IEEE Workshop on Nonlinear Circuit Networks
December 14-15, 2012

Investigation of Two-Layer Cellular Neural
Networks with Switching Only Coupling Templates
for Motion Picture Processing
Kazushige Natsuno, Yoshihiro Kato, Yoko Uwate and Yoshifumi Nishio
Dept. of Electrical and Electronic Eng.,
Tokushima University,
2-1 Minami-Josanjima,Tokushima,770-8506 JAPAN
Email: {natsushige, kkato, uwate, nishio}@ee.tokushima-u.ac.jp

Abstract— In this paper, we propose the new system of twolayer CNN and investigate the output characteristics. The proposed two-layer CNN has different structure of conventional
two-layer CNN. In particular, the proposed system is connected
to first-layer and second-layer with one coupling template. Also
coupling template is switched by each layer of input and output
values. In this study, we investigate the output characteristics forchanging input images.

I. I NTRODUCTION
Our society is called advanced information society. Becauseof this, the large size of data cause trouble over processing speed. Conventional digital computation methods haveproblem of processing speed. However analog computation
methods are high speed processing. We focus on new computation model of neural networks. The concept of neuralnetworks is neurobiology and adapted to integrated circuits.
The key features of neural networks are asynchronous parallel
processing, continuous-time dynamics and global interactionof network elements. Cellular Neural Networks (CNN) wereintroduced by Chua and Yang [1]. CNN is a type of mutual
coupling neural network. CNN is used the concept of cellular
automata [2]. The structure of CNN is grating coupling ofcircuit. The circuit is called a cell that has an effect on eachother. The structure of cell circuit is simple analog circuit.
The cell circuit is constructed from linear capacitor, linear
resistors, independent voltage source, linear and nonlinear
controlled sources. Two-layer CNN is constructed two conventional single-layer CNNs. The two-layer CNN has two
coupling template. In some two single-layer CNN, both layers
are effected on each other by two coupling templates. In some
image processing, the two-layer CNN is better than the singlelayer CNN [3]. Also, CNN with switching template is better
than the single-layer CNN [4].
In the moving image processing, a lot of images werecontinuously processed with time. We consider a new system
which new system be processed moving image by using theinput image and previous output image of other layer. In
this study, we propose the two-layer CNN with switching
only coupling template. The proposed system has only effectfrom the second-layer to the first-layer. The first-layer and thesecond-layer are connected by switching templates.
From simulation results, we confirm the effective moving
image processing of the proposed system.
II. CELLULAR NEURAL NETWORKIn this section, we explain about the single-layer CNN andthe two-layer CNN.
A. Single-layer CNNFig. 1.

Block diagram of the conventional single-layer CNN.

In this subsection, we explain the basic structure of theCNN. A block diagram of the conventional single-layer CNN
shown Fig. 1. The conventional single-layer CNN use twotemplates B and A in processing. Template B is used inprocessing of input image. Template of A is used in processingof feedback of output image.
The state equation and output equation are described asfollows.
State equation of the conventional single-layer CNN :- 111 -dvxij
dt= −vxij +i+r∑j+r∑A(i,j;k,l) vxkl (t)k=i−r l=j−r+i+r∑j+r∑

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

k=i−r l=j−r(|i − k| ≤ 1 , |j − l| ≤ 1).

(1)

Output equation of the conventional single-layer CNN :1
vyij (t) =(|vxij (t) + 1| − |vxij (t) − 1|).
(2)
2

B. Two-layer CNN

III. P ROPOSED T WO - LAYER CNN

Fig. 3.
Fig. 2.

Block diagram of the two-layer CNN.

