within of −1 to 1. When the CNN is used for image
processing, values of black and white are treated as 1 and −1,
respectively.
The r − neighborhood of C(i, j) in CNN is defined byvyi j (t) =Nr(i, j) = {C(k, l) | max{ |k − i|, |l − j| } ≤ r,
1 ≤ k ≤ M; 1 ≤ l ≤ N},(3)

where r is a positive integer number. Each cell has (2r + 1)2
neighborhood cells. Hence, the size of template is defined byr. If r is 1, the size of template is 3×3 matrix. Additionally,
if r is 2, the size of template is 5×5 matrix.
III. Cellular Neural Networks with Effect from Friend
Having Most Different Values and Its Friends
In this section, we explain the algorithm of the cellularneural networks with eﬀect from friend having most diﬀerent
values and its friends (DF-CNN). The DF-CNN is the methodof constituting new combinations of among cells. In this paper,
we consider the local connection of CNN as friendship. Then,in each cell, the neighboring cells are defined as friend cells.
Based on this, the algorithm of DF-CNN is described asfollows.

(b)
Fig. 2. New combination of feedback template. (a) The combination oncentering on the diﬀerent cell. (b) Elements of new feedback template.

Step 2: The combination centering on a cell C(i, j) ischanged into a combination centering on the diﬀerent cell likeFig. 2(a).
Moreover, the element of the feedback template of thediﬀerent friend and the center cell are replaced. With this,a new combination is constituted like Fig. 2(b).
Step 3: The value of each cell is updated according to
the Eqs. (1) and (2) using the new combinations of feedback
templates.
Step 4: Steps 1 to 4 are repeated every 0.0005 [τ].
B. In The Case of Control Template

A. In The Case of Feedback Template
Fig. 3.

Fig. 1.

Search the diﬀerent cell in output image.

Step 1: In each cell of output image, a cell with themost diﬀerent of the value of center cell C(i, j) is definedas “Diﬀerent cell” from eight neighboring cells like Fig. 1.

Search the diﬀerent cell in input image.

Step 1: In each cell of input image, a cell with the mostdiﬀerent of the value of center cell C(i, j) in output image
is defined as “Diﬀerent cell” from eight neighboring cells in
input image like Fig. 3.
Step 2: The combination centering on a cell C(i, j) ischanged into a combination centering on the diﬀerent cell likeFig. 4(a).
Moreover, the element of the control template of the diﬀerent friend and the center cell are replaced. With this, a new496

Edge detection template of 5×5 matrix :⎡⎤⎢⎢⎢ 0 0 0 0 0 ⎥⎥⎥⎢⎢⎢ 0 0 0 0 0 ⎥⎥⎥⎢⎢⎥⎥A = ⎢⎢⎢⎢⎢ 0 0 1 0 0 ⎥⎥⎥⎥⎥ ,⎢⎢⎢ 0 0 0 0 0 ⎥⎥⎥⎢⎣⎥⎦0 0 0 0 0⎡⎢⎢⎢ −1 −3 −4 −3⎢⎢⎢ −3 0
60⎢⎢
B = ⎢⎢⎢⎢⎢ −4 6 20 6⎢⎢⎢ −3 0
60⎢⎣−1 −3 −4 −3
I = −1.

(a)

⎤
−1 ⎥⎥
⎥
−3 ⎥⎥⎥⎥⎥−4 ⎥⎥⎥⎥ ,⎥−3 ⎥⎥⎥⎥⎦
−1
(5)

(b)
Fig. 4.
New combination of control template. (a) The combination oncentering on the diﬀerent cell. (b) Elements of new control template.

combination is constituted like Fig. 4(b).
Step 3: The value of each cell is updated according to
the Eqs. (1) and (2) using the new combinations of control
templates.
Step 4: Steps 1 to 4 are repeated every 0.0005 [τ].

(a)

(b)

(c)

(d)

Therefore, the value of each cell is updated by receiving
influences from the diﬀerent cell and its neighboring cells.
IV. Simulation Results
In this section, we show some simulation results for edge
detection and divide domains by using the DF-CNN. In
this study, boundary condition is fixed with mirror reflector
condition.
A. Edge Detection
In this subsection, we show some simulation results ofedge detection by using the DF-CNN. In edge detection,
the edge of the indistinct portion is not detected by using“Edge detection” template of 3×3 matrix. On the other hand,by using “Edge detection” template of 5×5 matrix, we candetect the edge of the indistinct portion. However, by using“Edge detection” template of 5×5 matrix, the detected edge
becomes bold line and some noises are left. In the DF-CNN,
we use only ”Edge detection” template of 3×3 matrix [6].
”Edge detection” templates of 3×3 matrix and 5×5 matrix
are described as follows.
Edge detection template of 3×3 matrix :
⎡
⎢⎢⎢ 0
⎢
A = ⎢⎢⎢⎢ 0
⎣
0

0
1
0

⎤
⎡
⎢⎢⎢ −1 −1
0 ⎥⎥⎥⎥⎢0 ⎥⎥⎥⎥ , B = ⎢⎢⎢⎢ −1 8
⎦
⎣
−1 −1
0

⎤
−1 ⎥⎥⎥⎥−1 ⎥⎥⎥⎥ , I = −1.
⎦
−1

(4)

Fig. 5. Edge detection result 1. (a) Input and initial state images (woman).
(b) Edge detection result using the conventional CNN with the 3×3 matrix
template. (c) Edge detection result using the conventional CNN with the 5×5
matrix template. (d) Edge detection result using the DF-CNN.

