Proceedings of International Joint Conference on Neural Networks, San Jose, California, USA, July 31 – August 5, 2011

Cellular Neural Networks
with Switching Two Types of Templates
Yoshihiro Kato, Yasuhiro Ueda, Yoko Uwate and Yoshifumi Nishio

Abstract— In this study, we propose Cellular Neural Networks with switching two types of templates. In the CNN,
space varying system is known that it can perform complex
processing. Generally, the space varying CNN is not easy todesign. However, we can set existing template on each cellof CNN by the proposed method. In binarization, complex
portions of input image are not processed well by using theconventional CNN. On the other hand, the complex portion canbe processed well by the proposed method. In the edge detection,
the indistinct portion is not detected by the conventional CNN
with “𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛” template of 3×3 matrix. It is difﬁcult
for CNN to recognize that it is the edge or not. Additionally,
the detected edge is too bold and some noises are left with
“𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛” template of 5×5 matrix. By switching thesetemplates in case, we can detect edge in indistinct position. In
pattern formation, generally, simple pattern is formed by using
one template. On the other hand, some complex patterns areformed by the proposed method. From some simulation results,
we conﬁrm that the proposed method is effective for various
image processing.

I. I NTRODUCTIONI

N 1988, Cellular Neural Networks (CNN) [1] were introduced by L. O. Chua and L. Yang. The idea of the CNN
was inspired from the architecture of the cellular automaton
and the neural networks. A different point from the conventional neural networks is that CNN has local connectivity
property. Since, the structure of CNN resembles that of animals’ retina. Therefore, CNN can be used for various image
processing applications [2]-[5] including pattern formation[6]. CNN is composed of the basic analog circuit units called
cells. The cell contains linear and nonlinear circuit elements
which are typically linear capacitors, linear resistors, linear
and nonlinear controlled sources. The performance of CNN
depends on the parameters called the template. The templateof CNN consists three elements as the feedback template 𝐴,
the control template 𝐵, and the constant bias 𝐼.
Generally, the conventional CNN depends on an input
image because of space invariant template. In the binarization, the complex portions of input image are not processed
well. Also, the processed image is rough by using only
“𝑆𝑚𝑜𝑜𝑡ℎ𝑖𝑛𝑔” template. In edge detection, the edge of theindistinct 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 can detect
the edge of the indistinct portion. However, the detectedYoshihiro Kato, Yasuhiro Ueda, Yoko Uwate and Yoshifumi Nishio arewith the Department of Electrical and Electronic Engineering, Tokushima
University, 2-1 Minami-Josanjima, Tokushima 770-8506, Japan (Phone:+81 88 656 7470; email: {kkato, yasuhiro, uwate, nishio}@ee.tokushimau.ac.jp).

978-1-4244-9636-5/11/$26.00 ©2011 IEEEedge becomes bold line and some noises are left. In patternformation, formed pattern is simple pattern by using one
template, like ripple and checkerboard pattern. Therefore, wenote space varying CNN which can perform processing more
complex than the conventional CNN. However, space varying
CNN is not easy to design.
In this study, we propose CNN with switching two typesof templates. Applied templates are decided by the input,
the output value, and the boundary parameters which are 𝐷1
and 𝐷2 . In the proposed method, we decide 𝐷1 and 𝐷2
as step 1. Then, the template is determined corresponding
to the input value of each cell, 𝐷1 and 𝐷2 . As step 2, theCNN processes the input image by the applied template. As
step 3, the steps 1 and 2 are carried out by using the output
value. As step 4, steps 2 and 3 are repeated. The switchingis performed according to time and the value of cell. The
proposed method is space and time varying. We show somesimulation results and conﬁrm its effectiveness.
The rest of this paper is structured as follows. In Sec. 2,
we review the basic of the standard CNN. In Sec. 3, weshow the algorithm of the CNN with switching two types oftemplates. In Sec. 4, some simulation results of the proposed
method are shown. The section 5 concludes the article.

