RISP

NCSP’16

International Workshop on
Nonlinear Circuits, Communications and Signal Processing

Honolulu, Hawaii, USA, March 6-9, 2016

Cellular Neural Networks with Changing Templates for Edge Detection and Half-Toning
Shohei Gotoda,† Yoko Uwate,† and Yoshifumi Nishio††Dept. of Electrical and Electronic Engineering, Tokushima University
2-1 Minami-Josanjima, Tokushima 770–8506, Japan
Email: {shohei, uwate, nishio}@ee.tokushima-u.ac.jp

Abstract

2. Cellular Neural Networks

In 1998, Cellular Neural Networks (CNN) were introduced.
The performance of the CNN depends on the parameters
called the template. If the template is influenced by the spacially and the temporally variation, CNN can perform complex processing. In this study, we propose a new method ofchanging templates. We apply the pseudoramdom numbers totemplate, the template is changed spacially and temporally.
We investigate the performance of the proposed method bysome simulations.

A basic unit circuit of CNN is called a cell. The cell contains linear elements and nonlinear elements. CNN is formed
from an array in a reticular pattern of many cells. We show
a two dimensional array composed of M × N identical cells
arranged in M rows and N columes.

1. Introduction
In recent years, many information has been increasing.
Generally, the von Neumann machine is used for many information processing. However, the von Neumann machine
cannot process information at a time. The Neural Networks
were proposed to solve this problem. This idea was based on
the human’s nervous system. The Neural Network is used inevery direction, such as an associative memory, pattern recognized, and so on. In 1998, the idea of CNN (Cellular Neural Networks) was inspired from the architecture of the Neural Networks and the Cellular Automata by L. O. Chua andL.Yang. [1]. The structure of CNN resembles the structure ofanimal retina. Therefore, CNN has been suitable for various
image processing. The performance of CNN depends on theparameters called the template. [2]- [5] The template has afeature that is not influenced by the spatially and temporallyvariation. This feature causes that CNN cannot complex processing. If the template is influenced by the spacially and thetemporally variation, CNN can perform complex processing.
In this study, we propose a new method of changing template of the CNN. We apply the pseudoramdom numbers totemplates in our method. We fix the range of the pseudorandom numbers and every constant additional number of times.
In order to confirm the effectiveness of the proposed method,
we perform some simulations in image processing by using
the proposed method. We compare our method with the conventional method for edge detection and half-toning.

Figure 1: Structure of CNN (3 × 3).

vu- 606 -BT-1

Σ∫dt vxf(･)AFigure 2: Block diagram of the conventional CNN.

vyA cell couples with only adjacent cells. Adjacent cells interact with one another. One cell receives information fromadjacent cells and indirect cells. The neighborhood determines the range, which one cell receives information. We
describe a state equation of the cell and an output equation ofthe cell below.
State Equation :
dvxij
dt

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

B(i,j;k,l) vukl (t) + T.

(1)

The example of the proposed method templates :
a11 + α11 a12 + α12 a13 + α13
A =  a21 + α21 a22 + α22 a2n + α23 a31 + α31 a32 + α32 a33 + α33
b11 + β11 b12 + β12 b13 + β13
B =  b21 + β21 b22 + β22 b23 + β23  (3)b31 + β31 b32 + β32 b33 + β33
αmn and βmn are pseudorandom numbers. Tp is every theconstant number of times. There are some problems to fix therange and the constant number of times.

k=i−r l=j−r

Output Equation :vyij(t)=vu
1(|vxij (t) + 1| − |vxij (t) − 1|).
2(2)mnBT-1Σ∫dt vx

vx , vy and vu are the state value, the output value and theinput value. In Eq (1), A is a feedback template, B is a feedforward template, T is a threshold. These values determine
the performance of CNN.

f(･)

vyA
mn

Figure 4: Block diagram of the proposed method.

4. Simulation Results
4.1 Edge Detection

Figure 3: Strucure of CNN.
The template has a feature that the spatial and the temporal
influence cannot effect the template. Therefore, the templatecannot perform complex processing. The template can perform complex processing in the adverse feature. We focus onthat feature.
3. Proposed Method
In this section, we explain CNN with changing templates.
The pseudorandom number is added to templates every theconstant number of times for changing templates. The range
and the adding number of times differ the kind of image
processing. The example of the proposed method templates
shows Eq. (3),In this section, we show simulation results of the edge detection by using our proposed method. Using templates of theedge detection is described as follows.
Edge detection template :
0 0 0A =  0 1 0 ,0 0 0
−1 −1 −1B =  −1 8 −1  , T = −1.
(4)−1 −1 −1
Edge detection template of the proposed method :
000
A =  0 1 + α 0 ,000
−1 + β −1 + β −1 + β
B =  −1 + β 8 + β −1 + β  , T = −1.(5)−1 + β −1 + β −1 + β- 607 -Figure 6(a) is an input image. To detect buildings inthe lower right of the image is difficult for the conventional
method of CNN. In the Fig 6(b) cannot detect buildings by theconventional method of CNN. However, the proposed methodof CNN can detect buildings in the Fig 6(c).
4.2 Half-toning
(a)

(b)

(c)
Figure 5: Simulation results. (a) Input image. (b) Simulation result of theconventional CNN. (c) Simulation result of the proposed method (Tα = 1,-0.2 ≤ α ≤ 0, Tβ = 5, 0 ≤ β ≤ 0.1.).
Figure 5(a) is an input image. The input image has indistinct portions. Indistinct portions are the pillar of the leftside and an outline of a woman’s face. Figure 5(b) shows thesimulation result of the conventional CNN. The conventional
CNN can not detect edge lines of indistinct portions. Figure 5(c) shows the simulation result of the proposed method.
In Fig. 5(c), the proposed method can detect edge lines ofindistinct portions.

