2013 International Workshop on Nonlinear Circuits,Communications and Signal Processing
NCSP'13, Isrand of Hawaii, Hawaii, USA. March 4-7, 2013

Investigation of Motion Picture Processing by Two-Layer Cellular Neural Networks
Switching Coupling Templates
Kazushige Natsuno, Yoshihiro Kato, Yoko Uwate and Yoshifumi Nishio
Dept. of Electrical and Electronic Engineering, Tokushima University
2-1 Minami-Josanjima,Tokushima, 770-8506, Japan
Phone;+81-88-656-7470, FAX:+81-88-656-7471
E-mail: natsushige, kkato, uwate, nishio@ee.tokushima-u.ac.jp

Abstract

only coupling template. The proposed system has only effect from the second-layer to the first-layer. The first-layer
In this paper, we propose the new system of two-layer CNN and the second-layer are connected by switching templates.
and investigate the output characteristics. In particular, theFrom simulation results, we confirm the effective motion
proposed system is connected to first-layer and second-layer picture processing of the proposed system.
with one coupling template. Also coupling template isswitched by each layer of input and output values. In this 2. Cellular Neural Network
study, we investigate the output characteristics for changing
In this section, we explain about the single-layer CNN andinput images.
the two-layer CNN.
1. Introduction
Our society is called advanced information society. Because of 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 interaction of network elements. Cellular Neural Networks (CNN)
were introduced by Chua and Yang [1]. CNN is a type ofmutual coupling neural network. CNN is used the concept ofcellular automata [2]. The structure of CNN is grating coupling of circuit. The circuit is called a cell that has an effecton each other. The structure of cell circuit is simple analogcircuit. The cell circuit is constructed from linear capacitor, linear resistors, independent voltage source, linear andnonlinear controlled sources. Two-layer CNN is constructed
two conventional single-layer CNNs. The two-layer CNN has
two coupling templates. In 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 thesingle-layer CNN [3]. Also, CNN with switching template isbetter than the single-layer CNN [4].
In the motion picture processing, a lot of images were continuously processed with time. We consider a new system
which the system be processed motion picture by using theinput image and previous output image of other layer. Inthis study, we propose the two-layer CNN with switching

2.1 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 two
templates B and A in processing. Template B is used in processing of input image. Template of A is used in processingof feedback of output image.

Figure 1: Block diagram of the single-layer CNN.
The state equation and output equation are described as follows.
State equation of the conventional single-layer CNN :- 448 -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 :vyij (t) =1(|vxij (t) + 1| − |vxij (t) − 1|).
2(2)2.2 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.

3. 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 on theconventional two-layer CNN. The feature of proposed system is the switching only coupling template. The coupling
template is switched two types. The only coupling templateis decided by the input values of the first-layer and the output values of the second-layer. The input value of each layer
are four type. Input values are switched every 10 [τ ]. After
10 [τ ], previous output value of first-layer CNN are inputedsecond-layer.

Figure 2: Block diagram of the two-layer CNN.
The state equations and output equations are described asfollows.
Figure 3: Block diagram of the proposed two-layer CNN.
The algorithm of the proposed system is shown as follows.
Step 1 : We determine the difference value Dij by the output
value v2yij of second-layer and the input value v1uij of firstlayer. The difference value is calculated by
Dij = v2yij − v1uij .
(7)State equation of second-layer CNN :j+ri+r
∑∑dv1 xij
A1(i,j;k,l) v1xkl (t)= −v1xij +dt
k=i−r l=j−r+i+r∑j+r∑

B1(i,j;k,l) v1ukl (t)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).

(3)

Step 2 : The boundary value and the difference value are compared. If Dij is not 0, the template of C1 is used. On the otherhand, if Dij is 0, the template of C2 is used. The switchingrule of coupling template is shown as follows.
Switching rule of coupling template :Output equation of first-layer CNN :1
v1 yij(t) =(|v1 xij(t) + 1| − |v1 xij(t) − 1|).(4)2k=i−r l=j−r+j+r∑

̸=0 : C1 template,Dij=0 : C2 template.

B2(i,j;k,l) v2ukl (t)k=i−r l=j−r

k=i−r l=j−r+i+r∑j+r∑+C21(i,j;k,l) v1ykl (t) + I2

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

B1(i,j;k,l) v1a ukl (t)k=i−r l=j−r

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

(8)

Step 3 : The value of each cell in the first-layer CNN is updated. The state equation and the output equation of firstlayer are described as follows.
State equation of first-layer CNN :j+ri+r
∑∑dv1a xij= −v1a xij +A1(i,j;k,l) v1a ykl (t)dtState equation of second-layer CNN :j+ri+r
∑∑dv2 xij= −v2xij +A2(i,j;k,l) v2xkl (t)dti+r∑Dij(5)+i+r
∑

j+r
∑

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

k=i−r l=j−r(6)- 449 -(|i − k| ≤ 1 , |j − l| ≤ 1),(a = 1, 2, 3, 4).

