4th International Forum on Advanced Technologies
March 8th-9 th, 2018,Tokushima, Japan

Cellular Neural Networks with Switching
Two Templates by Local Features of Neighborhood
Takahisa Ando , Yoko Uwate and Yoshifumi Nishio
Tokushima University, Tokushima 770-8501, Japan
E-mail:{ando,uwate,nishio}@ee.tokushima-u.ac.jp

1. Introduction
Cellular Neural Networks (CNN) was introduced by L. O. Chua and L. Yang in 1988 [1]. The idea of CNN
was inspired from the architecture of the cellular automata and Neural Network. CNN consists of analog
circuit and it is capable of high-speed parallel processing. CNN has local connectivity property and its
structure resembles the retina of human. Hence, CNN has been successfully used for various high-speed
parallel signals processing applications such as image processing, pattern recognition and so on [2]. The
performance of CNN depends on the parameters which is called the template. The template represents strengthof connection between cells. If the template influences exactly, CNN can perform complex processing. In
image processing of CNN, it is difficult to process complex parts of the input image; edge, background, etc. In
this study, we propose a CNN method of switching two templates by using the maximum and the minimum
output values surrounding the center cell. We apply the proposed method to some image processing andinvestigate its performance.
2. Cellular Neural Networks [1]Basic unit circuit of CNN is called cell. The cell consists of linear element
and nonlinear element. CNN contains an array in a reticular pattern of manycells. In image processing of CNN, processing is conducted by making one
cell to one pixel in the image data. We show a two dimensional arraycomposed of M × N identical cells arranged in M rows and N columns. The
array of CNN and the circuit of cell are shown in Fig. 1.
A cell couples with only adjacent cells. State and output equations of cellare described as follows.
State equation

Fig.1
𝑖+𝑟

𝑗+𝑟

𝑖+𝑟

The structure of CNN.

𝑗+𝑟𝑑𝑣𝑥(𝑖𝑗)= −𝑣𝑥(𝑖𝑗) + ∑ ∑ 𝐴(𝑖,𝑗;𝑘,𝑙) 𝑣𝑦(𝑘𝑙) (𝑡) ∑ ∑ 𝐵(𝑖,𝑗;𝑘,𝑙) 𝑣𝑢(𝑘𝑙) (𝑡)𝑑𝑡
𝑘=𝑖−𝑟 𝑙=𝑗−𝑟

𝑘=𝑖−𝑟 𝑙=𝑗−𝑟+ 𝑇.

(1)

Output equation𝑣𝑦(𝑖𝑗) (𝑡)
1= (|𝑣𝑥(𝑖𝑗) (𝑡) + 1|2− |𝑣𝑥(𝑖𝑗) (𝑡)− 1|).
In Eq (1), A, B and T are feedback template, feed forward template and threshold.
3. Proposed method
The feature of the proposed method is switching two templates byusing the maximum and the minimum output values (𝑣𝑦𝑚𝑎𝑥 : cell’smaximum output value, 𝑣𝑦𝑚𝑖𝑛 : cell’s minimum output value)surrounding the center cell. The concept of the proposed method isshown in Fig. 2. The algorithm of the proposed method is describedas follows.
Step 1 ) First, decide the center cell. Then, find the 𝑣𝑦𝑚𝑎𝑥 , and(24th International Forum on Advanced Technologies
March 8th-9 th, 2018,Tokushima, Japan𝑣𝑦𝑚𝑖𝑛 from the n × n neighborhood.
Step 2 ) Secondly, determine if the center cell has the maximum
or the minimum output value.

Fig.2

The concept of calculation.

Step 3 ) In case that the center cell has the maximum or the minimum output value, center cell is applied 2ndtemplate. In the other case, center cell is applied 1st template.
These steps are applied to all cells and repeated every 0.005 [τ].
4. Simulation result
We show simulation result of texture analysis and using templates are described as follows [3].
3 × 3 template
0.86
0.94
3.75
0.16 −1.56 1.25
𝐴 = [ 2.11 −2.81 3.75 ], B = [−2.89 1.09 −3.2], 𝑇 = 1.8.
−1.33 −2.58 −1.02
4.06
4.69 3.75(3)5 × 5 template
4.21 −1.56 1.56
3.36
0.62
4.06
−5
0.39
2.11 −1.87−2.89 4.53 −0.23 3.12 −2.89
3.9
0.31 −1.95 4.84 −0.31
𝐴 = 2.65
2.18 −4.68 −3.43 −2.81 , 𝐵 =0−4.06 0.93 −0.31 0.46 ,3.98
1.56 −1.17 −3.12 −3.2−0.62−52.340.62 −1.87[−3.75 −2.18 3.28
[ 3.59 −0.93 0.15
2.19 −0.62]
2.81 −1.87](4)

𝑇= −5.

(a) Input image.

(b) 3 × 3 template.
Fig.3(c) 5 × 5 template.

(d) Proposed method (n = 7).

Simulation result of texture analysis.

Figure 3 shows the input image and simulation results by using only 3 × 3 template, only 5 × 5 template,the proposed method. We define that 1st template is the “3 × 3 Texture analysis” template and 2nd template is
the “5 × 5 Texture analysis” template. In Fig. 3(d), the boundary of the region is clear and the texture content
is characterized different. In the proposed method, two templates are applied to cells according to the featuresof texture content.
5. Conclusion
In this study, we have proposed a CNN method. In the proposed method, two templates are switched by using
the maximum and the minimum output values containing the center cell in the neighborhood. We applied theproposed method to texture analysis. From the simulation results, the proposed method could apply twotemplates to each cell by the features of texture content. In the future works, we would like to investigate theperformance of the proposed method for another image processing.
Acknowledgment
This work was partly supported by JSPS Grant-in-Aid for Scientific Research 16K06357.
References[1] L. O. Chua and L. Yang, “Cellular Neural Networks: Theory,” IEEE Trans. Circuits Syst., vol. 35, pp.

4th International Forum on Advanced Technologies
March 8th-9 th, 2018,Tokushima, Japan
1257-1272, Oct. 1988.
[2] Z. H. Yang, Y. Nishio and A. Ushida,“Image processing of twolayer CNNs applications and stability,”
IEICE Trans. Fundamentals, vol. E85-A, no. 9, pp. 2052-2060, 2002.
[3] L. Kek, K.Karacs and T. Roska, “Cellular Wave Computing Library( Templates, Algorithms, andPrograms), Version 2.1, ” Cellular Sensory Wave Computers laboratory, Hungarian Academy of Sciencesk,
Budapest, Hungary, 2007.