II. C ELLULAR N EURAL N ETWORKSIn this section, we explain the basic 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 andnonlinear controlled sources. Cells are arranged in a reticularpattern 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. The CNN is an arrayof cells. Each cell is connected to its neighboring cells
according to a template. Usually, the template is the samefor all cells except for boundary cells. The CNN has thefeatures of time continuity, spatial discreteness, nonlinearityand parallel processing capability.
State equation :
𝑑𝑣𝑥𝑖𝑗
𝑑𝑡

=

−𝑣𝑥𝑖𝑗 +

𝑖+𝑟
∑

𝑗+𝑟
∑

𝐴(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦𝑘𝑙 (𝑡)𝑘=𝑖−𝑟 𝑙=𝑗−𝑟

+

𝑖+𝑟
∑

𝑗+𝑟
∑

𝐵(𝑖,𝑗;𝑘,𝑙) 𝑣𝑢𝑘𝑙 (𝑡) + 𝐼,(1)

𝑘=𝑖−𝑟 𝑙=𝑗−𝑟

1423

Output equation :𝑣𝑦𝑖𝑗 (𝑡) =State equation with the “Template 1” :1(∣𝑣𝑥𝑖𝑗 (𝑡) + 1∣ − ∣𝑣𝑥𝑖𝑗 (𝑡) − 1∣),2

(2)where 𝑣𝑥 , 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.
The 𝑟 − 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟ℎ𝑜𝑜𝑑 of 𝐶(𝑖, 𝑗) in CNN is deﬁned by

𝑑𝑣𝑥𝑖𝑗
𝑑𝑡

=

−𝑣𝑥𝑖𝑗 +

III. CNN WITH S WITCHING T EMPLATE
In this section, we explain the algorithm of the proposed
method. The proposed method is that two types of templates
are switched corresponding to the input and the output
values. The algorithm is shown as follows.
Step 1: We decide the boundary parameters which are
𝐷1 and 𝐷2 (𝐷1 <𝐷2 ). By these values, applied templates
are decided.
In the switching rule, the template is determined corresponding to the value of cell. If 𝑣𝑢 is under 𝐷1 or over 𝐷2 ,the “Template 1” is applied to the cell. While, if input value
𝑣𝑢 is over 𝐷1 and under 𝐷2 , the “Template 2” is applied
like Fig. 1.

𝑗+𝑟∑1

𝐴1 (𝑖, 𝑗; 𝑘, 𝑙)𝑣𝑥𝑘𝑙 (𝑡)𝑘=𝑖−𝑟1 𝑙=𝑗−𝑟1

+

𝑖+𝑟
∑1

𝑗+𝑟
∑1

𝐵1 (𝑖, 𝑗; 𝑘, 𝑙)𝑣𝑢𝑘𝑙 (𝑡) + 𝐼1

𝑘=𝑖−𝑟1 𝑙=𝑗−𝑟1(∣𝑖 − 𝑘∣ ≤ 𝑟1 , ∣𝑗 − 𝑙∣ ≤ 𝑟1 ).

(4)

State equation with the “Template 2” :
𝑑𝑣𝑥𝑖𝑗
𝑑𝑡

=

−𝑣𝑥𝑖𝑗 +

𝑖+𝑟
∑2

𝑗+𝑟
∑2

𝐴2 (𝑖, 𝑗; 𝑘, 𝑙)𝑣𝑥𝑘𝑙 (𝑡)𝑘=𝑖−𝑟2 𝑙=𝑗−𝑟2

𝑁 𝑟(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.

𝑖+𝑟
∑1

+

𝑖+𝑟
∑2

𝑗+𝑟
∑2

𝐵2 (𝑖, 𝑗; 𝑘, 𝑙)𝑣𝑢𝑘𝑙 (𝑡) + 𝐼2

𝑘=𝑖−𝑟2 𝑙=𝑗−𝑟2(∣𝑖 − 𝑘∣ ≤ 𝑟2 , ∣𝑗 − 𝑙∣ ≤ 𝑟2 ).

