平成24年度 電気関係学会四国支部連合大会

141-14
Investigation of Cellular Neural Networks
with Eﬀect from Friends of a Friend
Yoshihiro KATO Yoko UWATE Yoshifumi NISHIO(Tokushima University)

1. Introduction
In 1988, Cellular Neural Networks (CNN) [1] were introduced. CNN has the local connectivity property and it makes
the CNN tailor made for VLSI implementation. Furthermore, the structure of CNN resembles that of animals’ retina.
Therefore, CNN can be used for various image processing applications. In CNN, each cell is connected to its neighboring
cells according to a template. Then, each cell is inﬂuenced
by neighboring cells and its value is updated.
As the proverb “Birds of a feather ﬂock together” says, weare likely to become friendly with someone who have similar interests, values, purpose and so on. In this study, we
propose cellular neural networks with eﬀect from friends ofa friend (FF-CNN). The FF-CNN is the new method in consideration of the phenomena in such actual society. Generally, in the conventional CNN, each cell is connected toonly its neighboring cells. In this case, the information thata cell can obtain from its neighboring cells is limited. In
the proposed method, combinations of among cells are decided by the value of each cell. In each cell, a cell with thenearest value of center cell is deﬁned as “Best friend cell”
in eight neighboring cells. Then, the state value of each cellis updated under the inﬂuences of the best friend cell andits neighboring cells. We show some simulation results andconﬁrm its eﬀectiveness.

2. FF-CNN
In this section, we explain the algorithm of the FF-CNN.
The FF-CNN is the method of constituting a new combination between cells. The algorithm is described as follows.

(a)

(b)

Figure 1: Definition of the best friend cell. (a) The caseof input image. (b) The case of output image.
Step 1: In each cell of input image, a cell with the nearest
value of center cell C(i, j) is deﬁned as “Best friend cell” ineight neighboring cells.
Step 2: The combination centering on a cell C(i, j) ischanged into a combination centering on the best friend celllike Fig. 1(a).
Moreover, the element of template of the best friend andthe center cell are replaced. With this, a new combination
between cells is constituted.
Step 3: The value of each cell is updated according to thestate and the output equations using the new combination
between cells.
Step 4: In each cell of output image, a cell with thenearest value of center cell C(i, j) in input image is deﬁned as
the “Best friend cell” in eight neighboring cells like Fig. 1(b).
Step 5: Steps 2 to 4 are repeated every 0.0005 [τ ].
In the proposed method, each cell in input image is usedfor basis of deﬁnition of the best friend. Therefore, the statePowered by TCPDF (www.tcpdf.org)

value of each cell is updated by receiving inﬂuences from thebest friend cell and its neighboring cells.

3. Simulation Results
In this section, we show simulation results of image denoising by using the FF-CNN. Generally, in the conventional
CNN, “Small object remover” template [2] is used for image denoising. However, this template can not remove largesize noises and output value is converged to black or white.
Then, the conventional CNN can not perform with maintaining gray scale. As another method for image denoising,
noisy image is defused.
In the FF-CNN, we use “Heat dif f usion” template [2]for image denoising. Boundary condition is ﬁxed to +1.

(a)

(b)

(c)

(d)

Figure 2: Image denoising results. (a) Gray scale input
image. (b) Image denoising result using the conventional
CNN with “Small object remover” template. (c) Image denoising result using the conventional CNN with
“Heat dif f usion” template. (d) Image denoising result
using the FF-CNN with “Heat dif f usion” template.
Figure 2(b) shows the image denoising result by the conventional CNN using “Small object remover” template tothe gray scale image in Fig. 2(a). The small-size noises areremoved. However, the noises over certain size are not removed. Moreover, an output image is converged to black andwhite. Then, the right side object of the value near black has
disappeared. On the other hand, Fig. 2(c) shows the output
image by the conventional CNN using “Heat dif f usion”
template. The input image is diﬀused to black.
However, Fig. 2(d) shows the image denoising result by
the FF-CNN using “Heat dif f usion” template. All noisein the input image were removed regardless of gray scale.
Then, the right side object remained with keeping the valueof gray scale.
From these results, we consider that the FF-CNN is more
eﬀective than the conventional CNN for image denoising.

4. Conclusions
In this study, we have proposed cellular neural networks
with eﬀect from friends of a friend. The FF-CNN is thenew method in consideration of the phenomena in actual
society. From simulation results of image denoising, we consider that the large-size noises which remained by the conventional CNN were removed. Moreover, the right side object
remained with keeping the value of gray scale.
Reference[1] L. O. Chua and L. Yang, “Cellular Neural Networks: Theory,”
IEEE Trans. Circuits Syst., vol. 32, pp. 1257-1272, Oct. 1988.
[2] Cellular Sensory Wave Computers Laboratory Computer and Automation Research Institute Hungarian Academy of Sciences, “Cellular wave Computing Library (Template, Algorithms, and Programs)
Version 2.1”