(a)

In this section, we show simulation results of the halftoning by using our proposed method. Using templates of
the half-toning is described as follows. (0 ≤ ξ ≤ 1)
Half-Toning template :−0.07 −0.1 −0.07
A =  −0.1 1 + ξ −0.1  ,−0.07 −0.1 −0.07

0.07 0.1 0.07
B =  0.1 0.32 0.1  , T = 0.
(6)0.07 0.1 0.07
Half-Toning template of the proposed method :−0.07 −0.1 −0.07
A =  −0.1 2 + α −0.1  ,−0.07 −0.1 −0.07

0.07 + β 0.1 + β 0.07 + β
B =  0.1 + β 0.32 + β 0.1 + β  , T = 0.(7)0.07 + β 0.1 + β 0.07 + β

(b)

(a)

(b)

(c)

(c)

Figure 6: Simulation results. (a) Input image. (b) Simulation result of theconventional CNN. (c) Simulation result of the proposed method (Tα = 1,-0.16 ≤ α ≤ 0, Tβ = 5, 0 ≤ β ≤ 0.1).

Figure 7: Simulation results. (a) Input image. (b) Simulation result of theconventional CNN. (c) Simulation result of the proposed method (Tα = 4,-1.0 ≤ α ≤ 0, Tβ = 4, -0.01 ≤ β ≤ 0).

- 608 -Figure 7(a), around of the eyebrow and the whisker are
difficult to express the continuous tone imagery through theuse of dots by the proposed method of CNN. The proposed
method of CNN cannot express shades of color in theFig 7(b). However, Fig 7(c) can express clearly shades ofcolor by the proposed method of CNN.

results of the edge detection, our method can detect many indistinct portions. Our method can express shades of color
from the results of the half-toning. Hence, the proposed
method is more effective than the conventional CNN in image
processing.
References[1] L. O. Chua and L. Yang, “Cellular Neural Networks:Theory,” IEEE Trans. Circuits Syst., vol. 35, pp. 12571272, Oct. 1988.
[2] Martin Hänggi and George S Moschytz, “Cellular Neural Networks Analysis, Design and Optimization.“ Kluwer Academic Publishers.

(a)[3] F. Dirk and T. Ronald, “Coding of Binary Image Data
using Cellular Neural Networks and Iterative Annealing,”
Proc. of ECCTD‘03, vol. 1, pp. 229-232, Sep. 2003.

(b)[4] Z. H. Yang, Y. Nishio and A. Ushida, “Image
Processing of two-layer CNNs -applications andstability-,”IEICE. Trans. Fundamentals, vol. E85A, no. 9. pp. 2052-2060, Sept. 2002.

(c)[5] T. Kozek, K. R. Crounse, T. Roska and L. O. Chua,“Smart Image Scanning Algorithms for the CNN Universal Machine,” Proc. of NOLTA’95, vol. 2, pp. 707712, 1995.

Figure 8: Simulation results. (a) Input image. (b) Simulation result of theconventional CNN. (c) Simulation result of the proposed method (Tα = 3,-0.7 ≤ α ≤ 0, Tβ = 3, -0.06 ≤ β ≤ 0).

[6] Y. Kato, Y Uwate and Y Nishio, “Cellular Neural Networks with Switching Two Types of Templates,” Proc. ofIJCNN‘aa,pp. 1423-1428, Jun. 2011.

Figure 8(a) is a specialty image, which gray scale is ex- [7] L. Kek, K.Karacs and T .Roska, “Cellular Wave Computing Library(Templates, Algorithms, and Programs), Verpressed clearly in one image. Therefore, we can evaluatesion 2.1, ” Cellular Sensory Wave Computers laboratory,
whether to express clearly shading of color or not. The
Hungarian Academy of Sciencesk, Budapest, Hungary,conventional method of CNN can express white zone and2007.
black zone widely in the Fig 8(b). In the Fig 8(c), whitezone and black zone are expressed narrow by the proposed
method. From those results, the proposed CNN is more
effective than the conventional method of CNN in edge
detection and half-toning.
5. Conclusion
The template is the most important for the CNN. If the template is influenced by the spacially and the temporally variation, CNN can perform complex processing. Therefore, wefocus on template to improve CNN. In this study, we haveproposed the new method of changing templates. We applied
the pseudoramdom numbers to templates in our method. Inorder to confirm the effectiveness of the proposed method, weinvestigated the proposed method in image processing. We
performed the edge detection and the half-toning. From the- 609 -