平成21年度電気関係学会四国支部連合大会

336

18-12
Investigation of Convergence Process in D-CNN
Masakazu KAWAHARA Takashi INOUE Yoshifumi NISHIO(Tokushima University)

1. Introduction
Cellular Neural Networks (CNN) were introduced byChua and Yang in 1988 [1]. The CNN can be used forimage processing applications. Wiring weights of the cells
in the CNN are established by parameters called the template. In the previous study, we proposed CNN with dynamic template (D-CNN) [2]. In D-CNN, template is dynamically updated by learning. Then, we obtained new
output characteristics which divided to two colors. Also,
we confirmed that convergence of D-CNN is much more
rapid than the conventional CNN. However, in the previous study, our investigation about output characteristicof D-CNN was not enough. Therefore, in this study, weinvestigate the convergence process of D-CNN in detail.
We expect to understand how output images are obtained
for some input images.

2. D-CNN
In D-CNN, the template of cell is changed at each update by learning. Calculate the comparison of the output
value of each cell with the one-step-past outputs of thecell and its neighbor cells. The comparison equation isdescribed as follows.
Comparison Equation:
now
past
Dif (i, j; k, l) = |vy,(i,j)− vy,(k,l)
|.

now
now
past
aupdatedwinner = awinner + R1 (t)(vy,(i,j) − vy,(i,j) ).

(2)

now
now
past
aupdatedsecond = asecond + R2 (t)(vy,(i,j) − vy,(i,j) ).

(3)

R1 (t) and R2 (t) decrease at each calculation. The initial
learning rates are described as follows.
Initial Learning rate:
R10 (−0.1 ≤ R10 ≤ 0.1).
R20 = R10 /4.

(4)
(5)

3. Examination Method
In this study, we use “Diffusion” template.
Diffusion Template:

"
A=0.1
0.15
0.1

0.15
00.15

0.1
0.15
0.1

#"
,B =000000000(b)(c)

Figure 1: Simulation results. (a) Input image. (b) Output image using D-CNN (Type 1). (c) Output image using
D-CNN (Type 2).
in D-CNN. Firstly, we choose two similar pixels in the input image. Next, we investigate the convergence processof the two pixels with “Diffusion” template.

4. Simulation Results(1)

In the previous study, among the 9 calculated valuesof Dif (i, j; k, l), the cells with the smallest and the second smallest values are defined as “winner” and “second”,respectively (Type 1). In this study, we also investigate
when the largest and the second largest values defined as“winner” and “second”, respectively (Type 2).
In update algorithm, we change the learning rate of the“winner” and the “second” as follows.
Update Equation:

W inner :Second :(a)#, I = 0. (6)Figures 1(b) and (c) are output images in Type 1 andType 2, respectively. Usually, an output image converges
to one value by using “Diffusion” template. However, inthese results, the output images converge to two values.
We investigate convergence process and relationship between the converged values and the values of neighbor cells

(a)

(b)

Figure 2: Convergence process for Fig. 1(a). (a) Type 1(R10 =0.1). (b) Type 2 (R10 =0.1).
Figure 2 shows the convergence process in D-CNN. InFig. 2(a), we can say that the gray points converge to 0or −1. From this result, we can say that the convergenceprocess depends on the values of surrounding cells. In
this case, if surrounding cells have similar values, relatively
bright area converges to −1. However, if surrounding cells
have the values near 1, relatively bright area converges toaround 0. Since edges of the output image in Fig. 1(c)are more diffused than those of Fig. 1(b), the convergenceprocess has difference between Type 1 and Type 2.

5. Conclusions

In this study, we have investigated relationship between
neighbor cells and convergence process in the cellular neural network with dynamic template (D-CNN). Also, we
have investigated convergence process of some different
definition types as “winner” and “second” in D-CNN.
From simulation results, we confirmed the difference ofconvergence process in some color’s pixels in D-CNN. And
we feel that the prediction of output image using D-CNN
can be performed.
References[1] L.O. Chua and L. Yang, “Cellular Neural Networks:Theory,” IEEE Trans. Circuits Syst., vol. 32,
pp. 1257-1272, Oct. 1988.
[2] M. Kawahara, T. Inoue and Y. Nishio “Cellular Neural
Network with Dynamic Template and its Output Characteristics” Proc. of IJCNN’09, pp. 1552-1558, Jun. 2009