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

Investigation of Image Denoising
by Cellular Neural Networks
with Effect from Friend of a Friend
Yoshihiro Kato, Yoko Uwate and Yoshifumi Nishio
Department of Electrical and Electronic Engineering, Tokushima University,
2-1 Minami Josanjima, Tokushima 770-8506, Japan
Email: {kkato, uwate, nishio}@ee.tokushima-u.ac.jp
Abstract—In previous study, we have proposed “cellular neuralnetworks with effect from friend of a friend” (FF-CNN). The FFCNN is the method of constituting a new connection of amongcells in CNN. Then, we confirmed that the FF-CNN could perform
image denoising, edge-preserving smoothing and divide domains.
In this study, we investigate about image denoising by using theFF-CNN.

I. I NTRODUCTION
In recent years, our life teems with information by growth ofhigh information society. Generally, sequential digital circuit
is used for many information processing. However, the digital
circuit cannot perform real time processing. Then, Cellular
Neural Networks (CNN) [1] were introduced. The idea ofthe CNN was inspired from the architecture of the cellular
automata and the neural networks. A different point fromthe conventional neural networks is that CNN has local connectivity property. 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 [2]-[6].
Generally in the conventional CNN, template of 3×3 matrix
is used. In this case, the information that a cell can obtainfrom its neighboring cells is limited. Then, as approach toincrease the information, there is also an approach of extending
size of template. However, this approach has the potential tocollapse the local connectivity property of CNN. In previoustimes, method of changing connection of among cells withoutextending size of template has been proposed. Especially, amethod of inspired from the network theory is interesting for
us like a “Small-world cellular neural networks” [7].
In previous time, we have proposed “cellular neural networks with effect from friend of a friend” (FF-CNN) [8]. The
FF-CNN is the method of constituting a new connection ofamong cells in CNN. Then, we confirmed that the FF-CNNcould perform image denoising, edge-preserving smoothing
and divide domains. In this study, we investigate about image
denoising by using the FF-CNN from two way. At first, wecompare processing flow of the conventional CNN and theFF-CNN. In the second way, we discuss about why an object
remains.
The list of this paper is structured as follows. In Sec. 2, wereview the conventional of the conventional CNN. In Sec. 3,

we review the FF-CNN. In Sec. 4, some simulation resultsof image denoising by using the proposed method are shown.
In Sec. 5, we investigate about image denoising by using theFF-CNN The section 6 concludes the article.
II. C ELLULAR N EURAL N ETWORKSIn this section, we explain the conventional structure ofthe CNN. The CNN has M by N processing unit circuits
called cells. The cell contains linear and nonlinear circuit
elements which are typically linear capacitors, linear resistors,
linear and nonlinear controlled sources. Cells are arranged
in a reticular pattern to M line N row. We represent a cellC(i, j) using a variable i which denotes vertical position anda variable j which denotes horizontal position. The CNN isan array of cells. Each cell is connected to its neighboring
cells according to a template. Usually, the template is thesame for all cells except for boundary cells. The CNN has thefeatures of time continuity, spatial discreteness, nonlinearityand parallel processing capability. The state equation and theoutput equation of the CNN are shown as follows.
State equation :dvxij
dt= −vxij +i+r
∑

j+r
∑

A(i,j;k,l) vykl (t)k=i−r l=j−ri+r∑j+r∑B(i,j;k,l) vukl (t) + I,

(1)

1(|vxij (t) + 1| − |vxij (t) − 1|),2

(2)+

k=i−r l=j−r

Output equation :vyij (t) =where vx , vy and vu represent a state, an output and an inputof cell, respectively. In the Eq. (1), A is the feedback templateand B is the control template. These and the constant bias I
are collectively called general template. The output equation
is a piece-wise linear function. In fact, the output value ofCNN is within of −1 to 1. When the CNN is used for image
processing, values of black and white are treated as 1 and −1,respectively.

- 105 -III. C ELLULAR N EURAL N ETWORKS WITH E FFECT
FROM F RIEND OF A F RIEND
In this section, we explain about the algorithm of the cellularneural networks with effect from friend of a friend (FF-CNN).
It is new approach in consideration of the actual society whichis concept of effect from best friend and its friends. Then,
The FF-CNN is the method of constituting new connectionsof among cells. In this paper, we consider the local connectionof CNN as friendship. Then in each cell, the neighboring cells
are defined as friend cells. Based on this, the algorithm of FFCNN is described as follows.
Fig. 4.

Fig. 1.

Definition the best friend cell in output.

Definition the best friend cell in input.

Fig. 5.

The combination on centering on the best friend cell in output.

cells. In the proposed method, each cell in input image is used
for basis of definition the best friend. Therefore, the state valueof each cell is updated by receiving influences from the bestfriend cell and its neighboring cells.
Fig. 2.

The combination on centering on the best friend cell in input.

Fig. 3.

Elements of new template.

