ECCTD 2005 - European Conference on Circuit Theory and Design, Cork Ireland, 29 August - 2 September 2005

Image Processing Using Periodic Pattern Formationin Cellular Neural Networks
Taisuke Nishio ∗Abstract — In this paper, an image processing algorithm using periodic pattern formation in cellularneural networks is proposed. Applying this algorithm to a certain image, area having spatial uniformity is removed from the original image and only
parts without spatial uniformity remain. Simulation
results show that when this algorithm is applied toan image containing characters (texts), only characters are extracted.

1

INTRODUCTION

Cellular neural networks (CNNs) were introducedby Chua and Yang in 1988 [1]. The idea of theCNN was inspired from the architecture of the cellular automata and the neural networks. Unlike
the conventional neural networks, the CNN has local connectivity property. Since the structure of
the CNN resembles the structure of animals’ retina,
the CNN can be used for various image processing
applications including character extractions [2][3].
Also, the CNN is known to be able to generate periodic patterns [4][5].
It is amazing to imagine how the eye of animals performs image processing. Although the importance of computer vision has been recognizedwidely, it is still diﬃcult to develop a computer vision system with the performance of animals’ eye.
In computer vision, at ﬁrst, a feature of images isextracted, and next, various image processing anddetailed analyses are performed on its basis. However, it is diﬃcult to develop a universal feature
extraction method for various kinds of images inreal world. Hence, it is important to devise moregeneral feature extraction method, which does not
deeply depend on a type of images.
In this study, as a new approach for image processing, we propose a method using periodic pattern formation in the CNN. At ﬁrst, we investigate various CNN templates producing periodicpatterns. Next, we develop an image processing algorithm using one of the templates, which makessome spots only in the area having spatial uniformity. Simulation results show that when this algorithm is applied to images containing characters∗ Department
of Electrical and Electronic Engineering,
Tokushima
University,
2-1
MinamiJosanjima, Tokushima 770-8506, Japan.
Email:{taisuke, nishio}@ee.tokushima-u.ac.jp,
Tel.: +81-88-656-7470, Fax: +81-88-656-7471.

0-7803-9066-0/05/$20.00 ©2005 IEEEYoshifumi Nishio ∗(texts), only characters are extracted. Note thatthe purpose of this study is not to develop an algorithm extracting characters in images, but to ﬁndout some possible image-processing applications using periodic pattern formation of the CNN.
2CELLULAR NEURAL NETWORKS

The fundamental circuit unit of CNN is called acell. CNN consists of an array of cells. Each cellis connected only to its neighboring cells according
to a cloning template. A cloning template is thesame for all cells except for boundary cells. CNNs
have features of time continuity, spatial discreteness, nonlinearity and parallel processing capability. CNNs can perform rapid and various imageprocessing.
2.1

CNN Model

A simple CNN model is shown as follows.
State Equation:
dvxij (t)= −vxij (t)
dt
j+r
i+r

A(i,j;k,l) vykl (t)+k=i−r l=j−ri+r+j+rB(i,j;k,l) vukl (t)k=i−r l=j−r+I(1)Output Equation:
1
vyij (t) = (|vxij (t) + 1| − |vxij (t) − 1|)(2)2vx , vy and vu represent a state, an output and an
input of cell, respectively. A is the feedback template and B is the control template, these and bias
I are collectively called cloning template.
2.2

The r-neighborhood of a cell

Consider a two-dimensional array composed ofM × N cells arranged in M rows and N columns.
The generic cell placed on the ith row and thejth column is denoted by C(i, j), then, the rneighborhood of a cell C(i, j) is deﬁned as follows.
Nr (i, j)

= {C(k, l)|max{|k − i|, |l − j|} ≤ r,1 ≤ k ≤ M;

1 ≤ l ≤ N } (3)where r is a positive integer number.
Figures 1 and 2 show the r = 1 (3 × 3) neighborhood and the r = 2 (5 × 5) neighborhood,respectively.
(a)C(i,j)

C(i,j)

Figure 3: CHECKERBOARD Template (50 ×50 cells). (a) Initial state. (b) Output.
BI

Figure 1: the r = 1neighborhood.

3==00

PERIODIC PATTERN FORMATIONIN CELLULAR NEURAL NETWORKSCHECKERBOARD Template

This template forms the black and white alternate
pattern with the cycle of 2 cells. Although the alternate pattern with the cycle of 1 cell can be formed
easily, the checkerboard patterns with the cycle ofmore than 1 cell has not been reported. We foundthat it is possible to form the checkerboard patterns
with the cycle of more than 1 by increasing the sizeof the template.
−0.1 −1 −3 −1 −0.1
 −1 0.3 −2 0.3 −1 A =  −3 −2 −4 −2 −3 
 −1 0.3 −2 0.3 −1 −0.1 −1 −3 −1 −0.1
B = 0
I = 0(4)

3.2(5)

Figure 2: the r = 2neighborhood.

