Robust design of dilation and erosion CNN for gray scale image

Abstract

ABSTRACT The cellular neural/nonlinear network (CNN) is a powerful tool for image and video signal processing, as well as robotic and biological visions. The designs for CNN templates are one of the important i ssues for the practical applications of CNNs. This paper combines two CNN to implement the D ilation CNNs and Erosion CNN for gray scale images and proposes two theorems of robustness designs. The parameters of the templates can range between a hyper plane and a hyper surface in the first quartile. The simulations have been given. The results show the effectiveness of the theoretical results to be implemented in computer simulations. Keywords: Cellular neural network, Robust Design, Dilation, Erosion. 1. INTRODUCTION The CNN was firstly introduced by Chua & Yang [1,2] in 1988. Its original intention is to find out a structure of neural network easier to implement than the Hopfield neural networks[3], which requires fully-connected and grows exponentially with the size of the array. Now CNN has played important roles in many fields such as image and video signal processing, robotic and biological visions, and data prediction[3-8]. In an analog cellular neural network, the parameter levers usually have 5% ý 10% of perturbation [9]. So the robustness designs for CNN template parameters are important for the practical applications of CNN. Chua and Dogaru [3,5] have studied the robust designs of a large kind of CNN-uncoupled Boolean CNNs, which provides optimal design schemes for CNNs with prescribed tasks. Since then, some robust designs for uncoupled and coupled CNNs have been studied (for example see [10-20]), which have been used in image processing and pattern recognitions. Dilation CNN and Erosion CNN for binary image is proposed in Chua and Roska’s book[6]. Then Shu Jian[21] et al. designed the robust of them and proposed two theorems to guarantee the parameters of the templates can perform prescribed dilation or erosion CNN. The pa rameters of templates in [21] will range according the image. In this paper, we separate the original local rules of dilation or erosion CNN into two local rules, then we set up two parameters inequalities of templates to perform each local rules. The parameters of our templates need not range according the image, and parameters values of each template range between one hyper plane and hyper surface. The rest of this paper has organized as follows. Section 2.1 introduces the robust designs of the CNN. Section 2.2 describes and proves two local rules of the Combination C NN which implements the dilati on CNN for gray scale image. Section 2.3 describes and proves two local rules of the Combination CNN which implements erosion CNN for gray scale image. Section 3 gives the examples of the combination CNN. Conclusions have been addressed in Section 4.