IEEE Workshop on Nonlinear Circuit Networks
December 11-12, 2015

Cellular Neural Networks with Changing Templates
for Image Processing
Shohei Gotoda, Yoko Uwate and Yoshifumi Nishio
Dept. of Electrical and Electronic Engineering, Tokushima University
2-1 Minami-Josanjima, Tokushima 770–8506, Japan
Email: {shohei, uwate, nishio}@ee.tokushima-u.ac.jp

Abstract—In 1998, Cellular Neural Networks (CNN) wereintroduced. The performance of the CNN depends on the parameters called the template. If the template is influenced by
the spacially and the temporally variation, CNN can perform
complex processing. In this study, we propose a new methodof changing templates. We apply the pseudoramdom numbers
to template, the pseudoramdom numbers change template. We
investigate the performance of the proposed method by somesimulations.

C(1,1)

C(1,2)

C(1,3)

C(1,N)

C(2,1)

C(2,2)

C(2,3)

C(2,N)

C(3,1)

C(3,2)

C(3,3)

C(3,N)

I. INTRODUCTION
Recently, a lot of information have been existed in the word.
In general, digital circuits are used for information processing.
However, digital circuits cannot process many information inreal time. Therefore, Neural Networks were proposed. The
Neural Networks was based on the human’s nervous system.
This idea has features of nonlinearity and parallel processing.
Cellular Neural Networks (CNN) are a part of ideas which
are based on Neural Network. The idea of CNN was inspired
from the architecture of the Neural Networks and the Cellular
Automata by L.O.Chua in 1998[1]. The structure of CNN
resembles the structure of animal retina. Therefore, CNN havebeen suitable for various image processing. The performanceof CNN depends on the parameters called the template. The
template has feature that is not influenced by the spatiallyand temporally variation. This feature causes that CNN cannot
complex processing. If the template is influenced by thespacially and the temporally variation, CNN can perform
complex processing.
In this study, we propose a new method of changing templateof the CNN. We apply the pseudoramdom numbers to templates in our method,. In order to confirm the effectiveness ofthe proposed method, we perform some simulations in image
processing by proposed method.
II. C ELLULAR N EURAL N ETWORKS
A basic unit circuit of CNN is called cell. The cell contains
linear element and nonlinear element. CNN is formed froman array in a reticular pattern of many cells. We show a twodimensional array composed of M × N identical cells arrangedin M rows and N columes.

C(M,1)

C(M,N)

Fig. 1. M × N

A cell couples with only adjacent cells. Adjacent cells
interact with one another. Cells which don’t couple with onlyadjacent cells have an indirect influence. The range whichsome cells have influence one cell is defined by neighborhood.
We describe state equation of cell and output equation of cellbelow.
State Equation :dvxijdt= −vxij +i+r∑j+r∑A(i,j;k,l) vykl (t)k=i−r l=j−r+i+r∑j+r∑

B(i,j;k,l) vukl (t) + T.

(1)

1(|vxij (t) + 1| − |vxij (t) − 1|).
2

(2)

k=i−r l=j−r

Output Equation :vyij(t) =vx , vy and vu are state value, output value and input value.
In equation (1), A is feedback template, B is feedforward
template, T is threshold. These value determine performanceof CNN.
III. PROPODED METHOD
The proposed method changes templates in pseudorandom
numbers. We add pseudorandom numbers α to a template A,
and add pseudorandom numbers β to a template B. Pseudorandom numbers are added every the number of constantprocessing times Tp . The templates of the proposed method- 21 -show Eq.(1),The templates of proposed method :AB
a11 + α a12 + α a1n + α=  a21 + α a22 + α a2n + α am1 + α am2 + α amn + α
b11 + β b12 + β b1n + β=  b21 + β b22 + β b2n + β bm1 + β bm2 + β bmn + β(3)(a)(b)In this study, we add pseudorandom numbers to edge detection
template. The parameters of pseudorandom numbers are fixedwith α = -0.9 ∼ 0, β = -0.01 ∼ 0.
(c)Fig. 2. Simulation results. (a) Input image. (b) Simulation result of theconventional CNN. (c)Simulation result of the proposed method (α = -0.9
∼ 0 , β = -0.01 ∼ 0, Tp = 5 ).

IV. SIMULATION RESULTS
In this section, we show simulation results of the edge
detection by using our proposed method. Using templates ofthe edge detection is described as follows.
Edge detection template :A =B=

0 0 0
 0 1 0 ,
0 0 0


−1 −1 −1
 −1 8 −1  , T = −1.
−1 −1 −1

Figure 1(a) is an input image. The input image has indistinct
portions. Indistinct portions are the pillar of the left-side andan outline of a woman’s face. Figure 1(b) shows the simulation
result of the conventional CNN. The conventional CNN cannot detect edge lines of indistinct portions. Figure 1(c) shows
the simulation result of the proposed method. In Fig. 1(c), theproposed method can detect edge lines of indistinct portions.

(4)

Edge detection template of the proposed method :(b)

A

B


000
=  0 1 + α 0 ,000
−1 + β −1 + β=  −1 + β 8 + β−1 + β −1 + β(a)−1 + β−1 + β  , T = −1. (5)−1 + β(c)Fig. 3. Simulation results. (a) Input image. (b) Simulation result of theconventional CNN. (c)Simulation result of the proposed method (α = -0.9
∼ 0 , β = -0.01 ∼ 0, Tp = 5 ).

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Figure 1(a) is an input image. The input image has indistinct
portion. Indistinct portion is the building in the right partof the image. Figure 1(b) shows the simulation result of theconventional CNN. The conventional method of CNN can notdetect edge lines of indistinct portion. Figure 1(c) shows thesimulation result of the proposed method. In Fig. 1(c), theproposed method can detect edge lines of indistinct portion.
Moreover, our method can detect a hand of a man.
V. C ONCLUSION
In this study, we propose the new method of changing
templates. We apply the pseudoramdom numbers to templates
in our method. In order to confirm the effectiveness of the
proposed method, we investigate the proposed method inimage processing. In this case, we perform edge detection.
As a result, proposed method can detect more edge linesof indistinct portions than conventional method. Hence, theproposed method is more effective than the conventional CNN
in image processing.
R EFERENCES[1] L. O. Chua and L. Yang, “Cellular Neural Networks: Theory,” IEEE
Trans. Circuits Syst., vol. 35, pp. 1257-1272, Oct. 1988.
[2] Martin H 辰 nggi and George S Moschytz, “Cellular Neural Networks Analysis, Design and Optimization.“ Kluwer Academic Publishers.

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