2013 International Workshop on Nonlinear Circuits,Communications and Signal Processing
NCSP'13, Isrand of Hawaii, Hawaii, USA. March 4-7, 2013

Research of Cellular Neural Networks Inspired by Actual Friendship
Yoshihiro Kato, Yoko Uwate and Yoshifumi Nishio
Tokushima University
2–1 Minami Josanjima, Tokushima, Japan
Phone: +81-88-656-7470, FAX: +81-88-656-7471
E-mail: {kkato, uwate, nishio}@ee.tokushima-u.ac.jp

Abstract

2. Cellular Neural Networks

In previous study, we have proposed “Cellular neural networks with eﬀect from friend having most diﬀerent values
and its friends” (DF-CNN). The DF-CNN is the method ofconstituting a new connection of among cells in CNN. Especially in edge detection, the DF-CNN could detect mostedge including indistinct parts. In this study, we research
about edge detection by using the DF-CNN. First, we research about how eﬀective does the DF-CNN detect edge ofindistinct part compare with the conventional CNN using gradient images. Moreover, we discuss about relationship between function of the DF-CNN and results of edge detection.

The CNN has M by N processing unit circuits called cells.
The cell contains linear and nonlinear circuit elements.Cells
are arranged in a reticular pattern to M line N row. We represent a cell C(i, j) using a variable i which denotes verticalposition and a variable j which denotes horizontal position.
Each cell is connected to its neighboring cells according to atemplate. Usually, the template is the same for all cells except for boundary cells. The state equation and the output
equation of the CNN are shown as follows.
State equation :dv xi jdt

1. Introduction
Cellular Neural Networks (CNN) [1] were introduced byinspired from the cellular automata and the neural networks.
CNN has local connectivity property and it makes the CNN
tailor made for VLSI implementation. Then, the CNN has thefeatures of time continuity, spatial discreteness, nonlinearityand parallel processing capability. Furthermore, the structureof CNN resembles that of animals’ retina. Hence, CNN canbe used for various image processing applications.
In a previous study, we have proposed “Cellular neural networks with eﬀect from friend having most diﬀerent values
and its friends” (DF-CNN) [2]. The DF-CNN is the methodof constituting a new connection of among cells in CNN. Inparticular, connection of control template is determined byinput and output values and connection of feedback templateis determined by output values. Then, we confirmed that theDF-CNN could perform edge detection for general image anddivide domains. Especially in edge detection, the DF-CNN
could detect most edges including indistinct parts.
In this study, we research about edge detection by using
the DF-CNN. We research about how eﬀective does the DFCNN detect edge of indistinct part compare with the conventional CNN. In this comparison, we use gradient images
within black to white. Moreover, we discuss about relationship between function of the DF-CNN and result of edge detection.

=−v xi j +j+ri+r ∑∑A(i, j;k,l) vykl (t)k=i−r l= j−r+j+r
i+r ∑∑B(i, j;k,l) vukl (t) + I,(1)k=i−r l= j−r

Output equation :vyi j (t) =1(|v xi j (t) + 1| − |v xi j (t) − 1|),2

(2)where v x , vy and vu represent a state, an output and an inputof cell, respectively. In the Eq. (1), A is the feedback templateand B is the control template. These and the constant bias I
are collectively called general template. The output equation
is a piece-wise linear function. In fact, the output value ofCNN is within of −1 to 1. When the CNN is used for image
processing, values of black and white are treated as 1 and −1,respectively. r is a positive integer number. Each cell has(2r + 1)2 neighborhood cells. Hence, the size of templateis defined by r. If r is 1, the size of template is 3×3 matrix.
Additionally, if r is 2, the size of template is 5×5 matrix.
3. Cellular Neural Networks with Eﬀect from Friend
Having Most Diﬀerent Values and Its Friends
In this section, we explain the algorithm of the cellular neural networks with eﬀect from friend having most diﬀerent values and its friends (DF-CNN). The DF-CNN is the method of- 428 -constituting new combinations of among cells. In this pa- 3.2 In the Case of Control Template
per, we consider the local connection of CNN as friendship.
Then, in each cell, the neighboring cells are defined as friendcells. Based on this, the algorithm of DF-CNN is describedas follows.
3.1 In the Case of Feedback Template

Figure 3: Search the diﬀerent cell in input image.

