2020 RISP International Workshop on Nonlinear Circuits,Communications and Signal Processing (NCSP 2020)
Honolulu, Hawaii, USA, February 28 - March 2, 2020

Image Sharpening for Blurred Images with Multiple Processes
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

Abstractages. In the USM, first, the input image is smoothed. Secondly, a difference image between the input image and theThe Cellular Neural Networks (CNN) was developed by smooth image is created. Finally, the output image is a combiChua and Yang in 1998. The idea of the CNN was inspired nation of the input image and the difference image. However,from the architecture of the cellular automata and the neural little image sharpening for blurred images by using CNN hasnetworks. The performance of the CNN depends on the pa- been reported.
rameters which are called the template. The CNN is applied
In this study, we propose an algorithm to sharpen images
to various image processing by changing the template. How- by using CNN. Our proposed method is performed on blurred
ever, little has been reported on image sharpening for blurred images. In order to confirm the effectiveness of our proposed
images by using CNN. In this study, we propose an algorithm method, we evaluate simulation results.
to sharpen blurred images. Then, we apply the proposed algorithm to the input image and investigate the performance
2. CELLULAR NEURAL NETWORKS
by some simulations.
1. 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 [1].
Hence, the CNN has been successfully used for various highspeed parallel signals processing applications such as image
processing, pattern recognition and so on [1]. The CNN waspaired Neural Networks with the Cellular Automata by L.
O. Chua in 1998 [2]. The CNN consists of cells connectedeach other and the structure of CNN resembles the structureof the animal’s retina [3]. Therefore, the CNN has been applied to various image processing applications. The performance of CNN depends on the parameters which are called
the template. The template represents strength of connection
between each cell. The template consists of the feedback template, the feedforward template and the threshold. If the template influences exactly, we can investigate complex imageprocessing. 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 im-In this section, we describe the basic structure and processing flow of the simple CNN. The basic circuit unit of the CNN
is called a cell. The cell consists of linear element and nonlinear element. The CNN is formed from an array of manycells. We show a two dimensional array composed of M ×
N cells arranged in M rows and N columes. The structure ofthe CNN is shown in Fig. 1. Figure 2 shows the circuit ofcell.

Figure 1: The structure of CNN.
A cell is coupled with only adjacent cells. Adjacent cells interact with one another. Cells which do not couple with onlyadjacent cells have an indirect influence. The range whichsome cells influence one cell is defined by neighborhood. We
describe a state equation of cell and an output equation of cell567

Figure 2: The circuit of cell.
Figure 4: Block diagram.
below.
State Equation :dvx(ij)dt=−vx(ij) +i+r
X

j+r
X

3. PROPOSED METHOD
A(i,j;k,l) vy(kl) (t)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.

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−r

Output Equation :vy(ij) (t)=1(|vx(ij) (t) + 1| − |vx(ij) (t) − 1|). (2)2vx , vy and vu are state value, output value and input
value. Output equation represents piece-wise nonlinear function Fig 3.

Figure 5: 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): Second, the sharpened image isblurred to subtract the heat diffused image from the sharpened
image.
Step 3 (Logic Difference): Third, sharp lines of the sharpFigure 3: Piece-wise nonlinear function.
ened image are detected.
Step 4 (Logic OR with NOT): Fourth, sharp lines thatIn Eq. (1), A is feedback template, B is feedforward tem- cannot be detected in Logic Difference are detected.
plate, T is threshold. The performance of CNN is determined
Step 5 (Edge Detection): Fifth, sharp lines of a previousby these values.
step are enhanced.
Step 6 (Logic OR): Final, each cell’s output value of theWhen we process the image by using CNN, we should desharpened
image and the enhanced edge detected image istermine the size of system of neighborhood. When this size isadded.
Eachstep size is 0.05 [τ ].
big, the amount of information in system of neighborhood isincreasing. However, noise works easily. Generally, the size
which is used for image processing is 3×3. Figure 4 shows
block diagram of image processing with CNN.

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4. SIMULATION RESULTS
In this section, we show the simulation results of the proposed algorithm and the USM. Figure 2 shows how the image is processed in the proposed algorithm and the USM. Using templates of the proposed algorithm are described as follows [5].

