Resistive Grid Image Filtering: Input/Output Analysis via the CNN Framework

Recently, several researchers have proposed resistive grids as primary components in analog VLSI circuit implementations of various image processing algorithms. In this paper, we use the Cellular Neural Network framework developed by Chua and Yang to analyze the image filtering operation performed by the linear resistive grid. In particular, we show first in detail how the resistive grid can be cast as a CNN and discuss the use of frequency-domain techniques to characterize the input/output behavior of resistive grids of both infinite and finite size. These results lead to a theoretical justification of one of the “folk theorems” commonly held by researchers using resistive grids: Resistive grids are robust in the presence of variations in the values of the resistors. To the best of our knowledge, this conjecture has only been verified by simulation. Finally, we suggest an application to edge detection. In particular, we show that the filtering performed by the grid is similar to the exponential filter in the edge detection algorithm proposed by Shen and Castan.