Figure 2 shows the block diagram of the conventional twolayer CNN. The conventional two-layer CNN is constructed
two conventional single-layers CNN by coupling two templates C1 and C2 . The coupling templates are used to transferred data between both layers. In addition, the conventional
two-layer CNN has been confirmed to have more efficient
structure for high performance image processing.
The state equations and output equations are described asfollows.
State equation of second-layer CNN :j+ri+r∑∑dv1 xij= −v1xij +A1(i,j;k,l) v1xkl (t)dtk=i−r l=j−r+i+r∑j+r∑

Step 1 : We determine the difference value Dij by the output
value of second-layer and the input value of first-layer. The
difference value is calculated by

B1(i,j;k,l) v1ukl (t)Dij = v2yij − v1uij .

k=i−r l=j−r+i+r∑j+r∑

C12(i,j;k,l) v2ykl (t) + I1

k=i−r l=j−r(|i − k| ≤ 1 , |j − l| ≤ 1).

Block diagram of the proposed two-layer CNN.

In this section, we explain the system of the proposed twolayer CNN. Figure 3 shows the block diagram of the proposedsystem. The structure of the proposed system is based onconventional two-layer CNN. The feature of proposed systemis the switching only coupling template. In the only coupling
template, the coupling template is switched two types. The
only coupling template is decided by the input values of thefirst-layer and the output values of the second-layer. The input
value of each layer are two type. Input values switched at 10[τ ]. In after 10 [τ ], second-layer CNN are inputed previous
output value of first-layer CNN.
The algorithm of the proposed system is shown as follows.

(3)

Step 2 : The boundary value and the difference value arecompared. If Dij is not 0, the template of C1 is used. On
the other hand, if Dij is 0, the template of C2 is used. The
switching rule of coupling template is shown as follows.

Output equation of first-layer CNN :1
v1 yij(t) =(|v1 xij(t) + 1| − |v1 xij(t) − 1|). (4)2State equation of second-layer CNN :j+ri+r
∑∑dv2 xij= −v2xij +A2(i,j;k,l) v2xkl (t)dt(7)

Switching rule of coupling template :DijDij

̸= 0 : C1 template,= 0 : C2 template.

(8)

Step 3 : The value of each cell is updated. The state equationand the output equation of each layer are described as follows.

k=i−r l=j−r

+i+r
∑j+r
∑

State equation of first-layer CNN :j+ri+r
∑∑dv1a xij= −v1a xij +A1(i,j;k,l) v1a ykl (t)dt

B2(i,j;k,l) v2ukl (t)k=i−r l=j−r+i+r∑j+r∑

k=i−r l=j−r

C21(i,j;k,l) v1ykl (t) + I2+

k=i−r l=j−r(|i − k| ≤ 1 , |j − l| ≤ 1).
Output equation of second-layer CNN :1v2 yij(t) =(|v2 xij(t) + 1| − |v2 xij(t) − 1|).
2i+r
∑j+r
∑

B1(i,j;k,l) v1a ukl (t)k=i−r l=j−r(5)+i+r∑j+r∑

CS (i, j; k, l)v2a ykl (t) + I1

k=i−r l=j−r(6)- 112 -(|i − k| ≤ 1 , |j − l| ≤ 1), (a = 1, 2). (9)Output equation of first-layer CNN :1
v1a yij(t) =(|v1a xij(t) + 1| − |v1a xij (t) − 1|).
2
(a = 1, 2).

Using two type of coupling templates are described asfollows.
(10)

Coupling templates:0.1
C1 =  0.1
0.1

0.07
C2 =  0.1
0.07

State equation of second-layer CNN :dv21 xij
dt=−v21 xij +i+r∑j+r∑A2(i,j;k,l) v21 ykl (t)k=i−r l=j−r+i+r∑j+r∑

B2(i,j;k,l) v21 ukl (t) + I2

0.1
−1.5
0.1
0.1
0.32
0.1


0.1
0.1  ,0.1

0.07
0.1  .
0.07

(16)

k=i−r l=j−r(|i − k| ≤ 1 , |j − l| ≤ 1).
Output equation of second-layer CNN :1
v21 yij(t) =(|v21 xij(t) + 1| − |v21 xij(t) − 1|).
2(11)

(12)

In after 10 [τ ], state equation of second-layer CNN areupdated as follows.
State equation of second-layer CNN :dv2 xijdt=−v22 xij +i+r∑j+r∑(a)A2(i,j;k,l) v2ykl (t)Fig. 4.

