Resistive grid image filtering: input/output analysis via the CNN framework

The cellular neural network framework developed by L.O. Chua and L. Yang (IEEE Trans. Circuits Syst., vol.32, Oct. 1988) is used to analyze the image filtering operation performed by the VLSI linear resistive grid. In particular, it is shown in detail how the resistive grid can be cast as a CNN, and the use of frequency-domain techniques to characterize the input-output behavior of resistive grids of both infinite and finite size is discussed. These results lead to a theoretical justification of one of the so-called folk theorems commonly held by researchers using resistive grids: resistive grids are robust in the presence of variations in the values of the resistors. An application to edge detection is proposed. In particular, it is shown that the filtering performed by the grid is similar to the exponential filter in the edge detection algorithm proposed by J. Shen and S. Castan (1986)