Journal of Signal Processing, Vol.24, No.4, pp.191-194, July 2020

SELECTED PAPER AT NCSP'20

Sharpening of Blurred Images with Multiple Processesby 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

output image is obtained as a combination of the input anddifference images. However, little sharpening of blurred imCellular neural networks (CNNs) were developed by Chua ages by using CNNs has been reported.
and Yang in 1988. The CNN concept was inspired fromIn this study, we propose an algorithm to sharpen blurred
the architecture of cellular automata and neural networks. images by using CNNs. To confirm the effectiveness of our
The performance of a CNN depends on template parameters. proposed method, we evaluate simulation results.
CNNs can be applied to various types of image processing
by changing the template. However, little has been reported 2. Cellular Neural Networks (CNNs)
on the sharpening of blurred images by using a CNN. In thisstudy, we propose an algorithm to sharpen blurred images.
In this section, we describe the basic structure and proThen, we apply the proposed algorithm to the input images cessing flow of a simple CNN. The basic circuit unit of aand investigate the performance by simulations.
CNN is called a cell. The cell consists of linear and nonlinear
elements. The CNN is formed from an array of many cells.
We show a two-dimensional CNN composed of M × N
1. Introduction
cells arranged in M rows and N columns in Fig. 1. Figure 2
shows the circuit of the cell.
In recent years, an increasingly information-based society
has developed. In general, a von Neumann computer is usedfor information processing. However, a von Neumann computer cannot process a range amount of information in realtime. Therefore, neural networks were proposed. Which arebased on the human nervous system. Cellular neural networks(CNNs) were introduced by Chua and Yang in 1988 [1].
CNNs have been successfully used for various high-speed
parallel signal processing applications such as image processing and pattern recognition [1]. A CNN was paired with neural networks with cellular automata by Chua in 1988 [2]. ACNN consists of cells connected to each other and its structure resembles the structure of an animal’s retina [3]. Therefore, CNNs have been used in various image processing applications. The performance of a CNN depends on template
Figure 1: Structure of CNN
parameters. The template represents strength of connection
between each cell. The template consists of the feedback A cell is coupled with only adjacent cells. Adjacent cells
and feedforward templates and the threshold. If the template interact with one another. Cells that do not couple with only
works exactly, we can investigate complex image processing. adjacent cells have an indirect effect. The range which cells
Additionally, various applications of image processing and effect one cell is defined by a neighborhood. We describe thepattern recognition using CNNs have been reported.
state and output equations of a cell below.
Unsharp masking (USM) is a digital image processing
method used to sharpen images. In USM, first, the input image is smoothed. Secondly, a difference image between theinput image and the smooth image is created. Finally, theJournal of Signal Processing, Vol. 24, No. 4, July 2020

191

Figure 2: Circuit of cell
Figure 4: Block diagram

State Equation:
dvx(ij)dt=−vx(ij) ++i+r
i+r
j+r


3. Proposed Method

A(i,j;k,l) vy(kl) (t)k=i−r l=j−rj+r

B(i,j;k,l) vu(kl) (t) + T(1)

k=i−r l=j−r

Here, we describe the proposed algorithm using the CNN.
The proposed algorithm is composed of six steps and its
flowchart is shown in Fig. 5.

Output Equation:vy(ij) (t)=1(|vx(ij) (t) + 1| − |vx(ij) (t) − 1|) (2)2vx , vy and vu are the state, output, and input values, respectively. The Output equation is represented by the piecewise
nonlinear function Fig. 3.

Figure 5: Proposed algorithm
The processing steps of the proposed method are describedas follows.
Step 1 (Edge Detection): The input image is sharpened.
Step 2 (Heat Diffusion): The sharpened image is blurredto subtract the heat diffused image from the sharpened image.
Figure 3: Piecewise nonlinear function
In Eq. (1), A is the feedback template, B is the feedforward
template, and T is the threshold. The performance of theCNN is determined by their values.
When we process an image by using a CNN, we should
determine the size of the neighborhood of the system. Whenthe neighborhood is large, the amount of information in theneighborhood is large. Moreever, noise works easily. Generally, the size of the neighborhood used for image processing
is 3×3. Figure 4 shows a block diagram of image processing
with a CNN.
192Step 3 (Logic Difference): The sharp lines of the sharpened image are detected.
Step 4 (Logic OR with NOT): The sharp lines that cannot
be detected in the logic difference step are detected.
Step 5 (Edge Detection): The sharp lines detected in theprevious step are enhanced.
Step 6 (Logic OR): The cell’s value of the sharpened image is added to that of the enhanced edge detected image.
Each step size is 0.05 [τ ].

