平成18年度電気関係学会四国支部連合大会

314

Analysis of Small World CNN with Limited Connection Length

17 - 18

Masaru NAKANO,

Yoshifumi NISHIO(Tokushima University)(Tokushima University)

1．Introduction

(a)
(b)
(c)
Figure 2: Simulation result of diffusion (Lm =10). (a) Initial image.
(b) Output image at t =1000. (c) Steady state output image.
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Time

The Cellular Neural Network (CNN) has beensuccessfully used for various high speed parallel signals
processing applications such as image processing and patternrecognition. A few years ago, Tsuruta et al. have proposed
Small-World Cellular Neural Network (SWCNN) model,
which is constructed by introducing some random couplings
between separated cells (hereafter we call this connection SWconnection) [1]. Direction-Preserving SWCNN (DP-SWCNN)
is obtained by rewiring some original connections by SW
connections with keeping the direction [2].
Although SWCNN has some potential applications
including watermarking, circuit implementation iscomplicated because of SW connections with random
structure. In this study, we consider the case that the lengthof SW connection is limited to simplify the structure ofSWCNN and investigate the performance of the network.

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2 Proposed DP-SWCNN Model

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Lm

7090

Figure. 3: Convergence time.
Figure 1: SW connection between two cells of the proposed
DP-SWCNN.

1816x&ij (t ) = − xij (t ) + I ++∑A

ij ;klkl∈N r ( i , j )kl∉abykl (t )∑ B u (t ) + A

ij ;kl kl
kl∈N r ( i , j )ij ;aby pq (t )(1)

3．Simulation Results of Diffusion Analysis
We apply the proposed DP-SWCNN to diffusion
analysis. The size of the network is 128×128. Figure 2 shows
an example of the simulated results of diffusion with themaximum length of the SW connection Lm =10.
Figure 3 shows the relation between Lm and theconvergence time. Figure 4 shows the relation between Lm
and the characteristic path length of the small-world
network.

14
path length

The proposed DP-SWCNN is obtained by rewiring someoriginal connections of the regular CNN by SW connections
with random length less than a given maximum length Lm.
Further, we modify the connection method of theDP-SWCNN in [2]. Namely, the original connections from thetwo cells connected a SW connection are removed if theconnections are toward the same direction as the SW
connections as shown in Fig. 1.
The state equation of each cell C(i,j) of the proposed
DP-SWCNN is formulated by Eq. (1). In Eq. (1), ypq is theoutput of the two cells connected by the SW connections. Theparameters a and b denote the position numbers of theeliminated neighbor cells. In this study, we fix the rewiring
rate pc is equal to 1.

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LmFigure 4: Characteristic path length.

4．Conclusion
In this study, we have proposed a new type ofDP-SWCNN and have investigated its basic characteristics.
Development of new applications using the proposed
DP-SWCNN is an important future work.

Reference[1] K. Tsuruta, Z. Yang, Y. Nishio, A. Ushida, "Small-World Cellular
Neural Networks for Image Processing Applications," Proceedings ofEuropean Conference on Circuit Theory and Design (ECCTD'03), vol.
1, pp. 225-228, Sep. 2003.
[2] K. Tsuruta, Z. Yang, Y. Nishio, A. Ushida, "Diffusion Analysis ofDirection-Preserving Small-World CNN," Proceedings of IEEE
International Workshop on Cellular Neural Networks and theirApplications (CNNA'04), pp. 352-357, Jul. 2004.