平成21年度電気関係学会四国支部連合大会

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18-5

Interpolation of Gap between Two Lines
by Cellular Neural Networks
Yasuhiro UEDA Masakazu KAWAHARA Takashi INOUE Yoshifumi NISHIO(Tokushima University)

1. Introduction
Cellular Neural Networks (CNN) were introduced byChua and Yang in 1988 [1]. The structure of CNN imitated the retina of the animal. The idea of CNN wasinspired from the architecture of the cellular automata
and the neural networks. A diﬀerent point from a common neural network has the feature that CNN has local
connectivity property. The performance of the CNN isdecided by template, and the contents of processing aredetermined by changing the parameter.
In this study, we propose a method to interpolate a gap
between two separate lines by using CNN. We consider
that such a task is a kind of the subjective contour, which
is one of optic illusions. Computer simulations show thatthe proposed method successfully performs the interpolation.

target center remains by this template. Then, the one
point and the input image are added. After this, we using
BP, CLF, and CPD to the new image again. Finally, theinterpolated image is obtained by adding the input image
again.

3. Simulation Results
In this section, an example of the interpolations using
the proposed algorithm is shown.

2. Proposed Method
In this section, we describe the proposed method. Stability of the templates in this study has been conﬁrmed
in [2].
First, make two lines thick by “Black Propagation” template.
Black P ropagation T emplate (BP )[ 0.25A=

0.25
0.25

0.25
30.25

0.25
0.25
0.25

[ 0.50.5
0.5

0.5
30.5

0.5
0.5
0.5

, B = 0, I = −1.

[ 1110400−10CEN T ER2[ 1A=1116010−1][ 0, B=00020000], I = 3.25.

], B = 0 , I = −1.

A=111061−101(d)(e)(f)], B = 0 , I = −2.

], B = 0 , I = −2.

Figure 1: Simulation results. (a) Input image. (b) Output
image of BP and CLF. (c) New input image. (d) Output
image of second BP and CLF. (e) Output image of secondCPD. (e) Final output image.
Figure 1(a) is the input image with two lines with a gap
between them. Figure 1(c) is the new input image obtained by adding the one point after BP, CLF, and CPD
and the original input image. Figures 1(b) and (d) are
output of BP and CLF. Figure 1(e) is the interpolated
two lines. Finally, we add Figs. 1(a) and (e) and obtainthe ﬁnal output image in Fig. 1(f). Although slight distortion is in the interpolated portion, the task is able tobe performed.

4. Conclusions
In this study, we proposed an algorithm using CNN tointerpolate a gap between two lines without the measurement of the angle by digital calculations. For the future,
we study more complicated processing imitating the subjective contour.

…

CEN[T ER8(c)

(1)

(2)
The template transforms all the objects to solid black concave polygons with vertical, horizontal and diagonal edges
only.
Thirdly, contour of a black object is gradually cut downwith “Center Point Detector” template.
Center P oint Detector (CP D)
CEN T ER1
A=(b)]This template extends black to every directions.
Secondly, the gap between the two thick lines is ﬁlled
by “Concave Location Filler” template.
Concave Location F iller T emplate (CLF )
A=(a)

(3)

By using the eight templates in order, the contour of a
black object is peeled gradually. Only one point of theReferences[1] L.O. Chua and L. Yang, “Cellular Neural Networks:
Theory,” IEEE Trans. Circuits Syst., vol. 32, no. 10,pp. 1257-1272, Oct. 1988.
[2] Cellular Sensory Wave Computers Laboratory, Computer and Automation Research Institute, Hungarian
Academy of Science, “Cellular Wave Computing Library(Templates, Algorithms, and Programs), version 2.1.”