Cellular Neural Networks
with Partial Delay Output for Image Processing
Fumiki Sugano, Takahisa Ando, Yoko Uwate and Yoshifumi Nishio
Department of Electrical and Electronic Engineering, Tokushima University
2-1 Minami-Josanjima, Tokushima 770–8506, Japan
E-mail: {sugano, ando, uwate, nishio}@ee.tokushima-u.ac.jp

Abstract

2. Cellular Neural Networks [1]In the previous study, some researches were reported that
the Cellular Neural Networks with Delay Output (DCNN)
was applied to the image processing. However, that method
has a problem of the noise in image processing. In this study,
we propose a CNN method of adding partial delay output foredge detection. This is a new algorithm of adding delay output (DCNN) to the conventional CNN partially. We investigate the performance of the proposed method in edge detection by some input images.

In this section, we show the structure of the CNN. The basic circuit unit of the CNN is called cell. All cells are connected only to its neighboring cells. We show array composed of M ×N cells arranged in M rows and N columes.
The array of the CNN is shown in Fig. 1.

1. Introduction
In recent years, the amount of information is increasing.
Therefore, we need to process big data. However, conventional digital computation methods have problem of processing speed. On the other hand, analog computation methods
have ability of high speed processing. Therefore, the Neural Networks was proposed. The Neural Networks was basedon human’s nervous system. The Cellular Neural Networks
Figure 1: The structure of the CNN.
(CNN) was introduced by Chua and Yang [1]. The idea ofthe CNN was inspired from the architecture of the CellularAutomata and Neural Networks. The structure of the CNN
is cells connected each other and resembles the structure of
the animal’s retina. Hence, the CNN has been used for various image processing. Performance of the CNN depends on
the parameters which called the template. The template is thestrength of the connection between the cells.
Delayed Cellular Neural Network (DCNN) has proposed
to solve some dynamic image processing and it was applied
to the image processing [2]-[4]. In that method, image processing of the DCNN contained past information and it wasFigure 2: Block diagram of the conventional CNN.
obtained good results compared to the conventional CNN
method. However, it had problem that noise effect is observedin the output image.
Figure 2 shows the block diagram of the conventional
In this study, we propose a method of the CNN with partial CNN. In image processing of the conventional CNN, twodelay output (DCNN). We investigate the performance of the templates are used. Template A is feedback template andtemplate B is control template.
proposed method in edge detection.

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The state equation and output equation are described as follows.
State equation of the conventional CNN :dvxij
dt= −vxij +i+rXj+rX

A(i,j;k,l) vykl (t)k=i−r l=j−r

+i+r
Xj+r
X

B(i,j;k,l) vukl (t) + I(1)

k=i−r l=j−r

Output equation of the conventional CNN :1(|vxij (t) + 1| − |vxij (t) − 1|)vyij (t) =2

Figure 4: Block diagram of the DCNN.
(2)
Output equation of the DCNN :vx , vy and vu are state value, output value and input value.
Figure 3 shows piece-wise linear function. This outputequation expressed with such piece-wise linear function.
Then, the output value of the CNN is within of +1 to -1.

vyij (t)=1(|vxij (t) + 1| − |vxij (t) − 1|)2(4)4. Proposed method
In this section, we show the system of the proposed
method. The algorithm of the proposed system is shown as
follows.

Step 1 : First, calculate difference values between the output value of the center cell and the output values of theneighboring cells. In Fig. 5, we show the concept of calculation and each number is represented the output valueof each cell. ( 1 - 2 , 1 - 3 , · · · , 1 - 9 ).

Figure 3: Piece-wise linear function.
3. Delayed Cellular Neural Networks [2][3]In this section, we show the structure of the DCNN. Figure 4 shows the block diagram of the DCNN. Template D is
Delayed feedback template and τ is delay time.
The state equation and output equation are described as follows.
State equation of the DCNN :dvxij
dt= −vxij +i+r
Xj+r
X

Figure 5: The concept of calculation.

A(i,j;k,l) vykl (t)k=i−r l=j−r+i+r
Xj+rX

B(i,j;k,l) vukl (t)k=i−r l=j−r+i+r
Xj+rX

k=i−r l=j−r

D(i,j;k,l) vukl (t − τ )Step 2 : Second, count number of cells which have the difference value smaller than threshold value a. Then, let N
be the number of cells satisfying the following equation
(3)
(5).

