令和2年度電気・電子・情報関係学会四国支部連合大会 講演論文集 (愛媛大学)
2020 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (EHIME UNIV.)

1-10Cellular Neural Network:
Template Switching using Bistable-like Memristors
Pierre BINET, Yoko UWATE, and Yoshifumi NISHIO(INSA Toulouse/Tokushima University, Tokushima University, Tokushima University)
1. Introduction

3. Simulation Result

The Cellular Neural Network (CNN) is a network of simple analog cells that have local interactions with each otherin a defined neighborhood. These interactions are definedby templates which control input, output, as well as a
threshold value. The behavior of the network as a wholedepends largely on the propagation phenomenon and thevalue of these templates. Results diﬀer greatly with theneighborhood size: the 5x5 neighborhood brings noise to
the output while the 3x3 neighborhood lacks in precision.
Past researches investigated methods to bring the best of
two neighborhood sizes by allowing each cell of the CNN
to switch between 3x3 and 5x5 templates, using its output voltage to decide if it should switch. In this study,
we propose a new switching method using the Memristor
CNN (M-CNN) and switching depending on the value ofthe memristance state.

In this study, we tried to assess the result precision of
the new M-CNN template switching compared to the original center cell switching method, and to the original 5x5neighborhood methods, on the field of edge detection. As
can be seen on Fig. 1, the new method brings more detailcompared to all previous methods.

(a)

(b)

2. Proposed Method
We use the M-CNN which behavior is described by thefollowing set of co-dependent Ordinary Diﬀerential Equations (ODE):

Cx(ij)+dvx(ij) (t)vx(i,j) (t)vx(i,j) (t)+=−dtxm(i,j)xm(i,j) (t)∑∑A(i, j; k, l) ∗ vy(k,l)

Cell(k,l)∈Nr (i,j)+

B(i, j; k, l) ∗ vu(k,l) + I ∗ z(1)Cell(k,l)∈Nr (i,j)

dxm(i,j) (t)= k(vx(i,j) (t)) ∗dt
xm(i,j) (t) − xon
1−(− step(vx(i,j) (t)))2p
xof f − xon

Edge detection template. (c) Edge detection using the originalcenter cell method. (d) Voltage output simulation result of theproposed method.

4. Conclusion(2)

withk(vx(i,j) (t)) = −β ∗ vx(i,j) (t) +β−α
∗ (|vx(i,j) (t) + V t| − |vx(i,j) (t) − V t|)2(c)(d)
Figure 1: Simulation results. (a) Input image. (b) Simple 5x5(3)

We set the α and β parameters so that β/α > 1015 , resulting in bistable-like memristors with fast, step-functionlike switching characteristics between their low memristance state xon and their high memristance state xof f [1].
Inspired by the center-cell method investigated in previous
researches [2], we define a 7x7 neighborhood around a celland follow the next steps:
Step 1: In the neighborhood, find the average memristance state xavg (either xon or xof f ).
Step 2: Determine the center cell memristance state xm
Step 3: If xm = xavg , then switch to the 3x3 template. In
the other case, switch to the 5x5 template.
We apply these steps for every cell of the M-CNN and repeatthem every 0.005τ .

In this study we have proposed and demonstrated theabilities of a new method for template switching inside
the CNN, using the sharp switching characteristics of thebistable-like Memristor to bring more details to the output.
Future works include focusing on diﬀerent image analysis
templates, as well as understanding the impact of other
Memristor parameters to the output result.
References[1] R. Tetzlaﬀ, A. Ascoli, I. Messaris and L. O. Chua, ”Theoretical Foundations of Memristor Cellular Nonlinear Networks:
Memcomputing With Bistable-Like Memristors,” in IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 67, no.
2, pp. 502-515, Feb. 2020, doi: 10.1109/TCSI.2019.2940909.
[2] T. Ando, Y. Uwate and Y. Nishio, ”Image processing by
cellular neural networks with switching two templates,” 2017
IEEE Asia Pacific Conference on Postgraduate Research in
Microelectronics and Electronics (PrimeAsia), Kuala Lumpur,
2017, pp. 41-44, doi: 10.1109/PRIMEASIA.2017.8280359.