平成21年度電気関係学会四国支部連合大会

335

18-11

Template Learning of CNN
Using Neural Networks
Masashi NAKAGAWA Takashi INOUE Yoshifumi NISHIO(Tokushima University)

1. Introduction
Cellular Neural Networks (CNN) were introduced by
Chua and Yang in 1988. The idea of the CNN was inspired from the architecture of the cellular automata andthe neural networks. There is a parameter called a template in CNN. If the template changes, an output changes.
Although the template is very important in CNN, it isdiﬃcult to ﬁnd out a suitable template for a given task.
Then, it is the purpose of this study to make a suitable
template by learning of neural networks (NN) with an
input image and an ideal image (teacher image).

2. CNN and NN
The basic circuit unit of CNN is called a cell. It contains linear and nonlinear circuit elements. The CNN isan array of cells. Each cell is connected to neighboringcells. The state and the output equations of the cell are
shown as follows.
State equation:
j+ri+r
dvxij (t)A(i,j;k,l) vykl (t)= −vxij (t) +dt
k=i−r k=j−r+i+rj+rB(i,j;k,l) vukl (t) + I(1)

k=i−r k=j−r

Output equation:vyij (t) =1(|vxij + 1| − |vxij − 1|)
2

Step 2. The input image is processed by CNN using atemplate decided at random.
Step 3. The back propagation algorithm is applied toobtain more suitable CNN template using the difference between the obtained output image and theteacher image.
Step 4. The back propagation is repeated until the error
between the output and the teacher becomes smallenough.

4. Learing result
An input image and its reversed image (teacher image) are shown in Figs. 1 and 2, respectively. The black
pixels correspond to the value +1 and the white pixels
correspond to the value −1.

Figure 1: Input image

Figure 2: Teacher image
The learning curve is shown in Fig. 3. The horizontal
axis shows the number of learning and the vertical axis
shows the error. The result shows that the error between
the output image and the teacher image is approaching
zero.
0.03

(2)

where vx , vy and vu represent a state, an output andan input of cell, respectively. In (1), A is the feedback
template and B is the control template, these and bias I
are collectively called template.
Neural network is a mathematical model which imitates human brain function. The NN in this study is ahierarchical type which consists of three layers of an inputlayer, a hidden layer, and an output layer. The elements
called weight are between the layers, and these are greatly
concerned with a result. The back propagation algorithm
can decide suitable weight values for a given task by using
some input signals and their ideal output signals (teachersignals).

"error1.txt"

0.025

0.02

0.015

0.01

0.005

00

Step 1. One example of one-dimensional binary image(input image) and its reversed image (teacher image)are prepared.

1000

1500

2000

2500

3000

3500

4000

4500

5000

Figure 3: Learning curve
An example of the obtained templates after the learning is given as follows.
00.449175
0A=3. Template learning
In this study, we use the back propagation algorithmof NN to obtain a suitable template of CNN for a giventask. As the ﬁrst step, the simplest task which reverses
black and white of one-dimensional binary input images
is considered.
The simulations are carried out according to the following procedure.

500
B=0−1.477137
0

I = 1.603537

00.569888
000.779094
00−1.810602
00−2.0962310(3)

5. Conclusions
In this study, a template learning method of CNN has
been proposed. Computer simulations conﬁrmed the efﬁciency of the proposed method.
In the future, CNN templates for more complicatedtasks should be obtained by the proposed method.