Two Theorems on the Robust Designs for Dilation and Erosion CNNs

The cellular neural/nonlinear network (CNN) has become a new tool for image and signal processing, robotic and biological visions, and higher brain functions. Based our previous research, this paper set up two new theorems of robust designs for Dilation and Erosion CNNs processing gray-scale images, which provide parameter inequalities to determine parameter intervals for implementing prescribed image processing functions, respectively. Four numerical simulation examples for Dilation and Erosion CNNs are given to illustrate the effectiveness of our theorems.