平成22年度電気関係学会四国支部連合大会

310

18-11

CNN Template Learning by BPwith Annealing Noise
Masashi NAKAGAWA Yoko UWATE Yoshifumi NISHIO(Tokushima University)

Cellular Neural Networks(CNN) were introduced byChua and Yang in 1988. The idea of CNN was inspired
from the architecture of the cellular automata and theneural networks. The CNN can be used for various image processing application. The output image of CNN isdecided by the parameter called a template. Therefore, atemplate is the most important parameter in CNN. However, there is a problem that the design of the suitabletemplate for obtaining the ideal output image is diﬃcult.
Then, some template designs are proposed, for example,
Genetic Algorithm (GA) is representative.
In the previous study, we proposed template learningsof CNN using Back Propagation Algorithm (BP), andestimated the accuracy of learning [1]. Concretely, we
designed the template of CNN dynamically, by BP learning using the error between the output image and theideal image. Furthermore, we conducted more detailed
investigation by changing the number of learning times
and the learning rate in BP, we verified better conditionsof template designs.
However, there is a problem in BP that a solution sinks
into local minima, cannot reach the optimal solution. So,in this study, we add annealing noise inspired from Simulated Annealing (SA) to BP. We add annealing noiseat the time of renewal of a template in BP learning, weverify the conditions which slip out of local minima, andreach the optimal solution.

2. Proposed Algorithm

In SA, influence on search of a solution is reduced bydecreasing the temparture parameter T according to theschedule. So, in this study, we replace time line with
the number of learning times. Therefore, the more thenumber of learning times increase, the less adding noisedecreases.
We add annealing noise  to renewal equation of template.
RenewedBef ore= (A, B)

Figure 1: Input image.
Ideal image:

Figure 2: Ideal image.
The error curve is shown in Fig. 3. In this study, wechange two parameters; the number of learning times andthe learning rate. Three lines in Fig. 3 show the error ofrespective learning rates. The horizontal axis shows thenumber of learning times and the vertical axis shows theerror between the ideal image and the output image. We
set the value of “SN ratio” as 0.1 and the value of random
noise from −1.0 to 1.0.
45
0.1
0.25
0.5
40

35

30

We define annealing noise  as follow.
()
Current learning times
 = “SN ratio” × 1 −T otal learning times
×“random noise”,(1)(A, B)An example of an input image and its ideal image areshown in Figs. 1 and 2, respectively.
Input image:Error [%]1. Introduction+ D + ,(2)where, (A, B) is template, D is renewal quantity of template.
We verify whether the annealing noise prevent fromlapsing into local minima and being able to obtain theoptimal solution.

3. Simulation Results
In this section, we show error between the ideal image
and the output image obtained from learning results.

2520
0200

400600
Learning times

8001000

Figure 3: Error curve.
Fig. 3 shows three results. First, the bigger learning
rate set, the bigger error appears. Second, in the case oflearning rate “0.5”, all of the errors are big. Third, when
the number of learning times from 250 to 500, the error
tend to become small. However, all of errors are so big,
we have to improve our proposed method.

4. Conclusions
In this study, we have added annealing noise to BP,
and we verified its eﬀect by computer simulation. From
the results, we verified the good conditions of parameter.
However, all of errors are so big, we have to improve ourproposed method. Improving the method to obtain thesmaller error, and for more complicated images is ourimportant future works.
Reference[1] M.Nakagawa, T.Inoue and Y.Nishio, “CNN Template
Design Using Back Propagation Algorithm,” Proc. ofCNNA’10, pp. 47-51, Feb. 2010.