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Heat Diffusion template:
0.1 0.15 0.1
 0.1500.15  ,0.1 0.15 0.1


0 0 0
 0 0 0  , T = 0.
0 0 0

A =B

=(3)

Edge Detection template:


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

B

Figure 6: Simulation results. (a) Original image. (b) Input image. (c)(4)

Sharpened image. (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 00A =B=

00 ,0
0 0−1 0  , T = −1.
0 0020(5)Logic OR with NOT template:AB

0=  00
0=  00
00 ,0
0 0−1 0  , T = 1.
0 0020(6)Logic OR template:
A =B=

0 0 0
 0 2 0 ,0 0 0
0 0 0
 0 1 0  , T = 1.
0 0 0(7)In one instance, Fig. 6 show images which are processedby the proposed method and the USM. Figure 6(a) shows anoriginal image. The input image contains a bridge, a lake anda background of the forest. Figure 6(b) shows the simulation
result of Heat Diffusion applied to the input image by iteration of 100. The overall image is blurred. Figure 6(c) shows
the simulation result of Edge Detection applied to the inputimage. The overall image is sharpened compared to Fig. 6(c).
Figure 6(d) shows the simulation result of Heat Diffusion applied to the sharpened image. The overall image is blurredcompared to Fig. 6(c). Figure 6(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 6(f) shows
the simulation result of Logic OR with NOT applied to thesharpened image and the heat diffused image. The left side of
the forest which was not detected in Fig. 6(e) was detected.
Figure 6(g) shows the simulation result of Edge Detection applied to the enhanced image. The enhanced sharp lines of thesharpened image are detected compared to Fig. 6(g). Figure 6(h) shows the simulation result of Logic OR applied tothe sharpened image and the enhanced image. Not many unclear objects are remained. On the other hand, in Fig. 6(i),unclear objects are more remained compared to Fig. 6(h).
We process another image which is processed by the proposed method and the USM Figure 7(a) shows an original im-569

is similar to the target image. In Tab. 1, we show the SSIM ofeach output image.

(a)

(d)

(b)

(e)

(c)

Table 1: Structural Similarity
Figure 6(h) 0.6388
Figure 6(i) 0.4833
Figure 7(h) 0.7276
Figure 7(i) 0.6053(f)Figure 6(h)(i) are compared to Figure 6(a) and Figure 7(h)(i) are compared to Figure 7(a) for similarities. Figure 6(h) and Figure 7(h) are processed by using the proposed
method. Figure 6(i) and Figure 7(i) are processed by using
USM. From Tab. 1, the SSIM by using the proposed method
is higher than by using USM. From these simulation results,
the proposed method is more effective than USM.
5. CONCLUSION(g)(h)(i)

Figure 7: Simulation results 2. (a) Original image. (b) Input image. (c)Sharpened image. (d) Heat diffused image. (e) Logic difference. (f) Logic
OR with NOT. (g) Enhanced edge detected image. (h) Output image. (i)Unsharp masked image.

In this study, we have proposed an algorithm for sharpening blurred images by using CNN. Moreover, we have investigated blurred images by using the USM. Then, we haveevaluated similarities from the simulation results. As a result,our proposed method is more effective than the USM. In thefuture works, we would like to investigate the performance ofanother image.

age. The input image contains a woman and a reticulate background. Figure 7(b) shows the simulation result of Heat Diffusion applied to the input image by iteration of 100. Theoverall image is blurred. Figure 7(c) shows the simulation result of Edge Detection applied to the input image. The overall
image is more sharpened compared to Fig. 7(c). Figure 7(d)shows the simulation result of Heat Diffusion applied to thesharpened image. The overall image is more blurred compared to Fig. 7(c). Figure 7(e) shows the simulation result ofLogic Difference applied to the sharpened image and the heatdiffused image. The enhanced sharp lines of a reticulate background are detected. Figure 7(f) shows the simulation resultof Logic OR with NOT applied to the sharpened image andthe heat diffused image. The left side of the forest that was
not detected in Fig. 7(e) was detected. Figure 7(g) shows thesimulation result of Edge Detection applied to the enhancedimage. The enhanced sharp lines of the sharpened image aredetected compared to Fig. 7(g). Figure 7(h) shows the simulation result of Logic OR applied to the sharpened image andthe 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

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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,” Kluwer Academic Publishers Norwell,pp. 148. 2000.
[4] K. Nakai and A. Ushida. “On a Design Technique of Cellular Neural Network,”IEICE Transactions
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[5] T. Roska, L. Kek, L. Nemes, A. Zarandy, and P. Szolgay,“CNN Software Library (Templates and Algorithms), Version 7.3,” Analogical and Neural Computing Laboratory, Budapest, Hungary, 1999.