(9)Output equation of first-layer CNN :Using two type of coupling templates are described as fol1
v1a yij(t) =(|v1a xij(t) + 1| − |v1a xij (t) − 1|)lows.
2(a = 1, 2, 3, 4),(10) Coupling templates:
where, a means number of input and output images.
0.1 0.1
0.1
C1 =  0.1 −1.5 0.1  ,Step 4 : The value of each cell in the second-layer CNN is0.1 0.1
0.1updated. Until 10 [τ ] the state and the output equations aredescribed Eqs. (11) and (12), respectively. After 10 [τ ] the0.07 0.1 0.07
state and the output equations are described Eqs. (13) and0.32 0.1  .
C2 =  0.1(16)(14), respectively.
0.07 0.1 0.07
State equation of second-layer CNN (until 10 [τ ]) :dv21 xijdt= −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

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

(11)

Output equation of second-layer CNN (until 10 [τ ]) :1v21 yij(t) =(|v21 xij(t) + 1| − |v21 xij(t) − 1|). (12)
2(a)

(b)

(c)

(d)

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

(13)

Output equation of second-layer CNN (after 10 [τ ]) :Figure 4: Input images of first-layer. (a) Input image from 0
1
v21 yij(t) =(|v21 xij(t) + 1| − |v21 xij(t) − 1|). (14) [τ ]. (b) Input image from 10 [τ ]. (c) Input image from 202[τ ]. (d) Input image from 30 [τ ].
Step 5 : Step 1 to Step 4 are repeated every 0.005 [τ ].

In Fig. 4(a), a parson of right side is moving object. InFig. 4, the parson is moving on to right side from left side.
Figure 5 is used first input image of first-layer and initial state
In this section, we show simulation results of the motion
images of each layers. The results of the proposed systempicture processing by using the proposed system. In this simare shown in Figs. 6 and 7. Figure 6 shows the output imulation, we use the “3 × 3 inverse half toning” template,ages of the first-layer CNN. Figure 7 shows the output imwhich is found in [5]. Templates A, B, threshold I1 and I2 ofages of the second-layer CNN. Figs. 6(b) and 7(c) are similar
each layer are assigned as follows.
results. And Figs. 6(c) and 7(d) are similar results. We comThe template of proposed system :pare four images in Fig. 6. The moving object of Fig. 6(a) ischanged gray-scale value in Fig. 6(b). In Fig. 6(b), moving
A1 = A2 = 0,object of previous output is appeared. Moreover the mov
0.07 0.1
0.07
ing object of previous output has the characteristic of inverse
B1 = B2 =  0.1 0.32 0.1  ,gray-scale values. In comparison of Figs. 6(a) and (c), two
0.07 0.1
0.07
previous moving object of Fig. 6(c) is similar gray-scale valI1 = I2 = 0.
(15) ues of Fig. 6(a). Though, output of Fig. 6(c) is more dilute
4. Simulation Results- 450 -Figure 5: First input image of first-layer and initial state images of each layer.

(a)

(a)

(b)

(c)

(d)

Figure 7: Output images of second-layer CNN. (a) Output
image at 10 [τ ]. (b) Output image at 20 [τ ]. (c) Output imageat 30 [τ ]. (d) Output image at 40 [τ ].

(b)CNN. The first-layer and the second-layer are connectedswitching templates. From simulation results, we could saythat the proposed system makes it possible to characterize thetime course characteristic of moving object.
In the future works, we would like to process the proposed
CNN for difficult processing.
(c)

(d)

Acknowledgment
Figure 6: Output images of first-layer CNN. (a) Output imageat 10 [τ ]. (b) Output image at 20 [τ ]. (c) Output image at 30 This work was partly supported by JSPS Grant-in-Aid for[τ ]. (d) Output image at 40 [τ ].
Young Scientists 23700269.
References
than the output of two previous output. Much the same is true
on Figs. 6(b) and (d). In addition, in Fig. 6(d), right side object is more dilute than left side object. Therefore, old object
is more dilute than new object. The time course of moving
object could be discerned by dilute characteristic of output.
From these results, we can say that the proposed system
makes it possible to characterize the time course characteristic of moving object.
5. Conclusion
In this study, we have proposed two-layer CNN withswitching only coupling template. The feature of proposedsystem is the switching of coupling template. Outputs ofsecond-layer CNN have an effect on processing of first-layer[1] L. O. Chua and L. Yang, “Cellular Neural Networks:Theory,” IEEE Trans. Circuits Syst., vol. 32, pp. 1257-1272, Oct. 1988.
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