(b)

Input images of first-layer. (a) Input image 1. (b) Input image 2.

k=i−r l=j−r

+i+r
∑j+r
∑

B2(i,j;k,l) v1ykl (t) + I2

k=i−r l=j−r(|i − k| ≤ 1 , |j − l| ≤ 1).
Output equation of second-layer CNN :1
v22 yij(t) =(|v22 xij(t) + 1| − |v22 xij(t) − 1|).
2(13)

(14)

By repeating step1, template is changed.
Fig. 5.

Step 4 : Step 1 to Step 3 are repented every 0.005 [τ ].

First input image of first-layer and initial state image.

IV. S IMULATION R ESULTS
In this section, we show simulation results of moving image
processing by using the proposed system. In this simulation,
we use the 3×3 inverse halftoning template. Used templates
are found in [5]. Templates A, B, threshold I1 and I2 of eachlayer are assigned as follows.
The template of proposed system :
A1
B1
I1

= A2 = 0,0.07 0.1 0.07
0.32 0.1  ,= B2 =  0.1
0.07 0.1 0.07
= I2 = 0.

(a)Fig. 6.

(b)

Output images of first-layer CNN. (a) output image 1 (10 [τ ]). (b) output
image 2 (20 [τ ]).

(15)- 113 -(a)(b)

Fig. 7.

Output images of second-layer CNN. (a) output image 1 (10 [τ ]). (b) output
image 2 (20 [τ ]).

Figure 5 is background of input images in Figs. 4(a) and(b). In Fig. 4(a), a parson of right side is moving object. InFigs. 4(a) to (b), a parson is moving on to right side from leftside. The results of the proposed system are shown in Figs, 6
and 7. Figure 6 shows the output images of the first-layer
CNN. Figure 7 shows the output images of the second-layer
CNN. In Fig. 6(b), the image is appeared moving object ofprevious output. In addition, the moving object of previous
output has the characteristic of changing gray-scale values.
We compare Fig. 6(a) with Fig. 6(b). The moving object ofFig. 6(a) is changed gray-scale value for Fig. 6(b). Fromresults, we can say that the proposed system is effective ofmoving image processing.
V. C ONCLUSION
In this study, we have proposed two-layer CNN with switching only coupling template. The feature of proposed system isthe switching of coupling template. Outputs of second-layer
CNN has an effect on processing of first-layer CNN. The firstlayer and the second-layer are connected switching templates.
From simulation results, the proposed system could verify theeffect of moving image processing.
In the future works, we would like to process the proposed
CNN for a lot of image processing.
R EFERENCES[1] L. O. Chua and L. Yang, “Cellular Neural Networks:Theory,” IEEE Trans.
Circuits Syst., vol. 32, pp. 1257-1272, Oct. 1988.
[2] S.Wolfram, ”Computation theory of cellular automata,” Communicationsin Mathematical Physics, vol. 96, pp.15-57, 1984.
[3] Z. H. Yang, Y. Nishio and A. Ushida, “Image processing of twolayer CNNs -applications and stability-,” IEICE,Trans. Fundamentals,
vol. E85-A, no. 9, pp. 2052-2060, Sept. 2002.
[4] Y. KATO, Y. UEDA, Y. UWATE and Y. NISHIO, “Cellular Neural Networks with Switching Two Types of Templates,” Proc. of IJCNN’ 11,pp. 1423-1428, Jun. 2011.
[5] L. Kek, K.Karacs and T .Roska, “Cellular Wave Computing Library(Templates, Algorithms, and Programs), Version 2.1, ” CellularSensory Wave Computers laboratory, Hungarian Academy of Sciencesk,
Budapest, Hungary, 2007.

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