Step 1: In each cell of input image, a cell with the mostdiﬀerent of the value of center cell C(i, j) in output image
is defined as “Diﬀerent cell” from eight neighboring cells inStep 1: In each cell of output image, a cell with the most input image like Fig. 3.
diﬀerent of the value of center cell C(i, j) is defined as “Different cell” from eight neighboring cells like Fig. 1.
Figure 1: Search the diﬀerent cell in output image.

(a)
(a)

(b)
Figure 4: New combination of control template. (a) The combination on centering on the diﬀerent cell. (b) Elements ofFigure 2: New combination of feedback template. (a) The new control template.
combination on centering on the diﬀerent cell. (b) Elementsof new feedback template.
Step 2: The combination centering on a cell C(i, j) ischanged into a combination centering on the diﬀerent cell like
Step 2: The combination centering on a cell C(i, j) is Fig. 4(a).
changed into a combination centering on the diﬀerent cell like
Moreover, the element of the control template of the diﬀerFig. 2(a).
ent friend and the center cell are replaced. With this, a new
Moreover, the element of the feedback template of the dif- combination is constituted like Fig. 4(b).
ferent friend and the center cell are replaced. With this, a new
combination is constituted like Fig. 2(b).
Step 3: The value of each cell is updated according tothe Eqs. (1) and (2) using the new combinations of control
Step 3: The value of each cell is updated according to templates.
the Eqs. (1) and (2) using the new combinations of feedback
Step 4: Steps 1 to 4 are repeated every 0.005 [τ].
templates.
Step 4: Steps 1 to 4 are repeated every 0.005 [τ].
Therefore, the value of each cell is updated by receiving
influences from the diﬀerent cell and its neighboring cells.
(b)- 429 -4. Evaluation of Edge Detection
In the previous study, we have confirmed that the DF-CNN
could perform edge detection for general image. The DFCNN could detect most edge including indistinct parts. In
this section, we evaluate performance of the DF-CNN foredge detection. We compare the DF-CNN and two types of
the conventional CNNs with “Edgedetection” templates of
3×3 and 5×5 matrices. In this evaluation, we call the conventional CNN with “Edgedetection” template of 3×3 matrix
and the conventional CNN with “Edgedetection” template of3×3 matrix as “T ype A (3 × 3)” and “T ype B (5 × 5)”, respectively. Input images include gradient and fixed values parts
which are shown Figs. 5(a) to (d). In every image, boundaryof two parts become indistinct as it goes top of the image.
Figure 6 shows simulation results of using the “T ype A (3×3)”. In any cases, edge of indistinct boundary is diﬃcult todetected. However, detected edge is fine line as 1-pixel-wide.
Figure 7 shows simulation results of using the “T ype B (5 ×5)”. The boundary of two parts is detected better than using
the “T ype A (3×3)”. However, detected edge is bold line as 2pixel-wide. We take this reason as that un-boundary cells aredetected as edge by using “Edgedetection” template of 5×5
matrix. On the other hand, Fig. 8 shows simulation resultsof using the DF-CNN. We can see that the DF-CNN detect
indistinct portion better than the “T ype A (3 × 3)” and thedetected edge is fine line.

Figure 5(a)Figure 5(b)Figure 5(c)Figure 5(d)

(a)

(b)

(c)

(d)

Figure 5: Input images. (a) Gradient (white to whitish gray)and white. (b) Gradient (black to blackish gray) and black.
(c) Gradient (gray to whitish gray) and gray. (d) Gradient(gray to blackish gray) and gray.

(a)

(b)

(c)

(d)

Figure 6: Simulation results using the “T ype A (3 × 3)”.
(a) Output image for Fig. 5(a). (b) Output image for Fig. 5(b).
(c) Output image for Fig. 5(c). (d) Output image for Fig. 5(d).

Table 1: Detection Rate [%]DF-CNN Type A (3×3) Type B (5×5)
56.25
25.00
73.34
67.18
33.59
82.03
64.84
33.59
80.47
69.53
33.59
83.59

(a)
(b)
(c)
(d)
Table 1 shows the detection rate of each input image using
the DF-CNN, the “T ype A (3 × 3)” and the “T ype B (5 × 5)”. Figure 7: Simulation results using the “T ype B (5 × 5)”.
Ideal edge is assumed as a 1-pixel-wide line on the boundary (a) Output image for Fig. 5(a). (b) Output image for Fig. 5(b).
of two domains. And we evaluate each types by the ideal edge (c) Output image for Fig. 5(c). (d) Output image for Fig. 5(d).
as 100 [%] of baseline. From Tab. 1, the “T ype B (5 × 5)” hasdetection rate by it can detect indistinct portion in every cases.
However in fact, detected edge is bold line as 2-pixel-wide.
Then, the detection rate will decrease considering this point.
On the other hand, we can say that the detection rates of theDF-CNN are improving about two times compared with the“T ype A (3 × 3)”.
5. Change the Rank of Determine Diﬀerent Cell(a)