(5)

Output equation :1(∣𝑣𝑥𝑖𝑗 (𝑡) + 1∣ − ∣𝑣𝑥𝑖𝑗 (𝑡) − 1∣).
(6)
2
Step 3: After 0.005 [𝜏 ], the Steps 1 and 2 are carried out
by the output value 𝑣𝑦 . If 𝑣𝑦 is under 𝐷1 or over 𝐷2 , the“Template 1” is applied to the cell. While, if 𝑣𝑦 is over 𝐷1
and under 𝐷2 , the “Template 2” is applied.
Then, the proposed CNN switches the “Template 1” and“Template 2” according to the output value of the cell at
every 0.005 [𝜏 ].
Step 4: Steps 2 and 3 are repeated every 0.005 [𝜏 ].
𝑣𝑦𝑖𝑗 (𝑡) =Therefore, input image is processed by the two types oftemplates which are determined by the input, the output andthe boundary parameters.
IV. S IMULATION R ESULTS
In this section, we show some simulation results forbinarization, edge detection and pattern formation by using
the proposed method. The used templates are found in [7]and [8].
A. Binarization
In this subsection, we show some simulation results ofbinarization by using the proposed method. For this simulation, we use some general images including complex portion.
To emphasize complex portion, we use “𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛”
template of 3 × 3 matrix. “Template 1” and “Template 2”
are set to “𝑆𝑚𝑜𝑜𝑡ℎ𝑖𝑛𝑔” template and “𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛”
template of 3 × 3 matrix, respectively. These templates aresame size and carry out different processing. Also, 𝑟1 and 𝑟2
are set to 1. Templates for binarization are shown as follows.

Fig. 1.

Switching rule.

Step 2: The value of each cell is updated by the state
equation and the output equation as follows.

Smoothing template :This template can binarize of image.
⎡
⎡
⎤
0 0
0 1 0
𝐴 = ⎣ 1 2 1 ⎦, 𝐵 = ⎣ 0 0
0 0
0 1 0

⎤
0
0 ⎦ , 𝐼 = 0.
0

(7)

1424

(a)

(b)

(a)

(b)

(c)

(d)

(c)

(d)

Fig. 2. Simulation results 1. (a) Input image (Cameraman). (b) Binarization
result by the digital processing. (c) Binarization result using the conventional CNN. (d) Binarization result using the proposed method. (𝐷1 =−0.2,
𝐷2 =0.2).

Edge detection template of 3×3 matrix :This template can detect the edge of objects.
⎡
⎤
⎡
⎤
0 0 0
−1 −1 −1𝐴 = ⎣ 0 1 0 ⎦ , 𝐵 = ⎣ −1 8 −1 ⎦ , 𝐼 = −1.
0 0 0−1 −1 −1
(8)
In this simulation, output images were compared with theimages which are binarized by digital processing. The binarization method of digital processing are shown as follows.
If the value of each pixel is over zero, the pixel turn to black.
On the other hand, if the value of each pixel is under zero,
the pixel turn to white.
Figure 2 shows the simulation results using the proposed
method. In Fig. 2 (a), this input image including complex
portions such a camera and the pillars of buildings in the
background. 𝐷1 and 𝐷2 are set to −0.2 and 0.2. Figure. 2 (b)compares with binarized output image by the digital processing. In Fig. 2 (c), the complex portions are not processed wellby the conventional CNN. In Fig. 2 (d), binarization of thecomplex portion can be processed well by using the proposed
method.
Figure 3 shows the simulation results for another input
image. In Fig. 3 (a), this input image including complex
portions such a some texts and lower of image. 𝐷1 and 𝐷2

Fig. 3. Simulation results 2. (a) Input image (Text). (b) Binarization result
using the digital processing. (c) Binarization result using the conventional
CNN. (d) Binarization result using the proposed method. (𝐷1 =−0.1,
𝐷2 =0.2).

