平成23年度 電気関係学会四国支部連合大会

31-3
Combination of Two Neurons in Cellular Neural Networks
Nurul Amirah BINTI RAMLAN Yoshihiro KATO Yasuhiro UEDA
Yoko UWATE Yoshifumi NISHIO(Tokushima University)

1. Introduction
Cellular Neural Networks (CNN) were introduced byChua and Yang in 1988 [1]. The idea of the CNN was inspired from the architecture of cellular automata and neural networks. Unlike the conventional neural networks, theCNN has local connectivity property and since structure ofCNN resembles the structure of animals’ retina, CNN canbe used for various image processing applications. Wiring
weights of the cells are established by parameters called thetemplate. In the basic CNN, one template is used in oneprocess. For using two or more templates, lots of processing are necessary and processing time becomes longer. We
desired the simplest and proper size of CNN to apply themto image processing. In this study, as a new approach wepropose a combination method of two neurons for one cellin CNN. In our propose method, two templates are usedin one time. As a result, both templates’ eﬀects appear inoutput image.

Figure 1: Block diagram.
New “White propagation” template :[A2=00.5
0[ 0B2=2. Proposed Method

000.5
30.5
0
1000000.50],], I2 = −2.75.

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In this section, we explain the algorithm of the proposedmethod. Our proposed method provides two neurons withtwo diﬀerent templates for one cell. The state equations
and the output equations are described as follows.
State Equation :Neuron α :dvx1ijdt=−vx1ij +j+ri+r∑∑A1 (i, j; k, l)vy2kl (t)k=i−r l=j−rj+ri+r∑∑+B1 (i, j; k, l)vu1kl (t) + I1 ,(a)(b)(c)(d)(1)

k=i−r l=j−r

Neuron β :dvx2ij=dt−vx2ij +j+ri+r∑∑

A2 (i, j; k, l)vy2kl (t)k=i−r l=j−rj+ri+r∑∑+B2 (i, j; k, l)vy1kl (t) + I2 ,k=i−r l=j−r(|i − k| ≤ 1 , |j − l| ≤ 1).

Output Equation :vu2ij (t) = vy1ij (t)=vy2ij (t)=(2)1(|vx1ij (t) + 1| − |vx1ij (t) − 1|). (3)21(|vx2ij (t) + 1| − |vx2ij (t) − 1|). (4)2We define the input and the output values as vu1 , vu2 ,vy1 and vy2 . The initial states for Neurons α and β arethe same. vu1 is carried out with B1 template and sent toNeuron β. The output value vy2 is carried out with A1 andA2 templates in the feedback loops. In Neuron α, vy2 iscarried out with A1 , and in parallel, vy2 is also carried outwith A2 template in Neuron β. This processes continue
until the output converges. Our proposed method can be
expressed by the block diagram shown in Fig. 1.

3. Simulation Results
In this section, we show a simulation result using ourproposed method. We use “Hole filling” template in Neuron α and a new template based on“White propagation”
template in Neuron β .
“Hole filling” template :[ 0A1 =

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10131010][ 0, B1 =00040000], I1 = −1.

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Figure 2: Simulation result. (a) Input image. (b) Initialstate. (c) Output Neuron α. (d) Output of Neuron β.
From the simulation results, the output of Neuron α isobtained as Fig. 1(c) and it is the same as the case of thebasic CNN with“Hole filling” template. The connection
between vy1 and vu2 let the value from Neuron α directly
process to Neuron β in the same loop. Figure 1(d) is theoutput of Neuron β when the input value vu2 is processedwith the initial state in Fig. 1(b). Only enclosed shapethat exists in a black area of the initial state in Fig. 1(b) is
detected as the output. From the results we can say thatboth templates can be used simultaneously.

4. Conclusions
In this study, we have proposed combination of two neurons for one cell in CNN. In our proposed method, twotypes of templates can be confirmed to eﬀect in one output value because of the bond between two neurons. From
the results, we can say that our proposed method can combine two processes in one time because of the combinationof two neurons in one cell.
References[1] L.O. Chua and L. Yang, “Cellular Neural Networks: Theory,”
IEEE Trans. Circuits Syst., vol. 32, pp. 1257-1272, Oct. 1988.