Step 1: In each cell of input image, a cell with the mostnearest value of center cell C(i, j) is defined as “Best friendcell” in eight neighboring cells like Figs. 1 and 2.
Step 2: The combination centering on a cell C(i, j) ischanged into a combination centering on the best friend cell.
Moreover, the element of template of the best friend and thecenter cell C(i, j) are replaced. With this, a new combinationis constituted like Fig. 3.
Step 3: The value of each cell is updated according to theEqs. (1) and (2) using the new combination.
Step 4: In each cell of output image, a cell with the mostnearest value of center cell C(i, j) in input image is defined as“Best friend cell” in eight neighboring cells like Figs. 4 and 5.
Step 5: Steps 2 to 4 are repeated every 0.005 [τ ].
In every case when cell with the most nearest value are twoor more, the best friend cell is chose at random out of theirIV. S IMULATION R ESULTS
In this section, we show some simulation results of image
denoising by using the FF-CNN. Generally, in the conventional
CNN, “Small object remover” template [8] is used forimage denoising. However, output values are converged onblack or white by using this template. In fact, the conventional
CNN can not perform with maintained gray scale. As theother way for image denoising, noisy image is defused. In theFF-CNN, we use “Heat dif f usion” template [8] for image
denoising. Boundary condition is fixed to +1. Size of using
image is 128×128 [pixels].
Figure 6(b) shows the image denoising result by the conventional CNN using “Small object remover” template to grayscale image like Fig. 6(a). Noises are not removed completely.
Moreover, values of cells are converged on black or whitewhen the “Small object remover” template is used. Then,the right side object with gray scale has disappeared.
On the other hand, Fig. 7 shows the image denoising
result by the FF-CNN using “Heat dif f usion” template.
Figure 7(b) shows the output image by using the FF-CNN
to gray scale input image and the initial state image likeFigs. 6(c) and Fig. 7(a). All noise in the input image areremoved regardless of gray scale. Moreover, there is remainedwith keep the value of gray scale which is the object of theright side disappeared by the conventional CNN. Furthermore,
the angle of the right side object is sharp.

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(a)0 [τ ]

0.05 [τ ]0.1 [τ ]0.15 [τ ]0.2 [τ ]0.25 [τ ]0.3 [τ ]0.35 [τ ]0.4 [τ ]0.45 [τ ]0.5 [τ ]1 [τ ]

1.5 [τ ]2 [τ ]

2.5 [τ ](b)

Fig. 6.
Image denoising by the conventional CNN using“Small object remover” template. (a) Gray scale input and initialstate images. (b) Image denoising result for gray scale image.

(a)

(b)

Fig. 7. Image denoising by the FF-CNN. (a) Initial state image. (b) Image
denoising result for gray scale.

V. D ISCUSSION OF I MAGE D ENOISING BY THE FF-CNN
In this section, we investigate about image denoising byusing the FF-CNN from two way.
At first, we compare the processing flow of image denoising by the conventional CNN and the FF-CNN. Figure 8show the processing flow of image denoising by the conventional CNN. Some noises are removed by behavior of the“Small object remover” template. However, other noises
with certain size are remained. Furthermore, output values areconverged to black or white. Then, the right side object withgray scale has disappeared. Figure 9 show the processing flowof image denoising by the FF-CNN. The initial state image isset white image. And, the boundary values are set as black.
Therefor, the initial state image is processed from the outsideunder the influence of boundary cells. By behavior of the FFCNN, all noise in the input image are removed and the objectof the right side is remained with keep the value of gray scale.
In the second way, we discuss about why an object remains.
We consider that cells in the object choose the “Best friendcell” from the inside of object Fig. 10(a). On the other hand,cells in the background choose the “Best friend cell” from theback ground like Fig. 10(b). Then, in boundary between theobject and background, connections split up into the object
side and the background side Fig. 10(c). In the case ofFig. 8.
Processing flow of the conventional CNN using the“Small object remover” template.

large size object, connections in the object are strong because
connections are lot. Then, the large size object was remained.
On the other hand, in the case of small object, connectionsin the object are not strong because connections are low.
This phenomena like an actual phenomena which is large
companies have strength compared with small and mediumsized enterprises.
VI. C ONCLUSION
In this study, we investigated about image denoising byusing the FF-CNN from two way. At first, we compared
processing flow of the conventional CNN and the FF-CNN. In- 107 -0 [τ ]

5 [τ ]10 [τ ](a)15 [τ ]

20 [τ ](b)

25 [τ ](c)

30 [τ ]

45 [τ ]

35 [τ ]50 [τ ]

Fig. 10. Image denoising by the FF-CNN. (a) In the case of cell in thebackground. (b) In the case of cell in object. (c) Connections split up into theobject side and the background side.

40 [τ ]

the second way, we discussed about why an object remains.
From speculations, we considered that connections amongcells split up into the object side and the background side isboundary between object and background. Then, the large size
object was remained by connections in the object are strong
because connections are lot.
In the future works, we would like to try another determining condition of the “Best friend cell”.

55 [τ ]R EFERENCES

60 [τ ]

65 [τ ]

70 [τ ]

75 [τ ]

80 [τ ]

85 [τ ]

Fig. 9. Processing flow of the FF-CNN using the “Heat dif f usion”
template.

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