Abstract: Stability is of great importance in the research of Cellular Neural Networks（CNN）.Some references have shown that not all CNNs are completely stable.Several CNN templates give rise to an oscillatory periodic steady state，while others even exhibit an eternally transient phenomenon called chaos.In this paper，several mathematical criteria are proposed for complete stability of CNN，then primary application of image segmentation is introduced.Experimental results demonstrate that CNN has great advantages over traditional arithemetic operators（Prewitt，Sobel，Canny） respectively，which is suitable for image segmentation especially.

Key words: cellular neural network, complete stability, image segmentation

摘要： 在细胞神经网络（Cellular Neural Networks，CNN）的应用中，稳定性是一个关键问题。只有选择合理的参数模板，才能将其应用于图像处理中来，否则将导致整个网络振荡甚至混沌。因此，如何简便有效地分析和判断标准细胞神经网络模型的完全稳定性，是其成功应用的首要前提。在已有定理证明的基础上，给出一种简便快捷的完全稳定性判断方法，并成功应用于图像分割中，效果良好，与人眼的视觉感受相一致。

关键词: 细胞神经网络, 完全稳定性, 图像分割