Figure 5 shows the edge detection results. The almostedge is not detected using the conventional CNN with the“Edge detection” template of 3×3 matrix in Fig. 5(b). On
the other hand, the detected edge becomes bold line andmany noises are left using the conventional CNN with the“Edge detection” template of 5×5 matrix in Fig. 5(c). In
Fig. 5(d), by using the proposed method, the edge can bedetected more clearly and the detected edge is more fine line
than using the conventional CNN.
Figure 6 shows the edge detection results for another
input image. Fig. 6(a) contains some indistinct portion. The
indistinct portion is not detected using the conventional CNN
with the “Edge detection” template of 3×3 matrix in Fig. 6(b).

497

(a)

(b)

(a)

(b)

Fig. 7. Divides sparse domain from thick domain result by the DF-CNN.
(a) Input and initial state images (image size is 128×128 pixels). (b) Divide
domains result by the DF-CNN using the “Divide domains” template.

half in the input image remains as a black domain. At thesame time, the sparse domain of the right half in the input
image remains as a white domain. Thereby, we can see thatthe thick domain and the sparse domain can be divided with
the DF-CNN.
(c)

(d)

V. Conclusion

Fig. 6. Edge detection result 2. (a) Input and initial state images (pepper).
(b) Edge detection result using the conventional CNN with the 3×3 matrix
template. (c) Edge detection result using the conventional CNN with the 5×5
matrix template. (d) Edge detection result using the DF-CNN.

On the other hand, the detected edge becomes bold line andmany noises are left using the conventional CNN with the“Edge detection” template of 5×5 matrix in Fig. 6(c). Similar
to the above results, by using proposed method, the edge canbe detected more clearly and the detected edge is more fineline than using the conventional CNN in Fig. 6(d). Also, incomparison to Fig. 6(c), some noises are removed by using
the proposed method.
From these results, we can confirm that the proposed
method is more eﬀective than the conventional CNN for theedge detection. Also, the proposed method does not depend on
the image. This method has broad utility, because this systemneeds only the value of cell.
B. Divide Domains
In this subsection, we show other application using theDF-CNN. To divide sparse domain from thick domain,
we create and use “Divide domains” template based on“S mall ob ject remover” template [6]. The “Divide domains”
template is shown as follows.
Divide domains template :⎡⎤⎡⎤⎢⎢⎢ 1 1 1 ⎥⎥⎥⎢⎢⎢ 0 0 0 ⎥⎥⎥
⎢⎢⎢
⎥⎥⎥
⎢⎢⎢
⎥
A = ⎢⎢ 1 2 1 ⎥⎥ , B = ⎢⎢ 0 0 0 ⎥⎥⎥⎥ , I = −1.
(6)
⎣
⎦
⎣
⎦
1 1 1
0 0 0
Figure 7(b) shows the output image by the DF-CNN using
the “Divide domains” template. The thick domain of the left

In this study, we have proposed cellular neural networks
with eﬀect from friend having most diﬀerent values and its
friends. The DF-CNN is the new method in considerationof the phenomena in such actual society which likes “Evilcommunications corrupt good manners”. From some simulation results, we have confirmed that our proposed method
is eﬀective for edge detection and dividing sparse domainfrom thick domain in image. Especially, edge detection results
have improved by using simple system and existing templateof 3×3 matrix without extending size of template. Also our
proposed method is excellent about general versatility, because
this system needs only the value of cell. In the future works,
we would like to adapt the proposed system to multilayer
CNN.
Acknowledgment
This work was partly supported by JSPS Grant-in-Aid forYoung Scientists 23700269.
References[1] L. O. Chua and L. Yang, “Cellular Neural Networks: Theory,” IEEE
Trans. Circuits Syst., vol. 32, pp. 1257-1272, Oct. 1988.
[2] M. Namba and Z. Zhang, “Cellular Neural Network for Associative Memory and Its Application to Braille Image Recognition,” Proc. of IJCNN’06,
pp. 4716-4721, Jul. 2006.
[3] H. Koeppl and L. O. Chua, “An Adaptive Cellular Nonlinear Network and its Application,” Proc. of NOLTA’07, pp. 15-18, Sep. 2007.
[4] 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.
[5] K. Tsuruta, Z. Yang, Y. Nishio and A. Ushida, “Small-world cellular neural networks for image processing applications,” Proc. of ECCTD’03,
vol. 1, pp. 225-228, Sep. 2003.
[6] 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”.

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