are set to −0.1 and 0.2. Figure 3 (b) compares with binarized
output image by the digital processing. In Fig. 3 (c), binarization of complicated portions cannot be processed wellby the conventional CNN. On the other hand, in Fig. 3 (d),binarization of the complex portions which like cracks onboard and uneven paints can be processed well by using the
proposed method.
From these results, we consider that the proposed method
is more effective than the conventional CNN for binarization.
B. Edge detection
In this subsection, we show some simulation results ofedge detection using the proposed method. For this simulation, we use some general images including indistinct
portion. In these images, the value of the center cell is close
to that values of neighborhoods in many cases. There areincluded indistinct portion especially. Hence, the edge of theindistinct portion is not detected by using “𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛”
template of 3×3 matrix. To feed off information on the twoneighborhood value of cell, we extend the “𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛”
template like Eq. (9). In fact, “Template 1” and “Template 2”
are set to “𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛” template of 3 × 3 matrix and“𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛” template of 5 × 5 matrix, respectively.
These templates are different size and carry out similar
processing. Also, 𝑟1 and 𝑟2 are set to 1 and 2, respectively.

1425

(a)

(b)

(a)

(b)

(c)

(d)

(c)

(d)

(e)

(e)

Fig. 4. Simulation results 3. (a) Input image (Lenna). (b) Edge detection
result using the 3×3 matrix template. (c) Edge detection result using the
5×5 matrix template. (d) Edge detection result using the proposed method.
(𝐷1 =−0.2, 𝐷2 =0.2). (e) Distribution of 3×3 and 5×5 matrix template.

Fig. 5. Simulation results 4. (a) Input image (Pepper). (b) Edge detection
result using the 3×3 matrix template. (c) Edge detection result using the
5×5 matrix template. (d) Edge detection result using the proposed method.
(𝐷1 =0.3, 𝐷2 =0.6). (e) Distribution of 3×3 matrix template and 5×5 matrix
template.

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 −1 −1 −1⎢ −1 0
0
0
⎢
16
0
𝐵 = ⎢
⎢ −1 0⎣ −1 000−1 −1 −1 −1
𝐼 = −1.

method. In Fig. 4 (a), 𝐷1 and 𝐷2 are set to −0.2 and 0.2.
In Fig. 4 (a), the pillar on the left side in the backgroundis an indistinct portion. In Fig. 4 (b), this indistinct portion is not detected using the conventional CNN with the“𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛” template of 3×3 matrix. In Fig. 4 (c),although the edge of the indistinct portion is detected using
the conventional CNN with the “𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛” templateof 5×5 matrix, the detected edge becomes bold line and somenoises are left. In Fig. 4 (d), using the proposed method,the edge of the indistinct portion can be detected moreclearly and the detected edge is more ﬁne line than using
the conventional CNN. In Fig. 4 (e), black points show thecell using the “𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛” template of 3×3 matrix
and white points show the cell using the “𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛”
template of 5×5 matrix. From Fig. 4 (e), we can refer

⎤
−1
−1 ⎥
⎥
−1 ⎥
⎥,
−1 ⎦
−1
(9)