In this section, the developed cloning templates forperiodic pattern formation and the simulation results are shown.
3.1(b)RIPPLE Template

This template forms a pattern like a ripple.

0−0.2 −0.2 −0.20
 −0.200.2
0−0.2 
1.5
0.2 −0.2 
A =  −0.2 0.2
 −0.200.2
0−0.2 0−0.2 −0.2 −0.20(a)(b)

Figure 4: RIPPLE Template (200 × 200 cells).
(a) Initial state. (b) Output.
3.3

SPOT Template

This template makes white spots in a black area
having spatial uniformity and black spots in a whitearea having spatial uniformity. It is interesting thatthe spots are made only in areas wider than a certain size.
−0.25 −1
−1.5
−1 −0.25
 −1
2.5
7
2.5−1 

−1.5
7−23.25
7−1.5
A = 
 −12.57
2.5−1 −0.25 −1−1.5−1 −0.250 0 0 0 0
 0 0 0 0 0 

B = 
 0 0 1 0 0 
 0 0 0 0 0 
0 0 0 0 0
I=4

IMAGE PROCESSING0(6)

In this section, an image processing algorithm using
the pattern formation with the SPOT template isdeveloped.

(a)

(b)

Figure 5: SPOT Template (100 × 100 cells). (a)Initial state and input. (b) Output.

(1) original image.

(2) binarized image.

(3) pattern formation.

(4) pattern extraction.

(5) recalling the area with pattern.

(6) removing (5)from (2).

The proposing algorithm is shown in Fig. 6. The
SPOT template is used in this algorithm to form
periodic pattern. The parenthetic numbers in thechart correspond to the parenthetic numbers inFig 7. The other templates used in this algorithm
are shown in Appendix.

Figure 7: Simulation results for an image of a car.

Figure 6: Image processing algorithm.
The simulation results of this algorithm for animage of a car and an image of road sign are shown
below.
Figure 7 shows how the image is processed in theproposed algorithm. Figure 8 shows the image afternoise removal from Fig. 7(6). This result showsthat only the number on the number plate can beextracted by the algorithm.

Figure 8: Character extraction from a car image.

Figure 9 shows the original image of a road signof CNN” IEICE Transactions on Fundamentals,
in Japan. Figure 10 shows the image after applying
vol. E79-A, no. 10, pp. 1741-1746, Oct. 1996.
our algorithm to the image in Fig. 9. This result [4] K.R. Crounse and L.O. Chua, “Methods for Imshows that only the important information on theage Processing and Pattern Formation in Celluroad sign can be extracted by the algorithm.
lar Neural Networks: A Tutorial,” IEEE Trans.
Circuits Syst., vol.42, no.10, pp.583-601, Oct.
1995.
[5] K.R. Crounse, L.O. Chua, P.Thiran andG.Setti, “Characterization and Dynamics ofPattern Formation in Cellular Neural Networks,” International Journal of Bifurcationand Chaos, vol.6, no.9, pp.1703-1724, 1996.
A
A.1
Figure 9: Original gray-scale image of a road sign.

Other Templates Used in the Algorithm
Threshold Template0 0A =  0 20 00 0B =  0 00 0I

A.2

Figure 10: Character extraction from a road sign
image.
CONCLUSIONS

A.3

In this study, we proposed an image processing algorithm using periodic pattern formation in CNNs.
By computer simulations, we conﬁrmed that thisalgorithm could extract only important charactersfrom an image of a car and a road sign.
References[1] L.O. Chua and L. Yang, “Cellular Neural Networks: Theory,” IEEE Trans. Circuits Syst., A.4
vol.35, no.10, pp.1257-1272, Oct. 1988.
[2] T.Kozek,K.R.Crounse,T.Roska,andL.O.Chua, “Smart Image Scanning Algorithms for the CNN Universal Machine,”
International Symposium on Nonlinear Theory
and its Applications, vol.2, pp.707-712, 1995.
[3] Jun Kishida, Csaba Rekeczky, Yoshifumi Nishio
and Akio Ushida, ”Feature Extraction ofPostage Stamps Using an Iterative Approacht(7)Small Object Remover Template


1 1 1
A =  1 2 1 
1 1 1


0 0 0
B =  0 0 0 0 0 0I5=

00 0
00 0=0(8)Recall Template
0.5 0.5 0.5
A =  0.5 4 0.5 0.5 0.5 0.5

0 0 0
B =  0 4 0 
0 0 0
I=3(9)

Logic Diﬀerence Template


0 0 0
A =  0 2 0 
0 0 0

0 0 0
B =  0 −1 0 
0 0 0I=−1(10)