平成20年度電気関係学会四国支部連合大会

409

17-40

Improvement of Two-Layer Cellular Neural
Networks for Edge Detection
Masakazu KAWAHARA Takashi INOUE Yoshifumi NISHIO(Tokushima University)

1. Introduction

Diffusion template in the CNN :Cellular Neural Networks (CNN) were introduced byChua and Yang in 1988. The idea of the CNN was inspired
from the architecture of the cellular automata and the neural networks. The CNN has local connectivity property.
The former two-layer CNN had a feedforward multilayer CNN structure. The first layer and the second layer
influenced reciprocally.
In this study, we propose an improvement of two-layer
CNN for edge detection. We show effective edge detection
using the proposed two-layer CNN. Also, we obtain interesting result by feeding back the edge detection image toanother layer.
The state equation of the cell in the proposed two-layer
CNN are described as follows.
State equation of the first-layer :=−vx1ij +j+ri+r
X
X

A=

0.1
0.15
0.1

0.15
0
0.15

0.1
0.15
0.1

#"

,B =000000000#, I = 0.(4)Edge detection template in our two-layer CNN :The first layer template

"

A1 =

0.1
0.15
0.1

0.15
00.15

#0.1
0.15
0.1

"

000, B1 =The second layer template

"

A2 =

2. Proposed Two-Layer CNN Model

dvx1ij
dt"

11
1

1
3
1

1
1
1

#

"

, B2 =

Coupling template

"

C=

0.05
0.05
0.05

0.05
−0.4
0.05

0
00

0.05
0.05
0.05

00
0

00
00
0
0

000

#

, I1 = 0#, I2 = 0.1

#.

(5)

A1 (i, j; k, l)vx1kl (t)k=i−r l=j−r+j+ri+rXX

B1 (i, j; k, l)vu1kl (t)k=i−r l=j−r+j+ri+rX
XC(i, j; k, l)vy2kl (t) + I1 . (1)k=i−r l=j−r

(a)

(b)

(c)

State equation of the second-layer :dvx2ijdt=−vx2ij +j+ri+rXX

A2 (i, j; k, l)vx2kl (t)k=i−r l=j−r+j+ri+rXX

B2 (i, j; k, l)vu2kl (t) + I2 . (2)(d)

k=i−r l=j−r

In our two-layer CNN, we input an image to the firstlayer. Next, we calculate difference of output values ofthe first layer at different times, and the calculated value
is inputed to the second layer.
Difference of output value in the first layer :vu2ij = vy1ij |t=∆τ − vy1ij |t=0 .

(3)

Finally, the output of the second layer is feedbacked to
the first layer via the coupling template C. Namely, ourtwo-layer CNN has two features. The first feature is thatthe coupling template is used only from the second layer tothe first layer. The second feature is that the calculation
start time of the second layer is later than that of the firstlayer.

3. Simulation Results

In this section, we show effective edge detection result
and interesting result using our two-layer CNN. In thissimulation, ∆τ in Eq.(3) is set to 0.05.

(e)Figure 1: Simulation results. (a) Input image.
(b) Edge detection result using the CNN. (c) Diffusion result using template (4). (d) Output image of
second layer in our two-layer CNN. (e) Output imageof first layer in our two-layer CNN.
From these results, we can see that the edge detection
result is more effective than the conventional CNN. Also,
diffusion image is influenced to the edge detection image
and obtain interesting result like Fig.1(e).

4. Conclusions

In this study, we proposed an improvement of two-layer
CNN for edge detection. We investigated output characteristics of our two-layer CNN and obtain interesting result
by computer simulation.