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
| 1 −



 | 1 −..
.


| 1 −

3|<a|<a9|<a2

simulation result of the proposed method (τ = 10). The proposed method can detect edge lines of indistinct parts andreceive less noise effect compared to the DCNN by applying(5) the DCNN to indistinct parts.

Step 3 : Finally, determine the method according to the following equations. x is arbitrary value.
DCN N : N ≥ x
CN N : N < x

(6)
(a)

(b)

(c)

(d)

5. Simulation results
In this section, we show simulation results for edge detection by using the proposed method. In this simulation, we use
the 3×3 edge detection template and the DCNN edge detection template.
Templates A, B, threshold I are described as follows[4][5].
Edge detection templates of the conventional CNN :0 0 0A =  0 1 0 ,0 0 0
−1 −1 −1B =  −1 8 −1  , I = −1.
−1 −1 −1(7)Edge detection templates of the DCNN :(e)Figure 6: Simulation results 1. (a) Input image. (b) Simulation result of
0−1 −1 −1
the conventional CNN. (c) Simulation result of the DCNN (τ = 10). (d)0  , B =  −1 8 −1  ,Simulation result of the proposed method (τ = 10, a = 0.003, x = 5). (e)0−1 −1 −1Simulation result of difference (c) and (d).
−0.1 −0.1
0.1 −0.1  , I = −1.
(8)
We apply the proposed method to another input image. In−0.1 −0.1
Fig. 7, we show the input image and the simulation resultsof the edge detection. Figure 7(a) shows the input image.
In Fig. 6, we show the input image and the simulation re- The input image is woman’s face. In Fig. 7(b), we show thesults of the edge detection. Figure 6(a) shows the input image. simulation result of the conventional CNN. The conventionalIn the input image, indistinct parts are the right side of the red CNN cannot detect edge lines of woman’s face. In Fig. 7(c),pepper and the vegetable in the upper left. In Fig. 6(b), we we show the simulation result of the DCNN (τ = 10). Theshow the simulation result of the conventional CNN. The con- DCNN can detect edge lines of indistinct parts, however, reventional CNN cannot detect edge lines of the indistinct parts. mains the noise effect. In Fig. 7(d), we show the simulation
In Fig. 6(c), we show the simulation result of the DCNN (τ result of the proposed method (τ = 10). The proposed method= 10). The DCNN can detect edge lines of indistinct parts, can detect edge lines of indistinct parts and receive less noise
however, remains the noise effect. In Fig. 6(d), we show the effect compared to the DCNN.
0 0A =  0 10 0
−0.1
D =  −0.1
−0.1







- 110 -References[1] L. O. Chua and L. Yang, “CellularralNetworks
Theory.”IEEETrans.
cuits Syst., vol. 35, pp. 1257–1272, 1988.

(a)NeuCir-[2] T. Roska and L. O. Chua, “Cellular Neural Networks with Nonlinear and Delay-type Template Elements,” Int. J. Circuit Theory Applications. 20. pp. 463–481, 1992.

(b)[3] N. Takahashi, “On the Complete Stability or Cellular Neural Networks with Delay,” NLP Nonlinear Problem, vol. 98, pp. 31–38, 1999.
[4] T. Nakano, Y. Uwate and Y. Nishio. “Edge Detection by Using Switching System with Cellular Neural Networks and Delayed Cellular Neural Networks,”
SJCIEE, pp. 3, 2015.
(c)

(d)

[5] L. Kek, K. Karacs and T. Roska, “Cellular Wave Computing Library (Templates, Algorithms, and Programs), Version 2.1, Cellular Sensory Wave Computers laboratory, Hungarian Academy of Sciencesk, Budapest, Hungary, 2007.

(e)
Figure 7: Simulation results 2. (a) Input image. (b) Simulation result of
the conventional CNN. (c) Simulation result of the DCNN (τ = 10). (d)Simulation result of the proposed method (τ = 10, a = 0.003, x = 5). (e)Simulation result of difference (c) and (d).

6. Conclusion
In this study, we have proposed a CNN method of adding
delay output (DCNN) to the conventional CNN partially.
From the simulation results, the proposed method can detectedge lines of indistinct parts and decrease effect of noise compared to the DCNN. Therefore, the proposed method is more
effective than the conventional CNN and the DCNN in theedge detection. In the future works, we will investigate more
effective values a and N .

Acknowledgment
This work was partly supported by JSPS Grant-in-Aid for
Scientific Research 16K06357.

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