Figure 4 shows the simulation results using the proposed1426

that distinct parts are processed by the “𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛”
template of 3×3 matrix and indistinct parts are processed by
the “𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛” template of 5×5 matrix. In fact, thepart of edge which is difﬁcult to detect is processed by the“𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛” template of 5×5 matrix.
Figure 5 shows the simulation results for another input
image. In Fig. 5 (a), 𝐷1 and 𝐷2 are set to 0.3 and 0.6. The
almost edge is not detected using the conventional CNN withthe “𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛” template of 3×3 matrix in Fig. 5 (b).
On the other hand, the detected edge becomes bold line andsome 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 edgeof indistinct potion can be detected more clearly and thedetected edge is more ﬁne line than the conventional CNN.
Also, compare to Fig. 5 (c), some noises are removed byusing the proposed method. Also, the part of edge which
is difﬁcult to detect is processed by the “𝐸𝑑𝑔𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛”
template of 5×5 matrix.
From these results, we consider that the proposed method
is also more effective than the conventional CNN for theedge detection.
C. Pattern formation
In this subsection, we show some simulation results ofpattern formation by using the proposed method. To extend
pattern area, we use “𝐵𝑙𝑎𝑐𝑘 𝑝𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑖𝑜𝑛” template. “Template 1” and “Template 2” are set to “𝐵𝑙𝑎𝑐𝑘 𝑝𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑖𝑜𝑛”
template and “𝑅𝑖𝑝𝑝𝑙𝑒” template or “𝐶ℎ𝑒𝑐𝑘𝑒𝑟𝑏𝑜𝑎𝑟𝑑” template [8], respectively. These templates are different size andcarry out different processing. Also, 𝑟1 and 𝑟2 are set to 1
and 2. Templates for pattern formation are shown as follows.
Black propagation template :This template can increase black areas.
⎡⎤
0.25 0.25 0.25
3
0.25 ⎦ ,𝐴 = ⎣ 0.25
0.25 0.25 0.25
⎤
⎡
0 0 0
𝐵 = ⎣ 0 0 0 ⎦,0 0 0
𝐼 = 3.75.
(10)
Ripple template :This template forms a simple ripple pattern.
⎡

𝐴

=

𝐵

=

𝐼

=

0
⎢ −0.2⎢⎢ −0.2⎣ −0.2
0
⎡
0 0
⎢ 0 0
⎢
⎢ 0 0
⎣ 0 0
0 0
0.

−0.2
0
0.2
0
−0.2
0 0
0 0
0 0
0 0
0 0

−0.2 −0.2
0.2
0
1.5
0.2
0.2
0
−0.2 −0.2
⎤
0
0 ⎥
⎥
0 ⎥,
0 ⎦
0

⎤
0
−0.2 ⎥⎥−0.2 ⎥ ,−0.2 ⎦
0(11)

Checkerboard template :This template forms the black and white pattern with thecycle of 2 cells.
⎡

𝐴

=

𝐵

=

𝐼

=

−0.3
⎢ −1
⎢
⎢ −3
⎣ −1
−0.3
⎡
0 0
⎢ 0 0
⎢
⎢ 0 0
⎣ 0 0
0 0
0.

−1 −3 −1
0.5 −2 0.5−2 −4 −2
0.5 −2 0.5−1 −3 −1⎤
0 0 0
0 0 0 ⎥⎥
0 0 0 ⎥,
0 0 0 ⎦
0 0 0

⎤
−0.3
−1 ⎥
⎥
−3 ⎥ ,
−1 ⎦
−0.3

(12)

Figure 6 shows the simulation results. “Template 1” and“Template 2” are set to “𝐵𝑙𝑎𝑐𝑘 𝑝𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑖𝑜𝑛” template and“𝑅𝑖𝑝𝑝𝑙𝑒” template, respectively. Figure 6 (a) is including
some objects of different sizes and shapes. In Fig. 6 (b),formed pattern is simple ripple pattern in spite of some
objects of different sizes and shapes by using “𝑅𝑖𝑝𝑝𝑙𝑒” template. However, by using the proposed method like Fig. 6 (c),it is notable that formed patterns are different by some objectsof different sizes and shapes. That is because extended areas
are different by “𝐵𝑙𝑎𝑐𝑘 𝑝𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑖𝑜𝑛” template. Moreover,formed patterns are differed by changing the boundary parameters 𝐷1 and 𝐷2 like Figs. 6 (d) and (e).
Figure 7 shows the simulation results for another combination of template. “Template 1” and “Template 2” areset to “𝐵𝑙𝑎𝑐𝑘 𝑝𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑖𝑜𝑛” template and “𝐶ℎ𝑒𝑐𝑘𝑒𝑟𝑏𝑜𝑎𝑟𝑑”
template, respectively. In Fig. 7 (a), formed pattern ischeckerboard pattern by using “𝐶ℎ𝑒𝑐𝑘𝑒𝑟𝑏𝑜𝑎𝑑” template.
However, formed pattern is simple ripple pattern in spiteof some objects of different sizes and shapes by using the
proposed method like Fig. 7 (c). Moreover, formed patterns
are differed by changing the boundary parameters 𝐷1 and𝐷2 like Figs. 7 (c) and (d). Similar to the above results,
formed pattern becomes large, and while the place where
formed pattern collided had been held as a boundary line.
From these results, formed pattern changes dependingon the each size and shape of objects, the combination of
template and the boundary parameters 𝐷1 and 𝐷2 by using
the proposed method. Also, more complex patterns are able
to be formed .
V. C ONCLUSIONSIn this study, we have proposed cellular neural networks
with switching two types of templates. The proposed method
is that two types of templates were switched corresponding
to the input and the output values. From simulation results ofbinarization, the complex portion could be processed better.
Furthermore, we could detect the edge in indistinct position.
Moreover, from simulation results of pattern formation, we
have conﬁrmed that formed pattern changes depending on theeach size and shape of objects, the combination of templates
and the boundary parameters.
From some simulation results, we consider that our proposed method is effective for various image processing. In

