平成24年度 電気関係学会四国支部連合大会

241-24
One Direction Two-Layer Cellular Neural Networks
with Switching Templates
Kazushige Natsuno Yoshihiro Kato Yoko Uwate Yoshifumi Nishio(Tokushima University)

1. Introduction

State equation of the second-layer CNN :Cellular Neural Networks (CNN) have used the conceptof cellular automata. The two-layer CNN is constructed
as conventional two single-layer. Two single layer have aneﬀect on each other. In some image processing, the twolayer CNN is better than the single-layer CNN [1]. Also,
CNN with switching template is better than the singlelayer CNN [2]. Then, we consider the structure of two-layer
CNN that has only eﬀect the one side layer by switching
template.
In this study, we propose the one-direction two-layer
CNN with switching template. The proposed system has
only eﬀect from the ﬁrst-layer to the second-layer. Theﬁrst-layer and the second-layer are connected by switching
templates. In simulation results, we show eﬀective image
processing of the proposed system.

2. Proposed System

dv2 xij
dtj+ri+r∑∑−v2xij +=A2(i,j;k,l) v2xkl (t)k=i−r l=j−rj+ri+r∑∑+B2(i,j;k,l) v2ukl (t)k=i−r l=j−rj+ri+r∑∑C(i,j;k,l) v1ykl (t) + I2 .

+(3)

k=i−r l=j−r

Step 5 : Step 2 to Step 4 are repented every 0.005[τ ].

3. Simulation Results
In this section, we show simulation results of edge detection by using the proposed method. In this simulation,
T1 and T2 are set to 0.3 and 0.4, respectively.
Templates A, B, threshold I1 and I2 of each layer are
assigned as follows.
Edge detection[ template :]A1 = A2 =000010000,B1 = B2 =[ −1−1−1−18−1−1−1−1I1 = −0.13, I2 = −1.

]
,
(4)

Using coupling templates are described as follows.
Coupling templates:[Figure 1: Block diagram of the proposed system.

C1 =In this section, we explain the algorithm of the proposedsystem. The structure of the proposed system is based on
two-layer CNN in Fig 1. The proposed system has only
one coupling template that has eﬀect on the second-layerfrom the ﬁrst-layer.Thus the structure of the proposed system has an eﬀect only the one side layer. In addition, three
types of coupling template are switched. The coupling template is decided by the output value of the ﬁrst-layer andthe input value of the second-layer. The algorithm of theproposed system is shown as follows.
Step 1 : We determine the boundary values T1 and T2 .
Step 2 : We determine the diﬀerence value Dij by theoutput value of ﬁrst-layer and the input value of secondlayer. The diﬀerence value is calculated by
Dij = |v2uij (t) − v1yij (t)|.

(1)

Step 3 : The boundary value and the diﬀerence value arecompared. If |Dij | is over T1 and under T2 , the templateof C1 is used. On the other hand, if |Dij | is over T2 , thetemplate of C2 is used. if |Dij | is under T1 , the templateof C3 is used.
Step 4 : The value of each cell is updated by the state
equation and the output equation. used the value of eachsell to be update. The state equation and the output equation of each layer are described as follows.
State equation of the first-layer CNN :dv1 xijdt=−v1xij +j+ri+r∑∑A1(i,j;k,l) v1xkl (t)k=i−r l=j−r∑ ∑i+rj+r

B1(i,j;k,l) v1ukl (t) + I1 .

+k=i−r l=j−r

Powered by TCPDF (www.tcpdf.org)

(2)

C3 =

(a)

1
1
1

1
2
1

1
1
1

1
0

1
8
1

10

[ 0(b)]]
0, C2 =

[ 0.50.5
0.5

0.5
0.5
0.5

0.5
0.5
0.5]
,.

(5)

(c)(d)

Figure 2: Simulation result. (a) Input image. (b) Edge detection
result of the single-layer CNN. (c) Edge detection result of the firstlayer CNN. (d) Edge detection result of the second-layer CNN.

In Fig. 2(a), boundary line of the vegetable of centerside and the empty space is an indistinct portion. This
indistinct portion is not detected by using the single-layer
CNN in Fig. 2(b). The results of the proposed system areshown in Fig. 2(c) and (d). Figure. 2(c) shows the outputof the ﬁrst-layer. The boundary line of indistinct portion isdetected by low threshold. Figure. 2(d) shows the outputof the second-layer. The edge of the indistinct portion canbe distinctly detected. From these results, we can say thatthe proposed system is more eﬀective than the single-layer
CNN for edge detection.

4. Conclusions
In this study, we have proposed the one direction twolayer CNN with switching template. The proposed system
has only eﬀect the second-layer. The ﬁrst-layer and thesecond-layer are connected switching three types of templates. From simulation results, the proposed system could
more detect than the single-layer CNN.
References[1] 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.
[2] Y. KATO, Y. UEDA, Y. UWATE and Y. NISHIO, “Cellular Neural Networks with Switching Two Types of Templates,” Proc. ofIJCNN’ 11, pp. 1423-1428, Jun. 2011.