IEEE Workshop on Nonlinear Circuit Networks
December 13-14, 2019

Image Sharpening for Blurred Images
by Using Cellular Neural Networks
Kodai Kitamura, Yoko Uwate and Yoshifumi Nishio
Department of Electrical and Electronic Engineering, Tokushima University
2-1 Minami-Josanjima, Tokushima 770–8506, Japan
E-mail: {kitamura, uwate, nishio}@ee.tokushima-u.ac.jp

Abstract—The Cellular Neural Networks (CNN) was developedby Chua and Yang in 1998. The idea of the CNN was inspired
from the architecture of the cellular automata and the neuralnetworks. The performance of the CNN depends on the parameters which are called the template. The CNN is applied to various
image processing by changing the template. However, little has
been reported on image sharpening for blurred images by using
CNN. In this study, we propose an algorithm to sharpen image.
Then, we apply the proposed algorithm to the input image andinvestigate the performance by some simulations.

I. INTRODUCTION
In recent years, it has advanced information society. In
general, the von Neumann computer is used for many information processing. However, the von Neumann computer
cannot process many information in real time. Therefore,
Neural Networks were proposed. The idea was based on
the human’s nervous system. The Cellular Neural Networks(CNN) was introduced by L. O. Chua and L. Yang in 1988[?]. Hence, the CNN has been successfully used for various
high-speed parallel signals processing applications such asimage processing, pattern recognition and so on [?]. TheCNN was paired Neural Networks with the Cellular Automataby L. O. Chua in 1998 [?]. The CNN consists of cells
connected each other and the structure of CNN resembles
the structure of the animal’s retina [?]. Therefore, the CNN
has been applied to various image processing applications.
The performance of CNN depends on the parameters whichis called the template. The template represents strength ofconnection between each cell. The template consists of thefeedback template, the feedforward template and the threshold.
If the template influences exactly, we can investigate complex
image processing. Additionally, various applications for image
processing and pattern recognition of CNN have been reported.
In previous method, there is the Unsharp Masking (USM).
The USM is used as digital image processing to sharpen
images. In the USM, first, the input image is smoothed.
Secondly, a difference image between the input image andthe smooth image is created. Finally, the output image is acombination of the input image and the difference image.
However, little image sharpening for blurred images by using
CNN has been reported.
In this study, we propose an algorithm to sharpen imagesby using CNN. Our proposed method is performed on blurredimages. In order to confirm the effectiveness of our proposed
method, we evaluate simulation results.

II. CELLULAR NEURAL NETWORKSIn this section, we describe the basic structure and processing flow of the simple CNN. The basic circuit unit of the CNN
is called cell. The cell consists of linear element and nonlinear
element. The CNN is formed from an array of many cells.
We show a two dimensional array composed of M × N cells
arranged in M rows and N columes. The structure of the CNN
is shown in Fig. 1. Figure 2 shows the circuit of cell.

Fig. 1. The structure of the CNN.

Fig. 2. The circuit of cell.

A cell couples with only adjacent cells. Adjacent cells
interact with one another. Cells which do not couple with
only adjacent cells have an indirect influence. The range whichsome cells influence one cell is defined by neighborhood. We
describe state equation of cell and output equation of cellbelow.

-1-State Equation :dvx(ij)dt=−vx(ij) +i+r
X

j+r
X

A(i,j;k,l) vy(kl) (t)k=i−r l=j−r
i+r
X+j+r
X

B(i,j;k,l) vu(kl) (t) + T.

(1)

k=i−r l=j−rOutput Equation :1(|vx(ij) (t) + 1| − |vx(ij) (t) − 1|).
vy(ij) (t) =2

Fig. 5. Block diagram.

(2)

vx , vy and vu are state value, output value and input value.
Output equation represents piece-wise nonlinear function asshown in Fig 3.

III. PROPOSED METHOD
In this section, we show the proposed algorithm by using
CNN. The proposed algorithm is composed of six steps andthe flowchart is described as follows.

Fig. 3. Piece-wise nonlinear function.

In Eq. (1), A is feedback template, B is feedforward template,
T is threshold. The performance of CNN is determined bythese values.

(a) 3×3(b) 5×5

Fig. 4. Neighborhood area of cell.

When we process the image by using CNN, we should
determine the size of system of neighborhood. When this size
is big, the amount of information in system of neighborhood
is increasing. However, noise works easily. Figure 4 shows thesize of system of neighborhood. Generally, the size which isused for image processing is 3×3. In this study, we use 3×3
and 5×5 in combination. Figure 5 shows block diagram ofimage processing with CNN.

Fig. 6. The proposed algorithm.