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(a)

(b)

(c)

(a)

(b)

(c)

(d)

Fig. 7.
Simulation results 6. (a) Pattern formation result by using
only “𝐶ℎ𝑒𝑐𝑘𝑒𝑟𝑏𝑜𝑎𝑟𝑑” template. (b) Pattern formation result byswitching “𝐵𝑙𝑎𝑐𝑘 𝑝𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑖𝑜𝑛” template and “𝐶ℎ𝑒𝑐𝑘𝑒𝑟𝑏𝑜𝑎𝑟𝑑”
template. (𝐷1 =−0.3, 𝐷2 =0.3). (c) Pattern formation result by switching“𝐵𝑙𝑎𝑐𝑘 𝑝𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑖𝑜𝑛” template and “𝐶ℎ𝑒𝑐𝑘𝑒𝑟𝑏𝑜𝑎𝑑” template.
(𝐷1 =−0.2, 𝐷2 =0.2). (d) Pattern formation result by switching“𝐵𝑙𝑎𝑐𝑘 𝑝𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑖𝑜𝑛” template and “𝐶ℎ𝑒𝑐𝑘𝑒𝑟𝑏𝑜𝑎𝑑” template.
(𝐷1 =−0.7, 𝐷2 =0.7).

(d)

(e)

Fig. 6. Simulation results 5. (a) Input image. (b) Pattern formation result
by using only “𝑅𝑖𝑝𝑝𝑙𝑒” template. (c) Pattern formation result by switching “𝐵𝑙𝑎𝑐𝑘 𝑝𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑖𝑜𝑛” template and “𝑅𝑖𝑝𝑝𝑙𝑒” template. (𝐷1 =−0.3,
𝐷2 =0.3). (d) Pattern formation result by switching “𝐵𝑙𝑎𝑐𝑘 𝑝𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑖𝑜𝑛”
template and “𝑅𝑖𝑝𝑝𝑙𝑒” template. (𝐷1 =−0.2, 𝐷2 =0.2). (e) Pattern formation result by switching “𝐵𝑙𝑎𝑐𝑘 𝑝𝑟𝑜𝑝𝑎𝑔𝑎𝑡𝑖𝑜𝑛” template and “𝑅𝑖𝑝𝑝𝑙𝑒”
template. (𝐷1 =−0.7, 𝐷2 =0.7).

the future works, we would like to propose that the system
automatically decide the best 𝐷1 and 𝐷2 for edge detection
and binarization. Also, we investigate the phenomena about
pattern formation by the proposed CNN.
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[6] K. R. Crounse and L. O. Chua, “Methods for Image Processing and Pattern Formation in Cellular Neural Networks: A Tutorial,” IEEE Trans.
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[1] L. O. Chua and L. Yang, “Cellular Neural Networks: Theory,” IEEE
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[2] F. Dirk and T. Ronald, “Coding of Binary Image Data using Cellular Neural Networks and Iterative Annealing,” Proc. of ECCTD’03,
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