平成19年度電気関係学会四国支部連合大会

394

17-64

Output Characteristics of Cellular Neural
Networks Using Mixtured Template
Takashi INOUE

Masaru NAKANO Yoshifumi NISHIO(Tokushima University)

1. Introduction

3. Simulation and Results

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 and the neural networks. The CNN has local connectivity property.
Since the structure of the CNN resembles the structureof animals’ retina, the CNN can be used for various image processing applications. Wiring weights of the cells
are established by parameters called the template. If thetemplates of the cells in the CNN are identical, the system is called space-invariant system, or if not identical,
space-varying system. Typically, space-invariant system
is mainly used in the studies of CNN, because the cost
to implementation is cheap price but on the ﬂip side, thissystem holds the fault that the performance is limited eminently. In this study, we propose the mixtured templates
system as one of the space-varying template system. In
this system, distributions of templates are completely random. In this article, we get an interesting performancethat by mixtured two types of templates system.

Figure 2 shows the simulation results using the mixtured template which mixed “small object remover” (3)and “patch maker” (4) or (5). The Size of CNN is 128
× 128. Template (3) can put out small objects from binary images. Template (4) can extends black objects, andtemplate (5) can extends white objects.

1 1 10 0 0A =  1 2 1 ,B =  0 0 0 ,
I = 0. (3)1 1 10 0 0

0A= 10121001 ,B =  000010

{0I = 4.5. (4)0 ,I = −4.5. (5)0

2. Proposed CNN Model
The basic circuit unit of CNN is called a cell. It contains linear and nonlinear circuit elements. The CNN isan array of cells. Each cells are connected to neighboringcells.
The state equation of the cell is shown as follows.
State equation:
dvxij
xt

=−vxij +j+r
i+r
∑∑

(a)

(b)

(c)

(d)

A(i,j;k,l) vykl (t)k=i−r l=j−r

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

k=i−r l=j−r

Output equation:
1(|vxij (t) + 1| − |vxij (t) − 1|) (2)2vx , vy and vu represent a state, an output and an inputof cell, respectively. In the equation (1), A is the feedback
template and B is the control template, these and bias I
are collectively called template.
vyij (t) =Figure 2: Simulation results. (a) Input image.
(b) Only template (3). (c) Result using mixturedtemplate. (3) : (4) = 90 : 10. (d) (3) : (5) = 90 :10.
Figure 2 (b) shows the result using template (3). Figures 2 (c) and (d) show the results using mixtured template which template (3) and template (4) or (5) are mixed
at a rate of 9:1.
In the result (c), characteristic to the left area was improved. In the result (d), characteristic to the right area
was improved.

4. Conclusions
(a)

(b)

(c)

Figure 1:
Examples of mixtured template.
(a) white : black=75 : 25. (b) white : black=50 :50. (c) white : black=25 : 75.
Figure 1 shows examples of the mixtured template.
Black cells and white cells have diﬀerent templates. Mixture method is completely random.

In this study, we proposed the mixtured two types oftemplates system as one of the space-varying templates
systems. We investigated characteristic of proposed system by simulation. As a result, we clariﬁed that characteristic of CNN can be improved by proposed system.
Reference[1] L. O. Chua and L. Yang, ”Cellular Neural Networks:Theory” IEEE Trans. Circuits & Syst., vol. 32,pp. 1257-1272, Oct. 1988.