The processing steps of the proposed method are describedas follows.
Step 1 (Edge Detection): First, the input image is sharpened.
Step 2 (Heat Diffusion): Secondly, the sharpened image isblurred to subtract the heat diffused image from the sharpened
image.
Step 3 (Logic Difference): Thirdly, sharp lines of thesharpened image are detected.
Step 4 (Logic OR with NOT): Fourthly, sharp lines thatcannot be detected in Logic Difference are detected.
Step 5 (Edge Detection): Fifthly, sharp lines of a previous
step are enhanced.
Step 6 (Logic OR): Finally, each cell’s output value ofthe sharpened image and the enhanced edge detected image isadded. Each step is repeated at every 0.05 [τ ].
IV. SIMULATION RESULTS
In this section, we show the simulation results of theproposed algorithm and the USM. Figure 2 shows how the-2-

image is processed in the proposed algorithm and the USM.
Using templates of the proposed algorithm are described asfollows [?].
Heat Diffusion template:
0.1 0.15 0.1
00.15  ,=  0.150.1 0.15 0.1

0 0 0=  0 0 0  , T = 0.
0 0 0A

B(a)

(b)

(c)

(d)(e)(f)(g)(h)(i)(3)

Edge Detection template:
A =B=

0 0 0
 0 1 0 ,0 0 0
−1 −1 −1
 −1 8 −1  , T = 0.
−1 −1 −1

(4)
Fig. 7. Simulation results. (a) Original image. (b) Input image. (c) Sharpenedimage. (d) Heat diffused image. (e) Logic difference. (f) Logic OR with NOT.
(g) Enhanced edge detected image. (h) Output image. (i) Unsharp masked
image.

Logic Difference template:0=  00
0=  00AB

00 ,0
0 0−1 0  , T = −1.
0 0020(5)Logic OR with NOT template:AB0=  00
0=  00
00 ,0
0 0−1 0  , T = 1.
0 0020(6)Logic OR template:
A =B=0 00
0 00020010

00 ,000  , T = 1.
0(7)In one instance, Fig. 7 show images which are processedby the proposed method and the USM. Figure 7(a) shows an
original image. The input image contains a bridge, a lake anda background of the forest. Figure 7(b) shows the simulation
result of Heat Diffusion applied to the input image by iterationof 100. The overall image is blurred. Figure 7(c) shows
the simulation result of Edge Detection applied to the inputimage. The overall image is sharpened compared to Fig. 7(c).
Figure 7(d) shows the simulation result of Heat Diffusion
applied to the sharpened image. The overall image is blurredcompared to Fig. 7(c). Figure 7(e) shows the simulation resultof Logic Difference applied to the sharpened image and theheat diffused image. The enhanced sharp lines of a lake anda background of the forest are detected. Figure 7(f) shows
the simulation result of Logic OR with NOT applied to thesharpened image and the heat diffused image. The left side ofthe forest which was not detected in Fig. 7(e) was detected
Figure 7(g) shows the simulation result of Edge Detection
applied to the enhanced image. The enhanced sharp linesof the sharpened image are detected compared to Fig. 7(g).
Figure 7(h) shows the simulation result of Logic OR applied
to the sharpened image and the enhanced image. Not many
unclear objects are remained. On the other hand, in Fig. 7(i),unclear objects are more remained compared to Fig. 7(h).
We have evaluated the simulation results by the Structural
Similarity(SSIM). The SSIM evaluates the change of pixel
values, constant, and structure between the target images. The
value of the SSIM closer to 1 is similar to the target image.
In Tab. 1, we show the SSIM of each output image.

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TABLE I
S TRUCTURAL S IMILARITY
Figure 7(h)Figure 7(i)0.63880.4833Figure 7(h)(i) are compared to Figure 7(a) for similarities.
Figure 7(h) is processed by using the proposed method.
Figure 7(i) is processed by using USM. From Tab. 1, theSSIM by using the proposed method is higher than by using
USM. From this simulation result, the proposed method ismore effective than USM.
V. CONCLUSION
In this study, we have proposed an algorithm for sharpeningblurred images by using CNN. Moreover, we have investigatedblurred images by using the USM. Then, we have evaluatedsimilarities from the simulation result. As a result, our proposed method is more effective than the USM. In the future
works, we would like to investigate the performance of anotherimage.
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[2] L. O. Chua and L. Yang, “Cellular Neural Networks Theory,” IEEE Trans. Circuits Syst., vol. 35, pp. 1257-1272,1988.
[3] Martin Hnggi and George S Moschytz, “Cellular Neural Networks Analysis, Design and Optimization,”
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