平成19年度電気関係学会四国支部連合大会

395

17-65

Advanced Edge Detection Using Small World
Cellular Neural Network
Masaru NAKANO(Tokushima University)

Yoshifumi NISHIO(Tokushima University)

1. Introduction
A few years ago, Tsuruta et al. have proposed Small
World Cellular Neural Networks (SWCNN). SWCNN is thesystem that shortcut connections are introduced into theoriginal CNN and can be applied to some image processing tasks. We have investigated the performance of theSWCNN by changing the structure of the network keeping
the number of all branches same and have clariﬁed that
the SWCNN can realize edge detection of gray scale images. In this study, we propose a new SWCNN system forbetter edge detection of gray scale images.

-0.1 0.4 0.1
0.2 0.3 0.5
0.4 0.3 0.6

(a)

(b)

Figure 1: An example of Nr0 (i, j) of C(i, j) with neighbor-ing inputs (a). (a) Neighboring inputs. (b) Nr0 (i, j).

2. Proposed SWCNN Model
The CNN has nonlinear processing units called cells.
Cells are arranged in a reticular pattern to M lines and Nrows. We represent a cell C(i, j) using i which denotes vertical position and j which denotes horizontal position. The
state equation of the cell and parameters for edge detectionin the proposed SWCNN system are as follows.
State Equation:ẋij (t) = −xij (t) + I

X+A(i, j; k, l)ykl (t)C(k,l)∈N 0 r(i,j)

X−¯¯− C0 × ¯¯

B(i, j; k, l)ukl

C(k,l)∈N 0 r(i,j)

X

C(k,l)∈N 0 r(i,j)¯¯
C(i, j; k, l)ukl (t)¯¯.

(1)Parameters for edge detection:"
A=B=000010000#"−1−1−1,C =−1
8−1−1−1−1#004400,

44−40h4 0 −4 i h4−4−4,40044440−40−4−4,

04i h4,0−4040440−440−4,

44−4004i h0,

In this section, we explain the ﬂow of proposed method.
First, we perform the 8 diﬀerence processing with theSWCNN system and we get the ﬁrst 8 output images.
Next, we perform noise reduction from the ﬁrst output
images and we get the second output images. Next, we
perform or operation for 8 second output images and weget ﬁnal output image (Fig. 2 (b)).
Figure 2 shows the simulation result. Input imageis Fig. 2(a). We set the parameters as follows for thissimulation. umin = 0.001, umax = 0.2, Lm = 4, C0 =0.8. From the result, the complex hair edge lines can bedetected by the proposed system.

−4−440−4440,

iIn the state equation (1), Nr0 (i, j) describes the set ofneighboring cells which C(i, j) has. Nr (i, j) denote neighboring cells in the conventional CNN and is described by
the following equation.
Nr (i, j) = {C(k, l)| max |k − l|, |l − j| < r,
1 < k < M; 1 < l < N}

(2)

In the proposed SWCNN system, Nr (i, j) are changed according to the following condition (4).
umin ≤ |uij − ukl | ≤ umax

4. Simulation results, I = −1.

h−4 0 4 i h−4 −4 0 i h−4 −4 −4 i h0 −4 −4 i−4−4method has 8 diﬀrent sets, the ﬁnal output image is obtained by combining 8 output images. In the state equation (1), the 5th term decreases the unfavorable ingredientin output image. C0 is the parameter controling the eﬀectof this operation.

(3)

If the input ukl of neighboring cells C(k, l) satisﬁes theabove condition, the connections must be reconnected toshortcuts that have the same directions with the old connections with the distance Lm. Figure 1(b) shows an example of Nr0 (i, j) when the neighboring input of Fig. 1(a)is given to C(i, j). Since the template B for the proposed(a)(b)Figure 2: Simulation results of edge detection using theproposed SWCNN system. (a) Input image. (b) Output
image using the proposed SWCNN system.

4. Conclusions
In this article, we have proposed a new SWCNN system
and investigated the features and the usefulness. We haveapplied the proposed SWCNN to edge detection of grayscale images and we clariﬁed that the proposed SWCNN
system realized to detect the complex hair edge lines.
Reference[1] L.O. Chua and L. Yang, ”Cellular Neural Networks:
Theory And Applications,” IEEE Trans. Circuits & Syst.,
vol. 35, pp. 1257-1290, Oct. 1988.