Journal of Signal Processing, Vol. 24, No. 4, July 2020

4. Simulation Results
We show the simulation results of the proposed algorithm
and USM. Figure 5 shows how the image is processed in theproposed algorithm and USM. The templates used in the proposed algorithm are described as follows [4].
Heat Diffusion template:
0.1 0.15 0.1
00.15 A =  0.15
0.1 0.15 0.1


0 0 0
B =  0 0 0 , T = 00 0 0

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(3)

Edge Detection template:0 0 0A =  0 1 0 0 0 0
−1 −1 −1B =  −1 8 −1  , T = 0−1 −1 −1

Logic Difference template:0 0 0
A =  0 2 0 0 0 0


0 0 0
B =  0 −1 0  , T = −10 0 0

Logic OR with NOT template:A=

B=Logic OR template:

A

=

B

=




0 0 0
 0 2 0 0 0 0


0 0 0
 0 −1 0  , T = 10 0 0



0 0 0
 0 2 0 0 0 0


0 0 0
 0 1 0 , T = 10 0 0

Journal of Signal Processing, Vol. 24, No. 4, July 2020

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 image, (g) Enhanced edge-detected image, (h) Output image,and (i) Unsharp masked image

Figure 6 show images processed by the proposed method
and USM. Figure 6(a) shows the original image. The input
image contains a bridge, a lake and a forest. Figure 6(b)shows the simulation result obtained when heat diffusion isapplied to the input image with 100 iterations. The over(5) all image is blurred. Figure 6(c) shows the simulation result obtained when edge detection is applied to the input image. The overall image is sharpened compared with that inFig. 6(c). Figure 6(d) shows the simulation result obtained
when heat diffusion is applied to the sharpened image. The
overall image is blurred compared with that in Fig. 6(c). Figure 6(e) shows the simulation result when the logic difference
is applied to the sharpened and obtained heat-diffused image.
The sharpened lines of the lake and forest background aresharpened. Figure 6(f) shows the simulation result obtained(6) when logic OR with NOT is applied to the sharpened andheat-diffused image. The left side of the forest, which was
not detected in Fig. 6(e), was detected. Figure 6(g) shows thesimulation result obtained when edge detection is applied tothe enhanced image. The lines of the sharpened image are enhanced compared with those in Fig. 6(g). Figure 6(h) shows
the simulation result obtained when logic OR is applied tothe sharpened and enhanced image. Not many unclear objects remain. On the other hand, in Fig. 6(i), more unclear(7) objects remain than in Fig. 6(h).
We process another image by the proposed method and193

the changes in pixel values, constants, and structure between
the target images. An SSIM closer to 1 indicates greater similarity similar to the target image. In Tab. 1, we show theSSIM of each output image.
(a)

(b)

(d)

(e)

(f)

(g)

(h)

(i)

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

USM. Figure 7(a) shows the original image. The input image contains a woman and a reticulated background. Figure 7(b) shows the simulation result obtained when heat diffusion is applied to the input image with 100 iterations. Theoverall image is blurred. Figure 7(c) shows the simulation
result obtained when edge detection is applied to the input
image. The overall image is sharpened compared wtih thatin Fig. 7(c). Figure 7(d) shows the simulation result obtained when heat diffusion is applied to the sharpened image.
The overall image is blurred compared wtih that in Fig. 7(c).
Figure 7(e) shows the simulation result obtained when the
logic difference is applied to the sharpened and heat-diffusedimage. The lines of the reticulated background are sharpened. Figure 7(f) shows the simulation result obtained when
logic OR with NOT is applied to the sharpened and heatdiffused image. The left side of a background, which was
not detected in Fig. 7(e), was detected. Figure 7(g) shows thesimulation result obtained when edge detection is applied tothe enhanced image. The lines of the sharpened image are enhanced compared with those in Fig. 7(g). Figure 7(h) shows
the simulation result obtained when logic OR is applied tothe sharpened and enhanced image. Not many unclear objects remain. On the other hand, in Fig. 7(i), more unclear
objects remain than in Fig. 7(h). We evaluated the simulation
results using the structural similarity (SSIM), which evaluates

194

Table 1: Structural similarity
Figure 6(h) 0.6388
Figure 6(i) 0.4833
Figure 7(h) 0.7276
Figure 7(i) 0.6053(c)Figures 6(h)(i) are compared with Fig. 6(a), andFigs. 7(h)(i) are compared with Figure 7(a) in terms of similarity. Figs. 6(h) and 7(h) are processed by in terms of theproposed method, and Figs. 6(i) and 7(i) are processed byUSM. From Tab. 1, the SSIM obtained with using the proposed method is higher than that obtained by USM. Fromthese simulation results, the proposed method is more effective than USM.
5. Conclusion
In this study, we proposed an algorithm for sharpening
blurred images by using a CNN. Moreover, we investigated
the sharpening of blurred images by USM. Then, we evaluated similarities from the simulation results. Our proposed
method is more effective than USM. In future works, wewould like to investigate the performance for other images.
References[1] Z. H. Yang, Y. Nishio and A. Ushida: Image processing of two-layer CNNs applications and their stability, IEICE Trans. Fundamentals, Vol. E85-A, No. 9,
pp. 2052-2060, 2002.
[2] L. O. Chua and L. Yang: Cellular neural networks: Theory, IEEE Trans. Circuits Syst., Vol. 35, pp. 1257-1272,1988.
[3] M. Hanggi and G. S. Moschytz: Cellular Neural Networks Analysis, Design and Optimization, Kluwer
Academic Publishers, Norwell, 2000.
[4] 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.

Journal of Signal Processing, Vol. 24, No. 4, July 2020