(b)

(c)

(d)

In the proposed algorithm, a cell with the most diﬀerent of Figure 8: Simulation results using the DF-CNN. (a) Output
the value of center cell C(i, j) is defined as diﬀerent cell. In image for Fig. 5(a). (b) Output image for Fig. 5(b). (c) Output
this section, we investigate output characteristics for the cases image for Fig. 5(c). (d) Output image for Fig. 5(d).
of other cell is defined as the diﬀerent cell like a cell with 2nd
to 8th diﬀerent values, respectively.

- 430 -(a)

(e)

(b)

(f)

(c)

(g)

(d)
(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(h)

Figure 9: Simulation results for Fig. 5(c). (a) Case of themost diﬀerent cell. (b) Case of 2nd diﬀerent cell. (c) Case of
3rd diﬀerent cell. (d) Case of 4th diﬀerent cell. (e) Case of
5th diﬀerent cell. (f) Case of 6th diﬀerent cell. (g) Case of
7th diﬀerent cell. (h) Case of 8th diﬀerent cell.

Figure 9 shows simulation results of using Fig. 5(c) as input image. In Figs. 9(a) to (c), there is not much diﬀerence
between output images by cases of most, 2nd and 3rd diﬀerent cells, respectively. This reason is assumed be due to thatvalues of the most to 3rd diﬀerent cells are same side becauseof two parts are divided in to right and left side in Fig. 5(c).
On the other hand, the boundary is not detected in Figs. 9(d)and (e). However, the boundary is detected in Figs. 9(f) to (h)although value of cells are not converged.
Case of using Fig. 5(c) as input image has image dependence. Then, we use general image (Fig. 10(a)) as input image. Figures 10(b) to (i) show simulation results. Figure 10(b)shows output image by using the DF-CNN that defines a cellwith the most diﬀerent value as the diﬀerent cell. Most edge
is detected and value of cell is converged. Figures 10(c) to (i)show output images by cases of other cell is defined as the different cell, respectively. In every cases, each cell can obtain
informations from the 2-neighborhood. Thus, boundary ofindistinct portion is estimated at edge. However, convergenceof cell is diﬃcult as the diﬀerent cell is chosen from nearest
value of cell. Even if all un-converged cell converged, somenoises are left and detected edge is bold line.

Figure 10: Simulation results for general image. (a) Input
image. (b) Case of the most diﬀerent cell. (c) Case of 2nd
diﬀerent cell. (d) Case of 3rd diﬀerent cell. (e) Case of 4th
diﬀerent cell. (f) Case of 5th diﬀerent cell. (g) Case of 6th
diﬀerent cell. (h) Case of 7th diﬀerent cell. (i) Case of 8th
diﬀerent cell.

investigated output characteristics for the cases of other cellis defined as the diﬀerent cell like a cell with the 2nd to 8th
diﬀerent value, respectively. From these investigations, wecould say that the DF-CNN choose a cell with most diﬀerent
value is the method which eﬀectively obtain the value fromthe 2-neighborhood. In the future work, we would like to try
another determining condition of the “Diﬀerent cell”.
Acknowledgment

This work was partly supported by JSPS Grant-in-Aid forFrom these investigations, we can say that the DF-CNN
Young Scientists 23700269.
choose a cell with most diﬀerent value is the method whicheﬀectively obtain the value from the 2-neighborhood.
References
6. Conclusions[1] L. O. Chua and L. Yang, “Cellular Neural Networks: Theory,” IEEE
Trans. Circuits Syst., vol. 32, pp. 1257-1272, Oct. 1988.

In this study, we have researched about edge detection byusing the DF-CNN. First, we investigated about how eﬀective
does the DF-CNN detect edge of indistinct part compare withthe conventional CNN using gradient images. Moreover, we[2] Y. Kato, Y. Uwate and Y. Nishio, “Cellular Neural Networks with Effect from Friend Having Most Diﬀerent Values and its Friends,” Proc.
of APCCAS’12, pp. 495-498, Dec. 2012.

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