平成 26 年度電気関係学会四国支部連合大会 講演論文集 （2014 徳島大学）
2014 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (TOKUSHIMA)

1-17Cellular Neural Networks with Delay Output for Edge Detection
Taro NAKANO Tatsuya MASUOKA Yoko UWATE Yoshifumi NISHIO(Tokushima University)

1. Introduction

3. Simulation Result

In this study, we apply Cellular Neural Networks (CNN)with delay output (D-CNN) to image processing (edge detection). The D-CNN does not depend on only the current
information, however it processes an image after having
considered the past information. In a general way, the DCNN is applied motion image processing. On the otherhand, we applied it to image processing (edge detection).
We investigate how the D-CNN influenced image processing. As a result, we can obtain eﬀective results in theimage processing using the D-CNN.

Figure 2 shows simulation results of edge detection. Dtemplate has a characteristic of binary image representing
the concentric black and white rings.
Using template :A=

D=2. D-CNN
The state and the output equation of the cell are shownas follows. The state equation contains feedback template with time delay. The conventional CNN performs
image processing only depending on current information.
Though the D-CNN performs image processing depending
on not only current but past information.
State equation :
dvxij
dt

=−vxij +j+ri+r
∑
∑0
 00



0
 −10



0−10  , B =  −1
0−10
1
0−1
3.5−1



−1
8−1



−1−1  ,−10−1  , T = −1.
0

(a)

(3)

(b)

A(i,j;k,l) vykl (t)k=i−r l=j−r+j+ri+r∑∑

B(i,j;k,l) vukl (t)k=i−r l=j−r+j+ri+r∑∑D(i,j;k,l) vykl (t − τ) + T. (1)(c)=1(|vxij (t) + 1| − |vxij (t) − 1|).
2(e)result of the conventional CNN. (c) Simulation result of the DCNN (τ = 5). (d) Simulation result of the D-CNN (τ = 10).
(e) Simulation result of the logical diﬀerence in the D-CNN.

Output equation :vyij (t)(d)

Figure 2: Simulation results. (a) Input image. (b) Simulation

k=i−r l=j−r(2)
Figure 2(a) shows an input image. In the characteristicof an input image, the boundary of the pillar and background are indistinct. Figure 2(b) shows the result of theconventional CNN. The conventional CNN can not detect
indistinct parts. Figures 2(c) and (d) show results of theD-CNN. In the D-CNN, the boundary of the pillar andbackground can detect indistinct parts. Moreover we investigate how processing changed when we change delaytime. Figure 2(e) shows logic diﬀerence from τ = 10 to 5.
By the Fig. 2(e), even if delay time change, it detects littlediﬀerences are visually. The D-CNN can detect indistinct
parts of input image in edge detection.

Figure 1 shows block diagram of the D-CNN. In thestate equation, A is the feedback template, B is the control template, T is the bias and D is delay type feedbacktemplate. D template can substitute the value with various characteristics. From the above reason, it can expect
various image processing.

4. Conclusions
In this study, we applied the D-CNN to image processing (edge detection). The D-CNN adds a past output
value by feedback template. From simulation results, theD-CNN can detect indistinct parts of image. The D-CNN
has an eﬀective influence on image processing.

Figure 1: Block diagram of the D-CNN.

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